summaryrefslogtreecommitdiff
path: root/57532-h/57532-h.htm
blob: 4fb32cf74a65ea9979f4d68d45a7839172811c0a (plain) 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
2905
2906
2907
2908
2909
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
2960
2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
3027
3028
3029
3030
3031
3032
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
3058
3059
3060
3061
3062
3063
3064
3065
3066
3067
3068
3069
3070
3071
3072
3073
3074
3075
3076
3077
3078
3079
3080
3081
3082
3083
3084
3085
3086
3087
3088
3089
3090
3091
3092
3093
3094
3095
3096
3097
3098
3099
3100
3101
3102
3103
3104
3105
3106
3107
3108
3109
3110
3111
3112
3113
3114
3115
3116
3117
3118
3119
3120
3121
3122
3123
3124
3125
3126
3127
3128
3129
3130
3131
3132
3133
3134
3135
3136
3137
3138
3139
3140
3141
3142
3143
3144
3145
3146
3147
3148
3149
3150
3151
3152
3153
3154
3155
3156
3157
3158
3159
3160
3161
3162
3163
3164
3165
3166
3167
3168
3169
3170
3171
3172
3173
3174
3175
3176
3177
3178
3179
3180
3181
3182
3183
3184
3185
3186
3187
3188
3189
3190
3191
3192
3193
3194
3195
3196
3197
3198
3199
3200
3201
3202
3203
3204
3205
3206
3207
3208
3209
3210
3211
3212
3213
3214
3215
3216
3217
3218
3219
3220
3221
3222
3223
3224
3225
3226
3227
3228
3229
3230
3231
3232
3233
3234
3235
3236
3237
3238
3239
3240
3241
3242
3243
3244
3245
3246
3247
3248
3249
3250
3251
3252
3253
3254
3255
3256
3257
3258
3259
3260
3261
3262
3263
3264
3265
3266
3267
3268
3269
3270
3271
3272
3273
3274
3275
3276
3277
3278
3279
3280
3281
3282
3283
3284
3285
3286
3287
3288
3289
3290
3291
3292
3293
3294
3295
3296
3297
3298
3299
3300
3301
3302
3303
3304
3305
3306
3307
3308
3309
3310
3311
3312
3313
3314
3315
3316
3317
3318
3319
3320
3321
3322
3323
3324
3325
3326
3327
3328
3329
3330
3331
3332
3333
3334
3335
3336
3337
3338
3339
3340
3341
3342
3343
3344
3345
3346
3347
3348
3349
3350
3351
3352
3353
3354
3355
3356
3357
3358
3359
3360
3361
3362
3363
3364
3365
3366
3367
3368
3369
3370
3371
3372
3373
3374
3375
3376
3377
3378
3379
3380
3381
3382
3383
3384
3385
3386
3387
3388
3389
3390
3391
3392
3393
3394
3395
3396
3397
3398
3399
3400
3401
3402
3403
3404
3405
3406
3407
3408
3409
3410
3411
3412
3413
3414
3415
3416
3417
3418
3419
3420
3421
3422
3423
3424
3425
3426
3427
3428
3429
3430
3431
3432
3433
3434
3435
3436
3437
3438
3439
3440
3441
3442
3443
3444
3445
3446
3447
3448
3449
3450
3451
3452
3453
3454
3455
3456
3457
3458
3459
3460
3461
3462
3463
3464
3465
3466
3467
3468
3469
3470
3471
3472
3473
3474
3475
3476
3477
3478
3479
3480
3481
3482
3483
3484
3485
3486
3487
3488
3489
3490
3491
3492
3493
3494
3495
3496
3497
3498
3499
3500
3501
3502
3503
3504
3505
3506
3507
3508
3509
3510
3511
3512
3513
3514
3515
3516
3517
3518
3519
3520
3521
3522
3523
3524
3525
3526
3527
3528
3529
3530
3531
3532
3533
3534
3535
3536
3537
3538
3539
3540
3541
3542
3543
3544
3545
3546
3547
3548
3549
3550
3551
3552
3553
3554
3555
3556
3557
3558
3559
3560
3561
3562
3563
3564
3565
3566
3567
3568
3569
3570
3571
3572
3573
3574
3575
3576
3577
3578
3579
3580
3581
3582
3583
3584
3585
3586
3587
3588
3589
3590
3591
3592
3593
3594
3595
3596
3597
3598
3599
3600
3601
3602
3603
3604
3605
3606
3607
3608
3609
3610
3611
3612
3613
3614
3615
3616
3617
3618
3619
3620
3621
3622
3623
3624
3625
3626
3627
3628
3629
3630
3631
3632
3633
3634
3635
3636
3637
3638
3639
3640
3641
3642
3643
3644
3645
3646
3647
3648
3649
3650
3651
3652
3653
3654
3655
3656
3657
3658
3659
3660
3661
3662
3663
3664
3665
3666
3667
3668
3669
3670
3671
3672
3673
3674
3675
3676
3677
3678
3679
3680
3681
3682
3683
3684
3685
3686
3687
3688
3689
3690
3691
3692
3693
3694
3695
3696
3697
3698
3699
3700
3701
3702
3703
3704
3705
3706
3707
3708
3709
3710
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
3726
3727
3728
3729
3730
3731
3732
3733
3734
3735
3736
3737
3738
3739
3740
3741
3742
3743
3744
3745
3746
3747
3748
3749
3750
3751
3752
3753
3754
3755
3756
3757
3758
3759
3760
3761
3762
3763
3764
3765
3766
3767
3768
3769
3770
3771
3772
3773
3774
3775
3776
3777
3778
3779
3780
3781
3782
3783
3784
3785
3786
3787
3788
3789
3790
3791
3792
3793
3794
3795
3796
3797
3798
3799
3800
3801
3802
3803
3804
3805
3806
3807
3808
3809
3810
3811
3812
3813
3814
3815
3816
3817
3818
3819
3820
3821
3822
3823
3824
3825
3826
3827
3828
3829
3830
3831
3832
3833
3834
3835
3836
3837
3838
3839
3840
3841
3842
3843
3844
3845
3846
3847
3848
3849
3850
3851
3852
3853
3854
3855
3856
3857
3858
3859
3860
3861
3862
3863
3864
3865
3866
3867
3868
3869
3870
3871
3872
3873
3874
3875
3876
3877
3878
3879
3880
3881
3882
3883
3884
3885
3886
3887
3888
3889
3890
3891
3892
3893
3894
3895
3896
3897
3898
3899
3900
3901
3902
3903
3904
3905
3906
3907
3908
3909
3910
3911
3912
3913
3914
3915
3916
3917
3918
3919
3920
3921
3922
3923
3924
3925
3926
3927
3928
3929
3930
3931
3932
3933
3934
3935
3936
3937
3938
3939
3940
3941
3942
3943
3944
3945
3946
3947
3948
3949
3950
3951
3952
3953
3954
3955
3956
3957
3958
3959
3960
3961
3962
3963
3964
3965
3966
3967
3968
3969
3970
3971
3972
3973
3974
3975
3976
3977
3978
3979
3980
3981
3982
3983
3984
3985
3986
3987
3988
3989
3990
3991
3992
3993
3994
3995
3996
3997
3998
3999
4000
4001
4002
4003
4004
4005
4006
4007
4008
4009
4010
4011
4012
4013
4014
4015
4016
4017
4018
4019
4020
4021
4022
4023
4024
4025
4026
4027
4028
4029
4030
4031
4032
4033
4034
4035
4036
4037
4038
4039
4040
4041
4042
4043
4044
4045
4046
4047
4048
4049
4050
4051
4052
4053
4054
4055
4056
4057
4058
4059
4060
4061
4062
4063
4064
4065
4066
4067
4068
4069
4070
4071
4072
4073
4074
4075
4076
4077
4078
4079
4080
4081
4082
4083
4084
4085
4086
4087
4088
4089
4090
4091
4092
4093
4094
4095
4096
4097
4098
4099
4100
4101
4102
4103
4104
4105
4106
4107
4108
4109
4110
4111
4112
4113
4114
4115
4116
4117
4118
4119
4120
4121
4122
4123
4124
4125
4126
4127
4128
4129
4130
4131
4132
4133
4134
4135
4136
4137
4138
4139
4140
4141
4142
4143
4144
4145
4146
4147
4148
4149
4150
4151
4152
4153
4154
4155
4156
4157
4158
4159
4160
4161
4162
4163
4164
4165
4166
4167
4168
4169
4170
4171
4172
4173
4174
4175
4176
4177
4178
4179
4180
4181
4182
4183
4184
4185
4186
4187
4188
4189
4190
4191
4192
4193
4194
4195
4196
4197
4198
4199
4200
4201
4202
4203
4204
4205
4206
4207
4208
4209
4210
4211
4212
4213
4214
4215
4216
4217
4218
4219
4220
4221
4222
4223
4224
4225
4226
4227
4228
4229
4230
4231
4232
4233
4234
4235
4236
4237
4238
4239
4240
4241
4242
4243
4244
4245
4246
4247
4248
4249
4250
4251
4252
4253
4254
4255
4256
4257
4258
4259
4260
4261
4262
4263
4264
4265
4266
4267
4268
4269
4270
4271
4272
4273
4274
4275
4276
4277
4278
4279
4280
4281
4282
4283
4284
4285
4286
4287
4288
4289
4290
4291
4292
4293
4294
4295
4296
4297
4298
4299
4300
4301
4302
4303
4304
4305
4306
4307
4308
4309
4310
4311
4312
4313
4314
4315
4316
4317
4318
4319
4320
4321
4322
4323
4324
4325
4326
4327
4328
4329
4330
4331
4332
4333
4334
4335
4336
4337
4338
4339
4340
4341
4342
4343
4344
4345
4346
4347
4348
4349
4350
4351
4352
4353
4354
4355
4356
4357
4358
4359
4360
4361
4362
4363
4364
4365
4366
4367
4368
4369
4370
4371
4372
4373
4374
4375
4376
4377
4378
4379
4380
4381
4382
4383
4384
4385
4386
4387
4388
4389
4390
4391
4392
4393
4394
4395
4396
4397
4398
4399
4400
4401
4402
4403
4404
4405
4406
4407
4408
4409
4410
4411
4412
4413
4414
4415
4416
4417
4418
4419
4420
4421
4422
4423
4424
4425
4426
4427
4428
4429
4430
4431
4432
4433
4434
4435
4436
4437
4438
4439
4440
4441
4442
4443
4444
4445
4446
4447
4448
4449
4450
4451
4452
4453
4454
4455
4456
4457
4458
4459
4460
4461
4462
4463
4464
4465
4466
4467
4468
4469
4470
4471
4472
4473
4474
4475
4476
4477
4478
4479
4480
4481
4482
4483
4484
4485
4486
4487
4488
4489
4490
4491
4492
4493
4494
4495
4496
4497
4498
4499
4500
4501
4502
4503
4504
4505
4506
4507
4508
4509
4510
4511
4512
4513
4514
4515
4516
4517
4518
4519
4520
4521
4522
4523
4524
4525
4526
4527
4528
4529
4530
4531
4532
4533
4534
4535
4536
4537
4538
4539
4540
4541
4542
4543
4544
4545
4546
4547
4548
4549
4550
4551
4552
4553
4554
4555
4556
4557
4558
4559
4560
4561
4562
4563
4564
4565
4566
4567
4568
4569
4570
4571
4572
4573
4574
4575
4576
4577
4578
4579
4580
4581
4582
4583
4584
4585
4586
4587
4588
4589
4590
4591
4592
4593
4594
4595
4596
4597
4598
4599
4600
4601
4602
4603
4604
4605
4606
4607
4608
4609
4610
4611
4612
4613
4614
4615
4616
4617
4618
4619
4620
4621
4622
4623
4624
4625
4626
4627
4628
4629
4630
4631
4632
4633
4634
4635
4636
4637
4638
4639
4640
4641
4642
4643
4644
4645
4646
4647
4648
4649
4650
4651
4652
4653
4654
4655
4656
4657
4658
4659
4660
4661
4662
4663
4664
4665
4666
4667
4668
4669
4670
4671
4672
4673
4674
4675
4676
4677
4678
4679
4680
4681
4682
4683
4684
4685
4686
4687
4688
4689
4690
4691
4692
4693
4694
4695
4696
4697
4698
4699
4700
4701
4702
4703
4704
4705
4706
4707
4708
4709
4710
4711
4712
4713
4714
4715
4716
4717
4718
4719
4720
4721
4722
4723
4724
4725
4726
4727
4728
4729
4730
4731
4732
4733
4734
4735
4736
4737
4738
4739
4740
4741
4742
4743
4744
4745
4746
4747
4748
4749
4750
4751
4752
4753
4754
4755
4756
4757
4758
4759
4760
4761
4762
4763
4764
4765
4766
4767
4768
4769
4770
4771
4772
4773
4774
4775
4776
4777
4778
4779
4780
4781
4782
4783
4784
4785
4786
4787
4788
4789
4790
4791
4792
4793
4794
4795
4796
4797
4798
4799
4800
4801
4802
4803
4804
4805
4806
4807
4808
4809
4810
4811
4812
4813
4814
4815
4816
4817
4818
4819
4820
4821
4822
4823
4824
4825
4826
4827
4828
4829
4830
4831
4832
4833
4834
4835
4836
4837
4838
4839
4840
4841
4842
4843
4844
4845
4846
4847
4848
4849
4850
4851
4852
4853
4854
4855
4856
4857
4858
4859
4860
4861
4862
4863
4864
4865
4866
4867
4868
4869
4870
4871
4872
4873
4874
4875
4876
4877
4878
4879
4880
4881
4882
4883
4884
4885
4886
4887
4888
4889
4890
4891
4892
4893
4894
4895
4896
4897
4898
4899
4900
4901
4902
4903
4904
4905
4906
4907
4908
4909
4910
4911
4912
4913
4914
4915
4916
4917
4918
4919
4920
4921
4922
4923
4924
4925
4926
4927
4928
4929
4930
4931
4932
4933
4934
4935
4936
4937
4938
4939
4940
4941
4942
4943
4944
4945
4946
4947
4948
4949
4950
4951
4952
4953
4954
4955
4956
4957
4958
4959
4960
4961
4962
4963
4964
4965
4966
4967
4968
4969
4970
4971
4972
4973
4974
4975
4976
4977
4978
4979
4980
4981
4982
4983
4984
4985
4986
4987
4988
4989
4990
4991
4992
4993
4994
4995
4996
4997
4998
4999
5000
5001
5002
5003
5004
5005
5006
5007
5008
5009
5010
5011
5012
5013
5014
5015
5016
5017
5018
5019
5020
5021
5022
5023
5024
5025
5026
5027
5028
5029
5030
5031
5032
5033
5034
5035
5036
5037
5038
5039
5040
5041
5042
5043
5044
5045
5046
5047
5048
5049
5050
5051
5052
5053
5054
5055
5056
5057
5058
5059
5060
5061
5062
5063
5064
5065
5066
5067
5068
5069
5070
5071
5072
5073
5074
5075
5076
5077
5078
5079
5080
5081
5082
5083
5084
5085
5086
5087
5088
5089
5090
5091
5092
5093
5094
5095
5096
5097
5098
5099
5100
5101
5102
5103
5104
5105
5106
5107
5108
5109
5110
5111
5112
5113
5114
5115
5116
5117
5118
5119
5120
5121
5122
5123
5124
5125
5126
5127
5128
5129
5130
5131
5132
5133
5134
5135
5136
5137
5138
5139
5140
5141
5142
5143
5144
5145
5146
5147
5148
5149
5150
5151
5152
5153
5154
5155
5156
5157
5158
5159
5160
5161
5162
5163
5164
5165
5166
5167
5168
5169
5170
5171
5172
5173
5174
5175
5176
5177
5178
5179
5180
5181
5182
5183
5184
5185
5186
5187
5188
5189
5190
5191
5192
5193
5194
5195
5196
5197
5198
5199
5200
5201
5202
5203
5204
5205
5206
5207
5208
5209
5210
5211
5212
5213
5214
5215
5216
5217
5218
5219
5220
5221
5222
5223
5224
5225
5226
5227
5228
5229
5230
5231
5232
5233
5234
5235
5236
5237
5238
5239
5240
5241
5242
5243
5244
5245
5246
5247
5248
5249
5250
5251
5252
5253
5254
5255
5256
5257
5258
5259
5260
5261
5262
5263
5264
5265
5266
5267
5268
5269
5270
5271
5272
5273
5274
5275
5276
5277
5278
5279
5280
5281
5282
5283
5284
5285
5286
5287
5288
5289
5290
5291
5292
5293
5294
5295
5296
5297
5298
5299
5300
5301
5302
5303
5304
5305
5306
5307
5308
5309
5310
5311
5312
5313
5314
5315
5316
5317
5318
5319
5320
5321
5322
5323
5324
5325
5326
5327
5328
5329
5330
5331
5332
5333
5334
5335
5336
5337
5338
5339
5340
5341
5342
5343
5344
5345
5346
5347
5348
5349
5350
5351
5352
5353
5354
5355
5356
5357
5358
5359
5360
5361
5362
5363
5364
5365
5366
5367
5368
5369
5370
5371
5372
5373
5374
5375
5376
5377
5378
5379
5380
5381
5382
5383
5384
5385
5386
5387
5388
5389
5390
5391
5392
5393
5394
5395
5396
5397
5398
5399
5400
5401
5402
5403
5404
5405
5406
5407
5408
5409
5410
5411
5412
5413
5414
5415
5416
5417
5418
5419
5420
5421
5422
5423
5424
5425
5426
5427
5428
5429
5430
5431
5432
5433
5434
5435
5436
5437
5438
5439
5440
5441
5442
5443
5444
5445
5446
5447
5448
5449
5450
5451
5452
5453
5454
5455
5456
5457
5458
5459
5460
5461
5462
5463
5464
5465
5466
5467
5468
5469
5470
5471
5472
5473
5474
5475
5476
5477
5478
5479
5480
5481
5482
5483
5484
5485
5486
5487
5488
5489
5490
5491
5492
5493
5494
5495
5496
5497
5498
5499
5500
5501
5502
5503
5504
5505
5506
5507
5508
5509
5510
5511
5512
5513
5514
5515
5516
5517
5518
5519
5520
5521
5522
5523
5524
5525
5526
5527
5528
5529
5530
5531
5532
5533
5534
5535
5536
5537
5538
5539
5540
5541
5542
5543
5544
5545
5546
5547
5548
5549
5550
5551
5552
5553
5554
5555
5556
5557
5558
5559
5560
5561
5562
5563
5564
5565
5566
5567
5568
5569
5570
5571
5572
5573
5574
5575
5576
5577
5578
5579
5580
5581
5582
5583
5584
5585
5586
5587
5588
5589
5590
5591
5592
5593
5594
5595
5596
5597
5598
5599
5600
5601
5602
5603
5604
5605
5606
5607
5608
5609
5610
5611
5612
5613
5614
5615
5616
5617
5618
5619
5620
5621
5622
5623
5624
5625
5626
5627
5628
5629
5630
5631
5632
5633
5634
5635
5636
5637
5638
5639
5640
5641
5642
5643
5644
5645
5646
5647
5648
5649
5650
5651
5652
5653
5654
5655
5656
5657
5658
5659
5660
5661
5662
5663
5664
5665
5666
5667
5668
5669
5670
5671
5672
5673
5674
5675
5676
5677
5678
5679
5680
5681
5682
5683
5684
5685
5686
5687
5688
5689
5690
5691
5692
5693
5694
5695
5696
5697
5698
5699
5700
5701
5702
5703
5704
5705
5706
5707
5708
5709
5710
5711
5712
5713
5714
5715
5716
5717
5718
5719
5720
5721
5722
5723
5724
5725
5726
5727
5728
5729
5730
5731
5732
5733
5734
5735
5736
5737
5738
5739
5740
5741
5742
5743
5744
5745
5746
5747
5748
5749
5750
5751
5752
5753
5754
5755
5756
5757
5758
5759
5760
5761
5762
5763
5764
5765
5766
5767
5768
5769
5770
5771
5772
5773
5774
5775
5776
5777
5778
5779
5780
5781
5782
5783
5784
5785
5786
5787
5788
5789
5790
5791
5792
5793
5794
5795
5796
5797
5798
5799
5800
5801
5802
5803
5804
5805
5806
5807
5808
5809
5810
5811
5812
5813
5814
5815
5816
5817
5818
5819
5820
5821
5822
5823
5824
5825
5826
5827
5828
5829
5830
5831
5832
5833
5834
5835
5836
5837
5838
5839
5840
5841
5842
5843
5844
5845
5846
5847
5848
5849
5850
5851
5852
5853
5854
5855
5856
5857
5858
5859
5860
5861
5862
5863
5864
5865
5866
5867
5868
5869
5870
5871
5872
5873
5874
5875
5876
5877
5878
5879
5880
5881
5882
5883
5884
5885
5886
5887
5888
5889
5890
5891
5892
5893
5894
5895
5896
5897
5898
5899
5900
5901
5902
5903
5904
5905
5906
5907
5908
5909
5910
5911
5912
5913
5914
5915
5916
5917
5918
5919
5920
5921
5922
5923
5924
5925
5926
5927
5928
5929
5930
5931
5932
5933
5934
5935
5936
5937
5938
5939
5940
5941
5942
5943
5944
5945
5946
5947
5948
5949
5950
5951
5952
5953
5954
5955
5956
5957
5958
5959
5960
5961
5962
5963
5964
5965
5966
5967
5968
5969
5970
5971
5972
5973
5974
5975
5976
5977
5978
5979
5980
5981
5982
5983
5984
5985
5986
5987
5988
5989
5990
5991
5992
5993
5994
5995
5996
5997
5998
5999
6000
6001
6002
6003
6004
6005
6006
6007
6008
6009
6010
6011
6012
6013
6014
6015
6016
6017
6018
6019
6020
6021
6022
6023
6024
6025
6026
6027
6028
6029
6030
6031
6032
6033
6034
6035
6036
6037
6038
6039
6040
6041
6042
6043
6044
6045
6046
6047
6048
6049
6050
6051
6052
6053
6054
6055
6056
6057
6058
6059
6060
6061
6062
6063
6064
6065
6066
6067
6068
6069
6070
6071
6072
6073
6074
6075
6076
6077
6078
6079
6080
6081
6082
6083
6084
6085
6086
6087
6088
6089
6090
6091
6092
6093
6094
6095
6096
6097
6098
6099
6100
6101
6102
6103
6104
6105
6106
6107
6108
6109
6110
6111
6112
6113
6114
6115
6116
6117
6118
6119
6120
6121
6122
6123
6124
6125
6126
6127
6128
6129
6130
6131
6132
6133
6134
6135
6136
6137
6138
6139
6140
6141
6142
6143
6144
6145
6146
6147
6148
6149
6150
6151
6152
6153
6154
6155
6156
6157
6158
6159
6160
6161
6162
6163
6164
6165
6166
6167
6168
6169
6170
6171
6172
6173
6174
6175
6176
6177
6178
6179
6180
6181
6182
6183
6184
6185
6186
6187
6188
6189
6190
6191
6192
6193
6194
6195
6196
6197
6198
6199
6200
6201
6202
6203
6204
6205
6206
6207
6208
6209
6210
6211
6212
6213
6214
6215
6216
6217
6218
6219
6220
6221
6222
6223
6224
6225
6226
6227
6228
6229
6230
6231
6232
6233
6234
6235
6236
6237
6238
6239
6240
6241
6242
6243
6244
6245
6246
6247
6248
6249
6250
6251
6252
6253
6254
6255
6256
6257
6258
6259
6260
6261
6262
6263
6264
6265
6266
6267
6268
6269
6270
6271
6272
6273
6274
6275
6276
6277
6278
6279
6280
6281
6282
6283
6284
6285
6286
6287
6288
6289
6290
6291
6292
6293
6294
6295
6296
6297
6298
6299
6300
6301
6302
6303
6304
6305
6306
6307
6308
6309
6310
6311
6312
6313
6314
6315
6316
6317
6318
6319
6320
6321
6322
6323
6324
6325
6326
6327
6328
6329
6330
6331
6332
6333
6334
6335
6336
6337
6338
6339
6340
6341
6342
6343
6344
6345
6346
6347
6348
6349
6350
6351
6352
6353
6354
6355
6356
6357
6358
6359
6360
6361
6362
6363
6364
6365
6366
6367
6368
6369
6370
6371
6372
6373
6374
6375
6376
6377
6378
6379
6380
6381
6382
6383
6384
6385
6386
6387
6388
6389
6390
6391
6392
6393
6394
6395
6396
6397
6398
6399
6400
6401
6402
6403
6404
6405
6406
6407
6408
6409
6410
6411
6412
6413
6414
6415
6416
6417
6418
6419
6420
6421
6422
6423
6424
6425
6426
6427
6428
6429
6430
6431
6432
6433
6434
6435
6436
6437
6438
6439
6440
6441
6442
6443
6444
6445
6446
6447
6448
6449
6450
6451
6452
6453
6454
6455
6456
6457
6458
6459
6460
6461
6462
6463
6464
6465
6466
6467
6468
6469
6470
6471
6472
6473
6474
6475
6476
6477
6478
6479
6480
6481
6482
6483
6484
6485
6486
6487
6488
6489
6490
6491
6492
6493
6494
6495
6496
6497
6498
6499
6500
6501
6502
6503
6504
6505
6506
6507
6508
6509
6510
6511
6512
6513
6514
6515
6516
6517
6518
6519
6520
6521
6522
6523
6524
6525
6526
6527
6528
6529
6530
6531
6532
6533
6534
6535
6536
6537
6538
6539
6540
6541
6542
6543
6544
6545
6546
6547
6548
6549
6550
6551
6552
6553
6554
6555
6556
6557
6558
6559
6560
6561
6562
6563
6564
6565
6566
6567
6568
6569
6570
6571
6572
6573
6574
6575
6576
6577
6578
6579
6580
6581
6582
6583
6584
6585
6586
6587
6588
6589
6590
6591
6592
6593
6594
6595
6596
6597
6598
6599
6600
6601
6602
6603
6604
6605
6606
6607
6608
6609
6610
6611
6612
6613
6614
6615
6616
6617
6618
6619
6620
6621
6622
6623
6624
6625
6626
6627
6628
6629
6630
6631
6632
6633
6634
6635
6636
6637
6638
6639
6640
6641
6642
6643
6644
6645
6646
6647
6648
6649
6650
6651
6652
6653
6654
6655
6656
6657
6658
6659
6660
6661
6662
6663
6664
6665
6666
6667
6668
6669
6670
6671
6672
6673
6674
6675
6676
6677
6678
6679
6680
6681
6682
6683
6684
6685
6686
6687
6688
6689
6690
6691
6692
6693
6694
6695
6696
6697
6698
6699
6700
6701
6702
6703
6704
6705
6706
6707
6708
6709
6710
6711
6712
6713
6714
6715
6716
6717
6718
6719
6720
6721
6722
6723
6724
6725
6726
6727
6728
6729
6730
6731
6732
6733
6734
6735
6736
6737
6738
6739
6740
6741
6742
6743
6744
6745
6746
6747
6748
6749
6750
6751
6752
6753
6754
6755
6756
6757
6758
6759
6760
6761
6762
6763
6764
6765
6766
6767
6768
6769
6770
6771
6772
6773
6774
6775
6776
6777
6778
6779
6780
6781
6782
6783
6784
6785
6786
6787
6788
6789
6790
6791
6792
6793
6794
6795
6796
6797
6798
6799
6800
6801
6802
6803
6804
6805
6806
6807
6808
6809
6810
6811
6812
6813
6814
6815
6816
6817
6818
6819
6820
6821
6822
6823
6824
6825
6826
6827
6828
6829
6830
6831
6832
6833
6834
6835
6836
6837
6838
6839
6840
6841
6842
6843
6844
6845
6846
6847
6848
6849
6850
6851
6852
6853
6854
6855
6856
6857
6858
6859
6860
6861
6862
6863
6864
6865
6866
6867
6868
6869
6870
6871
6872
6873
6874
6875
6876
6877
6878
6879
6880
6881
6882
6883
6884
6885
6886
6887
6888
6889
6890
6891
6892
6893
6894
6895
6896
6897
6898
6899
6900
6901
6902
6903
6904
6905
6906
6907
6908
6909
6910
6911
6912
6913
6914
6915
6916
6917
6918
6919
6920
6921
6922
6923
6924
6925
6926
6927
6928
6929
6930
6931
6932
6933
6934
6935
6936
6937
6938
6939
6940
6941
6942
6943
6944
6945
6946
6947
6948
6949
6950
6951
6952
6953
6954
6955
6956
6957
6958
6959
6960
6961
6962
6963
6964
6965
6966
6967
6968
6969
6970
6971
6972
6973
6974
6975
6976
6977
6978
6979
6980
6981
6982
6983
6984
6985
6986
6987
6988
6989
6990
6991
6992
6993
6994
6995
6996
6997
6998
6999
7000
7001
7002
7003
7004
7005
7006
7007
7008
7009
7010
7011
7012
7013
7014
7015
7016
7017
7018
7019
7020
7021
7022
7023
7024
7025
7026
7027
7028
7029
7030
7031
7032
7033
7034
7035
7036
7037
7038
7039
7040
7041
7042
7043
7044
7045
7046
7047
7048
7049
7050
7051
7052
7053
7054
7055
7056
7057
7058
7059
7060
7061
7062
7063
7064
7065
7066
7067
7068
7069
7070
7071
7072
7073
7074
7075
7076
7077
7078
7079
7080
7081
7082
7083
7084
7085
7086
7087
7088
7089
7090
7091
7092
7093
7094
7095
7096
7097
7098
7099
7100
7101
7102
7103
7104
7105
7106
7107
7108
7109
7110
7111
7112
7113
7114
7115
7116
7117
7118
7119
7120
7121
7122
7123
7124
7125
7126
7127
7128
7129
7130
7131
7132
7133
7134
7135
7136
7137
7138
7139
7140
7141
7142
7143
7144
7145
7146
7147
7148
7149
7150
7151
7152
7153
7154
7155
7156
7157
7158
7159
7160
7161
7162
7163
7164
7165
7166
7167
7168
7169
7170
7171
7172
7173
7174
7175
7176
7177
7178
7179
7180
7181
7182
7183
7184
7185
7186
7187
7188
7189
7190
7191
7192
7193
7194
7195
7196
7197
7198
7199
7200
7201
7202
7203
7204
7205
7206
7207
7208
7209
7210
7211
7212
7213
7214
7215
7216
7217
7218
7219
7220
7221
7222
7223
7224
7225
7226
7227
7228
7229
7230
7231
7232
7233
7234
7235
7236
7237
7238
7239
7240
7241
7242
7243
7244
7245
7246
7247
7248
7249
7250
7251
7252
7253
7254
7255
7256
7257
7258
7259
7260
7261
7262
7263
7264
7265
7266
7267
7268
7269
7270
7271
7272
7273
7274
7275
7276
7277
7278
7279
7280
7281
7282
7283
7284
7285
7286
7287
7288
7289
7290
7291
7292
7293
7294
7295
7296
7297
7298
7299
7300
7301
7302
7303
7304
7305
7306
7307
7308
7309
7310
7311
7312
7313
7314
7315
7316
7317
7318
7319
7320
7321
7322
7323
7324
7325
7326
7327
7328
7329
7330
7331
7332
7333
7334
7335
7336
7337
7338
7339
7340
7341
7342
7343
7344
7345
7346
7347
7348
7349
7350
7351
7352
7353
7354
7355
7356
7357
7358
7359
7360
7361
7362
7363
7364
7365
7366
7367
7368
7369
7370
7371
7372
7373
7374
7375
7376
7377
7378
7379
7380
7381
7382
7383
7384
7385
7386
7387
7388
7389
7390
7391
7392
7393
7394
7395
7396
7397
7398
7399
7400
7401
7402
7403
7404
7405
7406
7407
7408
7409
7410
7411
7412
7413
7414
7415
7416
7417
7418
7419
7420
7421
7422
7423
7424
7425
7426
7427
7428
7429
7430
7431
7432
7433
7434
7435
7436
7437
7438
7439
7440
7441
7442
7443
7444
7445
7446
7447
7448
7449
7450
7451
7452
7453
7454
7455
7456
7457
7458
7459
7460
7461
7462
7463
7464
7465
7466
7467
7468
7469
7470
7471
7472
7473
7474
7475
7476
7477
7478
7479
7480
7481
7482
7483
7484
7485
7486
7487
7488
7489
7490
7491
7492
7493
7494
7495
7496
7497
7498
7499
7500
7501
7502
7503
7504
7505
7506
7507
7508
7509
7510
7511
7512
7513
7514
7515
7516
7517
7518
7519
7520
7521
7522
7523
7524
7525
7526
7527
7528
7529
7530
7531
7532
7533
7534
7535
7536
7537
7538
7539
7540
7541
7542
7543
7544
7545
7546
7547
7548
7549
7550
7551
7552
7553
7554
7555
7556
7557
7558
7559
7560
7561
7562
7563
7564
7565
7566
7567
7568
7569
7570
7571
7572
7573
7574
7575
7576
7577
7578
7579
7580
7581
7582
7583
7584
7585
7586
7587
7588
7589
7590
7591
7592
7593
7594
7595
7596
7597
7598
7599
7600
7601
7602
7603
7604
7605
7606
7607
7608
7609
7610
7611
7612
7613
7614
7615
7616
7617
7618
7619
7620
7621
7622
7623
7624
7625
7626
7627
7628
7629
7630
7631
7632
7633
7634
7635
7636
7637
7638
7639
7640
7641
7642
7643
7644
7645
7646
7647
7648
7649
7650
7651
7652
7653
7654
7655
7656
7657
7658
7659
7660
7661
7662
7663
7664
7665
7666
7667
7668
7669
7670
7671
7672
7673
7674
7675
7676
7677
7678
7679
7680
7681
7682
7683
7684
7685
7686
7687
7688
7689
7690
7691
7692
7693
7694
7695
7696
7697
7698
7699
7700
7701
7702
7703
7704
7705
7706
7707
7708
7709
7710
7711
7712
7713
7714
7715
7716
7717
7718
7719
7720
7721
7722
7723
7724
7725
7726
7727
7728
7729
7730
7731
7732
7733
7734
7735
7736
7737
7738
7739
7740
7741
7742
7743
7744
7745
7746
7747
7748
7749
7750
7751
7752
7753
7754
7755
7756
7757
7758
7759
7760
7761
7762
7763
7764
7765
7766
7767
7768
7769
7770
7771
7772
7773
7774
7775
7776
7777
7778
7779
7780
7781
7782
7783
7784
7785
7786
7787
7788
7789
7790
7791
7792
7793
7794
7795
7796
7797
7798
7799
7800
7801
7802
7803
7804
7805
7806
7807
7808
7809
7810
7811
7812
7813
7814
7815
7816
7817
7818
7819
7820
7821
7822
7823
7824
7825
7826
7827
7828
7829
7830
7831
7832
7833
7834
7835
7836
7837
7838
7839
7840
7841
7842
7843
7844
7845
7846
7847
7848
7849
7850
7851
7852
7853
7854
7855
7856
7857
7858
7859
7860
7861
7862
7863
7864
7865
7866
7867
7868
7869
7870
7871
7872
7873
7874
7875
7876
7877
7878
7879
7880
7881
7882
7883
7884
7885
7886
7887
7888
7889
7890
7891
7892
7893
7894
7895
7896
7897
7898
7899
7900
7901
7902
7903
7904
7905
7906
7907
7908
7909
7910
7911
7912
7913
7914
7915
7916
7917
7918
7919
7920
7921
7922
7923
7924
7925
7926
7927
7928
7929
7930
7931
7932
7933
7934
7935
7936
7937
7938
7939
7940
7941
7942
7943
7944
7945
7946
7947
7948
7949
7950
7951
7952
7953
7954
7955
7956
7957
7958
7959
7960
7961
7962
7963
7964
7965
7966
7967
7968
7969
7970
7971
7972
7973
7974
7975
7976
7977
7978
7979
7980
7981
7982
7983
7984
7985
7986
7987
7988
7989
7990
7991
7992
7993
7994
7995
7996
7997
7998
7999
8000
8001
8002
8003
8004
8005
8006
8007
8008
8009
8010
8011
8012
8013
8014
8015
8016
8017
8018
8019
8020
8021
8022
8023
8024
8025
8026
8027
8028
8029
8030
8031
8032
8033
8034
8035
8036
8037
8038
8039
8040
8041
8042
8043
8044
8045
8046
8047
8048
8049
8050
8051
8052
8053
8054
8055
8056
8057
8058
8059
8060
8061
8062
8063
8064
8065
8066
8067
8068
8069
8070
8071
8072
8073
8074
8075
8076
8077
8078
8079
8080
8081
8082
8083
8084
8085
8086
8087
8088
8089
8090
8091
8092
8093
8094
8095
8096
8097
8098
8099
8100
8101
8102
8103
8104
8105
8106
8107
8108
8109
8110
8111
8112
8113
8114
8115
8116
8117
8118
8119
8120
8121
8122
8123
8124
8125
8126
8127
8128
8129
8130
8131
8132
8133
8134
8135
8136
8137
8138
8139
8140
8141
8142
8143
8144
8145
8146
8147
8148
8149
8150
8151
8152
8153
8154
8155
8156
8157
8158
8159
8160
8161
8162
8163
8164
8165
8166
8167
8168
8169
8170
8171
8172
8173
8174
8175
8176
8177
8178
8179
8180
8181
8182
8183
8184
8185
8186
8187
8188
8189
8190
8191
8192
8193
8194
8195
8196
8197
8198
8199
8200
8201
8202
8203
8204
8205
8206
8207
8208
8209
8210
8211
8212
8213
8214
8215
8216
8217
8218
8219
8220
8221
8222
8223
8224
8225
8226
8227
8228
8229
8230
8231
8232
8233
8234
8235
8236
8237
8238
8239
8240
8241
8242
8243
8244
8245
8246
8247
8248
8249
8250
8251
8252
8253
8254
8255
8256
8257
8258
8259
8260
8261
8262
8263
8264
8265
8266
8267
8268
8269
8270
8271
8272
8273
8274
8275
8276
8277
8278
8279
8280
8281
8282
8283
8284
8285
8286
8287
8288
8289
8290
8291
8292
8293
8294
8295
8296
8297
8298
8299
8300
8301
8302
8303
8304
8305
8306
8307
8308
8309
8310
8311
8312
8313
8314
8315
8316
8317
8318
8319
8320
8321
8322
8323
8324
8325
8326
8327
8328
8329
8330
8331
8332
8333
8334
8335
8336
8337
8338
8339
8340
8341
8342
8343
8344
8345
8346
8347
8348
8349
8350
8351
8352
8353
8354
8355
8356
8357
8358
8359
8360
8361
8362
8363
8364
8365
8366
8367
8368
8369
8370
8371
8372
8373
8374
8375
8376
8377
8378
8379
8380
8381
8382
8383
8384
8385
8386
8387
8388
8389
8390
8391
8392
8393
8394
8395
8396
8397
8398
8399
8400
8401
8402
8403
8404
8405
8406
8407
8408
8409
8410
8411
8412
8413
8414
8415
8416
8417
8418
8419
8420
8421
8422
8423
8424
8425
8426
8427
8428
8429
8430
8431
8432
8433
8434
8435
8436
8437
8438
8439
8440
8441
8442
8443
8444
8445
8446
8447
8448
8449
8450
8451
8452
8453
8454
8455
8456
8457
8458
8459
8460
8461
8462
8463
8464
8465
8466
8467
8468
8469
8470
8471
8472
8473
8474
8475
8476
8477
8478
8479
8480
8481
8482
8483
8484
8485
8486
8487
8488
8489
8490
8491
8492
8493
8494
8495
8496
8497
8498
8499
8500
8501
8502
8503
8504
8505
8506
8507
8508
8509
8510
8511
8512
8513
8514
8515
8516
8517
8518
8519
8520
8521
8522
8523
8524
8525
8526
8527
8528
8529
8530
8531
8532
8533
8534
8535
8536
8537
8538
8539
8540
8541
8542
8543
8544
8545
8546
8547
8548
8549
8550
8551
8552
8553
8554
8555
8556
8557
8558
8559
8560
8561
8562
8563
8564
8565
8566
8567
8568
8569
8570
8571
8572
8573
8574
8575
8576
8577
8578
8579
8580
8581
8582
8583
8584
8585
8586
8587
8588
8589
8590
8591
8592
8593
8594
8595
8596
8597
8598
8599
8600
8601
8602
8603
8604
8605
8606
8607
8608
8609
8610
8611
8612
8613
8614
8615
8616
8617
8618
8619
8620
8621
8622
8623
8624
8625
8626
8627
8628
8629
8630
8631
8632
8633
8634
8635
8636
8637
8638
8639
8640
8641
8642
8643
8644
8645
8646
8647
8648
8649
8650
8651
8652
8653
8654
8655
8656
8657
8658
8659
8660
8661
8662
8663
8664
8665
8666
8667
8668
8669
8670
8671
8672
8673
8674
8675
8676
8677
8678
8679
8680
8681
8682
8683
8684
8685
8686
8687
8688
8689
8690
8691
8692
8693
8694
8695
8696
8697
8698
8699
8700
8701
8702
8703
8704
8705
8706
8707
8708
8709
8710
8711
8712
8713
8714
8715
8716
8717
8718
8719
8720
8721
8722
8723
8724
8725
8726
8727
8728
8729
8730
8731
8732
8733
8734
8735
8736
8737
8738
8739
8740
8741
8742
8743
8744
8745
8746
8747
8748
8749
8750
8751
8752
8753
8754
8755
8756
8757
8758
8759
8760
8761
8762
8763
8764
8765
8766
8767
8768
8769
8770
8771
8772
8773
8774
8775
8776
8777
8778
8779
8780
8781
8782
8783
8784
8785
8786
8787
8788
8789
8790
8791
8792
8793
8794
8795
8796
8797
8798
8799
8800
8801
8802
8803
8804
8805
8806
8807
8808
8809
8810
8811
8812
8813
8814
8815
8816
8817
8818
8819
8820
8821
8822
8823
8824
8825
8826
8827
8828
8829
8830
8831
8832
8833
8834
8835
8836
8837
8838
8839
8840
8841
8842
8843
8844
8845
8846
8847
8848
8849
8850
8851
8852
8853
8854
8855
8856
8857
8858
8859
8860
8861
8862
8863
8864
8865
8866
8867
8868
8869
8870
8871
8872
8873
8874
8875
8876
8877
8878
8879
8880
8881
8882
8883
8884
8885
8886
8887
8888
8889
8890
8891
8892
8893
8894
8895
8896
8897
8898
8899
8900
8901
8902
8903
8904
8905
8906
8907
8908
8909
8910
8911
8912
8913
8914
8915
8916
8917
8918
8919
8920
8921
8922
8923
8924
8925
8926
8927
8928
8929
8930
8931
8932
8933
8934
8935
8936
8937
8938
8939
8940
8941
8942
8943
8944
8945
8946
8947
8948
8949
8950
8951
8952
8953
8954
8955
8956
8957
8958
8959
8960
8961
8962
8963
8964
8965
8966
8967
8968
8969
8970
8971
8972
8973
8974
8975
8976
8977
8978
8979
8980
8981
8982
8983
8984
8985
8986
8987
8988
8989
8990
8991
8992
8993
8994
8995
8996
8997
8998
8999
9000
9001
9002
9003
9004
9005
9006
9007
9008
9009
9010
9011
9012
9013
9014
9015
9016
9017
9018
9019
9020
9021
9022
9023
9024
9025
9026
9027
9028
9029
9030
9031
9032
9033
9034
9035
9036
9037
9038
9039
9040
9041
9042
9043
9044
9045
9046
9047
9048
9049
9050
9051
9052
9053
9054
9055
9056
9057
9058
9059
9060
9061
9062
9063
9064
9065
9066
9067
9068
9069
9070
9071
9072
9073
9074
9075
9076
9077
9078
9079
9080
9081
9082
9083
9084
9085
9086
9087
9088
9089
9090
9091
9092
9093
9094
9095
9096
9097
9098
9099
9100
9101
9102
9103
9104
9105
9106
9107
9108
9109
9110
9111
9112
9113
9114
9115
9116
9117
9118
9119
9120
9121
9122
9123
9124
9125
9126
9127
9128
9129
9130
9131
9132
9133
9134
9135
9136
9137
9138
9139
9140
9141
9142
9143
9144
9145
9146
9147
9148
9149
9150
9151
9152
9153
9154
9155
9156
9157
9158
9159
9160
9161
9162
9163
9164
9165
9166
9167
9168
9169
9170
9171
9172
9173
9174
9175
9176
9177
9178
9179
9180
9181
9182
9183
9184
9185
9186
9187
9188
9189
9190
9191
9192
9193
9194
9195
9196
9197
9198
9199
9200
9201
9202
9203
9204
9205
9206
9207
9208
9209
9210
9211
9212
9213
9214
9215
9216
9217
9218
9219
9220
9221
9222
9223
9224
9225
9226
9227
9228
9229
9230
9231
9232
9233
9234
9235
9236
9237
9238
9239
9240
9241
9242
9243
9244
9245
9246
9247
9248
9249
9250
9251
9252
9253
9254
9255
9256
9257
9258
9259
9260
9261
9262
9263
9264
9265
9266
9267
9268
9269
9270
9271
9272
9273
9274
9275
9276
9277
9278
9279
9280
9281
9282
9283
9284
9285
9286
9287
9288
9289
9290
9291
9292
9293
9294
9295
9296
9297
9298
9299
9300
9301
9302
9303
9304
9305
9306
9307
9308
9309
9310
9311
9312
9313
9314
9315
9316
9317
9318
9319
9320
9321
9322
9323
9324
9325
9326
9327
9328
9329
9330
9331
9332
9333
9334
9335
9336
9337
9338
9339
9340
9341
9342
9343
9344
9345
9346
9347
9348
9349
9350
9351
9352
9353
9354
9355
9356
9357
9358
9359
9360
9361
9362
9363
9364
9365
9366
9367
9368
9369
9370
9371
9372
9373
9374
9375
9376
9377
9378
9379
9380
9381
9382
9383
9384
9385
9386
9387
9388
9389
9390
9391
9392
9393
9394
9395
9396
9397
9398
9399
9400
9401
9402
9403
9404
9405
9406
9407
9408
9409
9410
9411
9412
9413
9414
9415
9416
9417
9418
9419
9420
9421
9422
9423
9424
9425
9426
9427
9428
9429
9430
9431
9432
9433
9434
9435
9436
9437
9438
9439
9440
9441
9442
9443
9444
9445
9446
9447
9448
9449
9450
9451
9452
9453
9454
9455
9456
9457
9458
9459
9460
9461
9462
9463
9464
9465
9466
9467
9468
9469
9470
9471
9472
9473
9474
9475
9476
9477
9478
9479
9480
9481
9482
9483
9484
9485
9486
9487
9488
9489
9490
9491
9492
9493
9494
9495
9496
9497
9498
9499
9500
9501
9502
9503
9504
9505
9506
9507
9508
9509
9510
9511
9512
9513
9514
9515
9516
9517
9518
9519
9520
9521
9522
9523
9524
9525
9526
9527
9528
9529
9530
9531
9532
9533
9534
9535
9536
9537
9538
9539
9540
9541
9542
9543
9544
9545
9546
9547
9548
9549
9550
9551
9552
9553
9554
9555
9556
9557
9558
9559
9560
9561
9562
9563
9564
9565
9566
9567
9568
9569
9570
9571
9572
9573
9574
9575
9576
9577
9578
9579
9580
9581
9582
9583
9584
9585
9586
9587
9588
9589
9590
9591
9592
9593
9594
9595
9596
9597
9598
9599
9600
9601
9602
9603
9604
9605
9606
9607
9608
9609
9610
9611
9612
9613
9614
9615
9616
9617
9618
9619
9620
9621
9622
9623
9624
9625
9626
9627
9628
9629
9630
9631
9632
9633
9634
9635
9636
9637
9638
9639
9640
9641
9642
9643
9644
9645
9646
9647
9648
9649
9650
9651
9652
9653
9654
9655
9656
9657
9658
9659
9660
9661
9662
9663
9664
9665
9666
9667
9668
9669
9670
9671
9672
9673
9674
9675
9676
9677
9678
9679
9680
9681
9682
9683
9684
9685
9686
9687
9688
9689
9690
9691
9692
9693
9694
9695
9696
9697
9698
9699
9700
9701
9702
9703
9704
9705
9706
9707
9708
9709
9710
9711
9712
9713
9714
9715
9716
9717
9718
9719
9720
9721
9722
9723
9724
9725
9726
9727
9728
9729
9730
9731
9732
9733
9734
9735
9736
9737
9738
9739
9740
9741
9742
9743
9744
9745
9746
9747
9748
9749
9750
9751
9752
9753
9754
9755
9756
9757
9758
9759
9760
9761
9762
9763
9764
9765
9766
9767
9768
9769
9770
9771
9772
9773
9774
9775
9776
9777
9778
9779
9780
9781
9782
9783
9784
9785
9786
9787
9788
9789
9790
9791
9792
9793
9794
9795
9796
9797
9798
9799
9800
9801
9802
9803
9804
9805
9806
9807
9808
9809
9810
9811
9812
9813
9814
9815
9816
9817
9818
9819
9820
9821
9822
9823
9824
9825
9826
9827
9828
9829
9830
9831
9832
9833
9834
9835
9836
9837
9838
9839
9840
9841
9842
9843
9844
9845
9846
9847
9848
9849
9850
9851
9852
9853
9854
9855
9856
9857
9858
9859
9860
9861
9862
9863
9864
9865
9866
9867
9868
9869
9870
9871
9872
9873
9874
9875
9876
9877
9878
9879
9880
9881
9882
9883
9884
9885
9886
9887
9888
9889
9890
9891
9892
9893
9894
9895
9896
9897
9898
9899
9900
9901
9902
9903
9904
9905
9906
9907
9908
9909
9910
9911
9912
9913
9914
9915
9916
9917
9918
9919
9920
9921
9922
9923
9924
9925
9926
9927
9928
9929
9930
9931
9932
9933
9934
9935
9936
9937
9938
9939
9940
9941
9942
9943
9944
9945
9946
9947
9948
9949
9950
9951
9952
9953
9954
9955
9956
9957
9958
9959
9960
9961
9962
9963
9964
9965
9966
9967
9968
9969
9970
9971
9972
9973
9974
9975
9976
9977
9978
9979
9980
9981
9982
9983
9984
9985
9986
9987
9988
9989
9990
9991
9992
9993
9994
9995
9996
9997
9998
9999
10000
10001
10002
10003
10004
10005
10006
10007
10008
10009
10010
10011
10012
10013
10014
10015
10016
10017
10018
10019
10020
10021
10022
10023
10024
10025
10026
10027
10028
10029
10030
10031
10032
10033
10034
10035
10036
10037
10038
10039
10040
10041
10042
10043
10044
10045
10046
10047
10048
10049
10050
10051
10052
10053
10054
10055
10056
10057
10058
10059
10060
10061
10062
10063
10064
10065
10066
10067
10068
10069
10070
10071
10072
10073
10074
10075
10076
10077
10078
10079
10080
10081
10082
10083
10084
10085
10086
10087
10088
10089
10090
10091
10092
10093
10094
10095
10096
10097
10098
10099
10100
10101
10102
10103
10104
10105
10106
10107
10108
10109
10110
10111
10112
10113
10114
10115
10116
10117
10118
10119
10120
10121
10122
10123
10124
10125
10126
10127
10128
10129
10130
10131
10132
10133
10134
10135
10136
10137
10138
10139
10140
10141
10142
10143
10144
10145
10146
10147
10148
10149
10150
10151
10152
10153
10154
10155
10156
10157
10158
10159
10160
10161
10162
10163
10164
10165
10166
10167
10168
10169
10170
10171
10172
10173
10174
10175
10176
10177
10178
10179
10180
10181
10182
10183
10184
10185
10186
10187
10188
10189
10190
10191
10192
10193
10194
10195
10196
10197
10198
10199
10200
10201
10202
10203
10204
10205
10206
10207
10208
10209
10210
10211
10212
10213
10214
10215
10216
10217
10218
10219
10220
10221
10222
10223
10224
10225
10226
10227
10228
10229
10230
10231
10232
10233
10234
10235
10236
10237
10238
10239
10240
10241
10242
10243
10244
10245
10246
10247
10248
10249
10250
10251
10252
10253
10254
10255
10256
10257
10258
10259
10260
10261
10262
10263
10264
10265
10266
10267
10268
10269
10270
10271
10272
10273
10274
10275
10276
10277
10278
10279
10280
10281
10282
10283
10284
10285
10286
10287
10288
10289
10290
10291
10292
10293
10294
10295
10296
10297
10298
10299
10300
10301
10302
10303
10304
10305
10306
10307
10308
10309
10310
10311
10312
10313
10314
10315
10316
10317
10318
10319
10320
10321
10322
10323
10324
10325
10326
10327
10328
10329
10330
10331
10332
10333
10334
10335
10336
10337
10338
10339
10340
10341
10342
10343
10344
10345
10346
10347
10348
10349
10350
10351
10352
10353
10354
10355
10356
10357
10358
10359
10360
10361
10362
10363
10364
10365
10366
10367
10368
10369
10370
10371
10372
10373
10374
10375
10376
10377
10378
10379
10380
10381
10382
10383
10384
10385
10386
10387
10388
10389
10390
10391
10392
10393
10394
10395
10396
10397
10398
10399
10400
10401
10402
10403
10404
10405
10406
10407
10408
10409
10410
10411
10412
10413
10414
10415
10416
10417
10418
10419
10420
10421
10422
10423
10424
10425
10426
10427
10428
10429
10430
10431
10432
10433
10434
10435
10436
10437
10438
10439
10440
10441
10442
10443
10444
10445
10446
10447
10448
10449
10450
10451
10452
10453
10454
10455
10456
10457
10458
10459
10460
10461
10462
10463
10464
10465
10466
10467
10468
10469
10470
10471
10472
10473
10474
10475
10476
10477
10478
10479
10480
10481
10482
10483
10484
10485
10486
10487
10488
10489
10490
10491
10492
10493
10494
10495
10496
10497
10498
10499
10500
10501
10502
10503
10504
10505
10506
10507
10508
10509
10510
10511
10512
10513
10514
10515
10516
10517
10518
10519
10520
10521
10522
10523
10524
10525
10526
10527
10528
10529
10530
10531
10532
10533
10534
10535
10536
10537
10538
10539
10540
10541
10542
10543
10544
10545
10546
10547
10548
10549
10550
10551
10552
10553
10554
10555
10556
10557
10558
10559
10560
10561
10562
10563
10564
10565
10566
10567
10568
10569
10570
10571
10572
10573
10574
10575
10576
10577
10578
10579
10580
10581
10582
10583
10584
10585
10586
10587
10588
10589
10590
10591
10592
10593
10594
10595
10596
10597
10598
10599
10600
10601
10602
10603
10604
10605
10606
10607
10608
10609
10610
10611
10612
10613
10614
10615
10616
10617
10618
10619
10620
10621
10622
10623
10624
10625
10626
10627
10628
10629
10630
10631
10632
10633
10634
10635
10636
10637
10638
10639
10640
10641
10642
10643
10644
10645
10646
10647
10648
10649
10650
10651
10652
10653
10654
10655
10656
10657
10658
10659
10660
10661
10662
10663
10664
10665
10666
10667
10668
10669
10670
10671
10672
10673
10674
10675
10676
10677
10678
10679
10680
10681
10682
10683
10684
10685
10686
10687
10688
10689
10690
10691
10692
10693
10694
10695
10696
10697
10698
10699
10700
10701
10702
10703
10704
10705
10706
10707
10708
10709
10710
10711
10712
10713
10714
10715
10716
10717
10718
10719
10720
10721
10722
10723
10724
10725
10726
10727
10728
10729
10730
10731
10732
10733
10734
10735
10736
10737
10738
10739
10740
10741
10742
10743
10744
10745
10746
10747
10748
10749
10750
10751
10752
10753
10754
10755
10756
10757
10758
10759
10760
10761
10762
10763
10764
10765
10766
10767
10768
10769
10770
10771
10772
10773
10774
10775
10776
10777
10778
10779
10780
10781
10782
10783
10784
10785
10786
10787
10788
10789
10790
10791
10792
10793
10794
10795
10796
10797
10798
10799
10800
10801
10802
10803
10804
10805
10806
10807
10808
10809
10810
10811
10812
10813
10814
10815
10816
10817
10818
10819
10820
10821
10822
10823
10824
10825
10826
10827
10828
10829
10830
10831
10832
10833
10834
10835
10836
10837
10838
10839
10840
10841
10842
10843
10844
10845
10846
10847
10848
10849
10850
10851
10852
10853
10854
10855
10856
10857
10858
10859
10860
10861
10862
10863
10864
10865
10866
10867
10868
10869
10870
10871
10872
10873
10874
10875
10876
10877
10878
10879
10880
10881
10882
10883
10884
10885
10886
10887
10888
10889
10890
10891
10892
10893
10894
10895
10896
10897
10898
10899
10900
10901
10902
10903
10904
10905
10906
10907
10908
10909
10910
10911
10912
10913
10914
10915
10916
10917
10918
10919
10920
10921
10922
10923
10924
10925
10926
10927
10928
10929
10930
10931
10932
10933
10934
10935
10936
10937
10938
10939
10940
10941
10942
10943
10944
10945
10946
10947
10948
10949
10950
10951
10952
10953
10954
10955
10956
10957
10958
10959
10960
10961
10962
10963
10964
10965
10966
10967
10968
10969
10970
10971
10972
10973
10974
10975
10976
10977
10978
10979
10980
10981
10982
10983
10984
10985
10986
10987
10988
10989
10990
10991
10992
10993
10994
10995
10996
10997
10998
10999
11000
11001
11002
11003
11004
11005
11006
11007
11008
11009
11010
11011
11012
11013
11014
11015
11016
11017
11018
11019
11020
11021
11022
11023
11024
11025
11026
11027
11028
11029
11030
11031
11032
11033
11034
11035
11036
11037
11038
11039
11040
11041
11042
11043
11044
11045
11046
11047
11048
11049
11050
11051
11052
11053
11054
11055
11056
11057
11058
11059
11060
11061
11062
11063
11064
11065
11066
11067
11068
11069
11070
11071
11072
11073
11074
11075
11076
11077
11078
11079
11080
11081
11082
11083
11084
11085
11086
11087
11088
11089
11090
11091
11092
11093
11094
11095
11096
11097
11098
11099
11100
11101
11102
11103
11104
11105
11106
11107
11108
11109
11110
11111
11112
11113
11114
11115
11116
11117
11118
11119
11120
11121
11122
11123
11124
11125
11126
11127
11128
11129
11130
11131
11132
11133
11134
11135
11136
11137
11138
11139
11140
11141
11142
11143
11144
11145
11146
11147
11148
11149
11150
11151
11152
11153
11154
11155
11156
11157
11158
11159
11160
11161
11162
11163
11164
11165
11166
11167
11168
11169
11170
11171
11172
11173
11174
11175
11176
11177
11178
11179
11180
11181
11182
11183
11184
11185
11186
11187
11188
11189
11190
11191
11192
11193
11194
11195
11196
11197
11198
11199
11200
11201
11202
11203
11204
11205
11206
11207
11208
11209
11210
11211
11212
11213
11214
11215
11216
11217
11218
11219
11220
11221
11222
11223
11224
11225
11226
11227
11228
11229
11230
11231
11232
11233
11234
11235
11236
11237
11238
11239
11240
11241
11242
11243
11244
11245
11246
11247
11248
11249
11250
11251
11252
11253
11254
11255
11256
11257
11258
11259
11260
11261
11262
11263
11264
11265
11266
11267
11268
11269
11270
11271
11272
11273
11274
11275
11276
11277
11278
11279
11280
11281
11282
11283
11284
11285
11286
11287
11288
11289
11290
11291
11292
11293
11294
11295
11296
11297
11298
11299
11300
11301
11302
11303
11304
11305
11306
11307
11308
11309
11310
11311
11312
11313
11314
11315
11316
11317
11318
11319
11320
11321
11322
11323
11324
11325
11326
11327
11328
11329
11330
11331
11332
11333
11334
11335
11336
11337
11338
11339
11340
11341
11342
11343
11344
11345
11346
11347
11348
11349
11350
11351
11352
11353
11354
11355
11356
11357
11358
11359
11360
11361
11362
11363
11364
11365
11366
11367
11368
11369
11370
11371
11372
11373
11374
11375
11376
11377
11378
11379
11380
11381
11382
11383
11384
11385
11386
11387
11388
11389
11390
11391
11392
11393
11394
11395
11396
11397
11398
11399
11400
11401
11402
11403
11404
11405
11406
11407
11408
11409
11410
11411
11412
11413
11414
11415
11416
11417
11418
11419
11420
11421
11422
11423
11424
11425
11426
11427
11428
11429
11430
11431
11432
11433
11434
11435
11436
11437
11438
11439
11440
11441
11442
11443
11444
11445
11446
11447
11448
11449
11450
11451
11452
11453
11454
11455
11456
11457
11458
11459
11460
11461
11462
11463
11464
11465
11466
11467
11468
11469
11470
11471
11472
11473
11474
11475
11476
11477
11478
11479
11480
11481
11482
11483
11484
11485
11486
11487
11488
11489
11490
11491
11492
11493
11494
11495
11496
11497
11498
11499
11500
11501
11502
11503
11504
11505
11506
11507
11508
11509
11510
11511
11512
11513
11514
11515
11516
11517
11518
11519
11520
11521
11522
11523
11524
11525
11526
11527
11528
11529
11530
11531
11532
11533
11534
11535
11536
11537
11538
11539
11540
11541
11542
11543
11544
11545
11546
11547
11548
11549
11550
11551
11552
11553
11554
11555
11556
11557
11558
11559
11560
11561
11562
11563
11564
11565
11566
11567
11568
11569
11570
11571
11572
11573
11574
11575
11576
11577
11578
11579
11580
11581
11582
11583
11584
11585
11586
11587
11588
11589
11590
11591
11592
11593
11594
11595
11596
11597
11598
11599
11600
11601
11602
11603
11604
11605
11606
11607
11608
11609
11610
11611
11612
11613
11614
11615
11616
11617
11618
11619
11620
11621
11622
11623
11624
11625
11626
11627
11628
11629
11630
11631
11632
11633
11634
11635
11636
11637
11638
11639
11640
11641
11642
11643
11644
11645
11646
11647
11648
11649
11650
11651
11652
11653
11654
11655
11656
11657
11658
11659
11660
11661
11662
11663
11664
11665
11666
11667
11668
11669
11670
11671
11672
11673
11674
11675
11676
11677
11678
11679
11680
11681
11682
11683
11684
11685
11686
11687
11688
11689
11690
11691
11692
11693
11694
11695
11696
11697
11698
11699
11700
11701
11702
11703
11704
11705
11706
11707
11708
11709
11710
11711
11712
11713
11714
11715
11716
11717
11718
11719
11720
11721
11722
11723
11724
11725
11726
11727
11728
11729
11730
11731
11732
11733
11734
11735
11736
11737
11738
11739
11740
11741
11742
11743
11744
11745
11746
11747
11748
11749
11750
11751
11752
11753
11754
11755
11756
11757
11758
11759
11760
11761
11762
11763
11764
11765
11766
11767
11768
11769
11770
11771
11772
11773
11774
11775
11776
11777
11778
11779
11780
11781
11782
11783
11784
11785
11786
11787
11788
11789
11790
11791
11792
11793
11794
11795
11796
11797
11798
11799
11800
11801
11802
11803
11804
11805
11806
11807
11808
11809
11810
11811
11812
11813
11814
11815
11816
11817
11818
11819
11820
11821
11822
11823
11824
11825
11826
11827
11828
11829
11830
11831
11832
11833
11834
11835
11836
11837
11838
11839
11840
11841
11842
11843
11844
11845
11846
11847
11848
11849
11850
11851
11852
11853
11854
11855
11856
11857
11858
11859
11860
11861
11862
11863
11864
11865
11866
11867
11868
11869
11870
11871
11872
11873
11874
11875
11876
11877
11878
11879
11880
11881
11882
11883
11884
11885
11886
11887
11888
11889
11890
11891
11892
11893
11894
11895
11896
11897
11898
11899
11900
11901
11902
11903
11904
11905
11906
11907
11908
11909
11910
11911
11912
11913
11914
11915
11916
11917
11918
11919
11920
11921
11922
11923
11924
11925
11926
11927
11928
11929
11930
11931
11932
11933
11934
11935
11936
11937
11938
11939
11940
11941
11942
11943
11944
11945
11946
11947
11948
11949
11950
11951
11952
11953
11954
11955
11956
11957
11958
11959
11960
11961
11962
11963
11964
11965
11966
11967
11968
11969
11970
11971
11972
11973
11974
11975
11976
11977
11978
11979
11980
11981
11982
11983
11984
11985
11986
11987
11988
11989
11990
11991
11992
11993
11994
11995
11996
11997
11998
11999
12000
12001
12002
12003
12004
12005
12006
12007
12008
12009
12010
12011
12012
12013
12014
12015
12016
12017
12018
12019
12020
12021
12022
12023
12024
12025
12026
12027
12028
12029
12030
12031
12032
12033
12034
12035
12036
12037
12038
12039
12040
12041
12042
12043
12044
12045
12046
12047
12048
12049
12050
12051
12052
12053
12054
12055
12056
12057
12058
12059
12060
12061
12062
12063
12064
12065
12066
12067
12068
12069
12070
12071
12072
12073
12074
12075
12076
12077
12078
12079
12080
12081
12082
12083
12084
12085
12086
12087
12088
12089
12090
12091
12092
12093
12094
12095
12096
12097
12098
12099
12100
12101
12102
12103
12104
12105
12106
12107
12108
12109
12110
12111
12112
12113
12114
12115
12116
12117
12118
12119
12120
12121
12122
12123
12124
12125
12126
12127
12128
12129
12130
12131
12132
12133
12134
12135
12136
12137
12138
12139
12140
12141
12142
12143
12144
12145
12146
12147
12148
12149
12150
12151
12152
12153
12154
12155
12156
12157
12158
12159
12160
12161
12162
12163
12164
12165
12166
12167
12168
12169
12170
12171
12172
12173
12174
12175
12176
12177
12178
12179
12180
12181
12182
12183
12184
12185
12186
12187
12188
12189
12190
12191
12192
12193
12194
12195
12196
12197
12198
12199
12200
12201
12202
12203
12204
12205
12206
12207
12208
12209
12210
12211
12212
12213
12214
12215
12216
12217
12218
12219
12220
12221
12222
12223
12224
12225
12226
12227
12228
12229
12230
12231
12232
12233
12234
12235
12236
12237
12238
12239
12240
12241
12242
12243
12244
12245
12246
12247
12248
12249
12250
12251
12252
12253
12254
12255
12256
12257
12258
12259
12260
12261
12262
12263
12264
12265
12266
12267
12268
12269
12270
12271
12272
12273
12274
12275
12276
12277
12278
12279
12280
12281
12282
12283
12284
12285
12286
12287
12288
12289
12290
12291
12292
12293
12294
12295
12296
12297
12298
12299
12300
12301
12302
12303
12304
12305
12306
12307
12308
12309
12310
12311
12312
12313
12314
12315
12316
12317
12318
12319
12320
12321
12322
12323
12324
12325
12326
12327
12328
12329
12330
12331
12332
12333
12334
12335
12336
12337
12338
12339
12340
12341
12342
12343
12344
12345
12346
12347
12348
12349
12350
12351
12352
12353
12354
12355
12356
12357
12358
12359
12360
12361
12362
12363
12364
12365
12366
12367
12368
12369
12370
12371
12372
12373
12374
12375
12376
12377
12378
12379
12380
12381
12382
12383
12384
12385
12386
12387
12388
12389
12390
12391
12392
12393
12394
12395
12396
12397
12398
12399
12400
12401
12402
12403
12404
12405
12406
12407
12408
12409
12410
12411
12412
12413
12414
12415
12416
12417
12418
12419
12420
12421
12422
12423
12424
12425
12426
12427
12428
12429
12430
12431
12432
12433
12434
12435
12436
12437
12438
12439
12440
12441
12442
12443
12444
12445
12446
12447
12448
12449
12450
12451
12452
12453
12454
12455
12456
12457
12458
12459
12460
12461
12462
12463
12464
12465
12466
12467
12468
12469
12470
12471
12472
12473
12474
12475
12476
12477
12478
12479
12480
12481
12482
12483
12484
12485
12486
12487
12488
12489
12490
12491
12492
12493
12494
12495
12496
12497
12498
12499
12500
12501
12502
12503
12504
12505
12506
12507
12508
12509
12510
12511
12512
12513
12514
12515
12516
12517
12518
12519
12520
12521
12522
12523
12524
12525
12526
12527
12528
12529
12530
12531
12532
12533
12534
12535
12536
12537
12538
12539
12540
12541
12542
12543
12544
12545
12546
12547
12548
12549
12550
12551
12552
12553
12554
12555
12556
12557
12558
12559
12560
12561
12562
12563
12564
12565
12566
12567
12568
12569
12570
12571
12572
12573
12574
12575
12576
12577
12578
12579
12580
12581
12582
12583
12584
12585
12586
12587
12588
12589
12590
12591
12592
12593
12594
12595
12596
12597
12598
12599
12600
12601
12602
12603
12604
12605
12606
12607
12608
12609
12610
12611
12612
12613
12614
12615
12616
12617
12618
12619
12620
12621
12622
12623
12624
12625
12626
12627
12628
12629
12630
12631
12632
12633
12634
12635
12636
12637
12638
12639
12640
12641
12642
12643
12644
12645
12646
12647
12648
12649
12650
12651
12652
12653
12654
12655
12656
12657
12658
12659
12660
12661
12662
12663
12664
12665
12666
12667
12668
12669
12670
12671
12672
12673
12674
12675
12676
12677
12678
12679
12680
12681
12682
12683
12684
12685
12686
12687
12688
12689
12690
12691
12692
12693
12694
12695
12696
12697
12698
12699
12700
12701
12702
12703
12704
12705
12706
12707
12708
12709
12710
12711
12712
12713
12714
12715
12716
12717
12718
12719
12720
12721
12722
12723
12724
12725
12726
12727
12728
12729
12730
12731
12732
12733
12734
12735
12736
12737
12738
12739
12740
12741
12742
12743
12744
12745
12746
12747
12748
12749
12750
12751
12752
12753
12754
12755
12756
12757
12758
12759
12760
12761
12762
12763
12764
12765
12766
12767
12768
12769
12770
12771
12772
12773
12774
12775
12776
12777
12778
12779
12780
12781
12782
12783
12784
12785
12786
12787
12788
12789
12790
12791
12792
12793
12794
12795
12796
12797
12798
12799
12800
12801
12802
12803
12804
12805
12806
12807
12808
12809
12810
12811
12812
12813
12814
12815
12816
12817
12818
12819
12820
12821
12822
12823
12824
12825
12826
12827
12828
12829
12830
12831
12832
12833
12834
12835
12836
12837
12838
12839
12840
12841
12842
12843
12844
12845
12846
12847
12848
12849
12850
12851
12852
12853
12854
12855
12856
12857
12858
12859
12860
12861
12862
12863
12864
12865
12866
12867
12868
12869
12870
12871
12872
12873
12874
12875
12876
12877
12878
12879
12880
12881
12882
12883
12884
12885
12886
12887
12888
12889
12890
12891
12892
12893
12894
12895
12896
12897
12898
12899
12900
12901
12902
12903
12904
12905
12906
12907
12908
12909
12910
12911
12912
12913
12914
12915
12916
12917
12918
12919
12920
12921
12922
12923
12924
12925
12926
12927
12928
12929
12930
12931
12932
12933
12934
12935
12936
12937
12938
12939
12940
12941
12942
12943
12944
12945
12946
12947
12948
12949
12950
12951
12952
12953
12954
12955
12956
12957
12958
12959
12960
12961
12962
12963
12964
12965
12966
12967
12968
12969
12970
12971
12972
12973
12974
12975
12976
12977
12978
12979
12980
12981
12982
12983
12984
12985
12986
12987
12988
12989
12990
12991
12992
12993
12994
12995
12996
12997
12998
12999
13000
13001
13002
13003
13004
13005
13006
13007
13008
13009
13010
13011
13012
13013
13014
13015
13016
13017
13018
13019
13020
13021
13022
13023
13024
13025
13026
13027
13028
13029
13030
13031
13032
13033
13034
13035
13036
13037
13038
13039
13040
13041
13042
13043
13044
13045
13046
13047
13048
13049
13050
13051
13052
13053
13054
13055
13056
13057
13058
13059
13060
13061
13062
13063
13064
13065
13066
13067
13068
13069
13070
13071
13072
13073
13074
13075
13076
13077
13078
13079
13080
13081
13082
13083
13084
13085
13086
13087
13088
13089
13090
13091
13092
13093
13094
13095
13096
13097
13098
13099
13100
13101
13102
13103
13104
13105
13106
13107
13108
13109
13110
13111
13112
13113
13114
13115
13116
13117
13118
13119
13120
13121
13122
13123
13124
13125
13126
13127
13128
13129
13130
13131
13132
13133
13134
13135
13136
13137
13138
13139
13140
13141
13142
13143
13144
13145
13146
13147
13148
13149
13150
13151
13152
13153
13154
13155
13156
13157
13158
13159
13160
13161
13162
13163
13164
13165
13166
13167
13168
13169
13170
13171
13172
13173
13174
13175
13176
13177
13178
13179
13180
13181
13182
13183
13184
13185
13186
13187
13188
13189
13190
13191
13192
13193
13194
13195
13196
13197
13198
13199
13200
13201
13202
13203
13204
13205
13206
13207
13208
13209
13210
13211
13212
13213
13214
13215
13216
13217
13218
13219
13220
13221
13222
13223
13224
13225
13226
13227
13228
13229
13230
13231
13232
13233
13234
13235
13236
13237
13238
13239
13240
13241
13242
13243
13244
13245
13246
13247
13248
13249
13250
13251
13252
13253
13254
13255
13256
13257
13258
13259
13260
13261
13262
13263
13264
13265
13266
13267
13268
13269
13270
13271
13272
13273
13274
13275
13276
13277
13278
13279
13280
13281
13282
13283
13284
13285
13286
13287
13288
13289
13290
13291
13292
13293
13294
13295
13296
13297
13298
13299
13300
13301
13302
13303
13304
13305
13306
13307
13308
13309
13310
13311
13312
13313
13314
13315
13316
13317
13318
13319
13320
13321
13322
13323
13324
13325
13326
13327
13328
13329
13330
13331
13332
13333
13334
13335
13336
13337
13338
13339
13340
13341
13342
13343
13344
13345
13346
13347
13348
13349
13350
13351
13352
13353
13354
13355
13356
13357
13358
13359
13360
13361
13362
13363
13364
13365
13366
13367
13368
13369
13370
13371
13372
13373
13374
13375
13376
13377
13378
13379
13380
13381
13382
13383
13384
13385
13386
13387
13388
13389
13390
13391
13392
13393
13394
13395
13396
13397
13398
13399
13400
13401
13402
13403
13404
13405
13406
13407
13408
13409
13410
13411
13412
13413
13414
13415
13416
13417
13418
13419
13420
13421
13422
13423
13424
13425
13426
13427
13428
13429
13430
13431
13432
13433
13434
13435
13436
13437
13438
13439
13440
13441
13442
13443
13444
13445
13446
13447
13448
13449
13450
13451
13452
13453
13454
13455
13456
13457
13458
13459
13460
13461
13462
13463
13464
13465
13466
13467
13468
13469
13470
13471
13472
13473
13474
13475
13476
13477
13478
13479
13480
13481
13482
13483
13484
13485
13486
13487
13488
13489
13490
13491
13492
13493
13494
13495
13496
13497
13498
13499
13500
13501
13502
13503
13504
13505
13506
13507
13508
13509
13510
13511
13512
13513
13514
13515
13516
13517
13518
13519
13520
13521
13522
13523
13524
13525
13526
13527
13528
13529
13530
13531
13532
13533
13534
13535
13536
13537
13538
13539
13540
13541
13542
13543
13544
13545
13546
13547
13548
13549
13550
13551
13552
13553
13554
13555
13556
13557
13558
13559
13560
13561
13562
13563
13564
13565
13566
13567
13568
13569
13570
13571
13572
13573
13574
13575
13576
13577
13578
13579
13580
13581
13582
13583
13584
13585
13586
13587
13588
13589
13590
13591
13592
13593
13594
13595
13596
13597
13598
13599
13600
13601
13602
13603
13604
13605
13606
13607
13608
13609
13610
13611
13612
13613
13614
13615
13616
13617
13618
13619
13620
13621
13622
13623
13624
13625
13626
13627
13628
13629
13630
13631
13632
13633
13634
13635
13636
13637
13638
13639
13640
13641
13642
13643
13644
13645
13646
13647
13648
13649
13650
13651
13652
13653
13654
13655
13656
13657
13658
13659
13660
13661
13662
13663
13664
13665
13666
13667
13668
13669
13670
13671
13672
13673
13674
13675
13676
13677
13678
13679
13680
13681
13682
13683
13684
13685
13686
13687
13688
13689
13690
13691
13692
13693
13694
13695
13696
13697
13698
13699
13700
13701
13702
13703
13704
13705
13706
13707
13708
13709
13710
13711
13712
13713
13714
13715
13716
13717
13718
13719
13720
13721
13722
13723
13724
13725
13726
13727
13728
13729
13730
13731
13732
13733
13734
13735
13736
13737
13738
13739
13740
13741
13742
13743
13744
13745
13746
13747
13748
13749
13750
13751
13752
13753
13754
13755
13756
13757
13758
13759
13760
13761
13762
13763
13764
13765
13766
13767
13768
13769
13770
13771
13772
13773
13774
13775
13776
13777
13778
13779
13780
13781
13782
13783
13784
13785
13786
13787
13788
13789
13790
13791
13792
13793
13794
13795
13796
13797
13798
13799
13800
13801
13802
13803
13804
13805
13806
13807
13808
13809
13810
13811
13812
13813
13814
13815
13816
13817
13818
13819
13820
13821
13822
13823
13824
13825
13826
13827
13828
13829
13830
13831
13832
13833
13834
13835
13836
13837
13838
13839
13840
13841
13842
13843
13844
13845
13846
13847
13848
13849
13850
13851
13852
13853
13854
13855
13856
13857
13858
13859
13860
13861
13862
13863
13864
13865
13866
13867
13868
13869
13870
13871
13872
13873
13874
13875
13876
13877
13878
13879
13880
13881
13882
13883
13884
13885
13886
13887
13888
13889
13890
13891
13892
13893
13894
13895
13896
13897
13898
13899
13900
13901
13902
13903
13904
13905
13906
13907
13908
13909
13910
13911
13912
13913
13914
13915
13916
13917
13918
13919
13920
13921
13922
13923
13924
13925
13926
13927
13928
13929
13930
13931
13932
13933
13934
13935
13936
13937
13938
13939
13940
13941
13942
13943
13944
13945
13946
13947
13948
13949
13950
13951
13952
13953
13954
13955
13956
13957
13958
13959
13960
13961
13962
13963
13964
13965
13966
13967
13968
13969
13970
13971
13972
13973
13974
13975
13976
13977
13978
13979
13980
13981
13982
13983
13984
13985
13986
13987
13988
13989
13990
13991
13992
13993
13994
13995
13996
13997
13998
13999
14000
14001
14002
14003
14004
14005
14006
14007
14008
14009
14010
14011
14012
14013
14014
14015
14016
14017
14018
14019
14020
14021
14022
14023
14024
14025
14026
14027
14028
14029
14030
14031
14032
14033
14034
14035
14036
14037
14038
14039
14040
14041
14042
14043
14044
14045
14046
14047
14048
14049
14050
14051
14052
14053
14054
14055
14056
14057
14058
14059
14060
14061
14062
14063
14064
14065
14066
14067
14068
14069
14070
14071
14072
14073
14074
14075
14076
14077
14078
14079
14080
14081
14082
14083
14084
14085
14086
14087
14088
14089
14090
14091
14092
14093
14094
14095
14096
14097
14098
14099
14100
14101
14102
14103
14104
14105
14106
14107
14108
14109
14110
14111
14112
14113
14114
14115
14116
14117
14118
14119
14120
14121
14122
14123
14124
14125
14126
14127
14128
14129
14130
14131
14132
14133
14134
14135
14136
14137
14138
14139
14140
14141
14142
14143
14144
14145
14146
14147
14148
14149
14150
14151
14152
14153
14154
14155
14156
14157
14158
14159
14160
14161
14162
14163
14164
14165
14166
14167
14168
14169
14170
14171
14172
14173
14174
14175
14176
14177
14178
14179
14180
14181
14182
14183
14184
14185
14186
14187
14188
14189
14190
14191
14192
14193
14194
14195
14196
14197
14198
14199
14200
14201
14202
14203
14204
14205
14206
14207
14208
14209
14210
14211
14212
14213
14214
14215
14216
14217
14218
14219
14220
14221
14222
14223
14224
14225
14226
14227
14228
14229
14230
14231
14232
14233
14234
14235
14236
14237
14238
14239
14240
14241
14242
14243
14244
14245
14246
14247
14248
14249
14250
14251
14252
14253
14254
14255
14256
14257
14258
14259
14260
14261
14262
14263
14264
14265
14266
14267
14268
14269
14270
14271
14272
14273
14274
14275
14276
14277
14278
14279
14280
14281
14282
14283
14284
14285
14286
14287
14288
14289
14290
14291
14292
14293
14294
14295
14296
14297
14298
14299
14300
14301
14302
14303
14304
14305
14306
14307
14308
14309
14310
14311
14312
14313
14314
14315
14316
14317
14318
14319
14320
14321
14322
14323
14324
14325
14326
14327
14328
14329
14330
14331
14332
14333
14334
14335
14336
14337
14338
14339
14340
14341
14342
14343
14344
14345
14346
14347
14348
14349
14350
14351
14352
14353
14354
14355
14356
14357
14358
14359
14360
14361
14362
14363
14364
14365
14366
14367
14368
14369
14370
14371
14372
14373
14374
14375
14376
14377
14378
14379
14380
14381
14382
14383
14384
14385
14386
14387
14388
14389
14390
14391
14392
14393
14394
14395
14396
14397
14398
14399
14400
14401
14402
14403
14404
14405
14406
14407
14408
14409
14410
14411
14412
14413
14414
14415
14416
14417
14418
14419
14420
14421
14422
14423
14424
14425
14426
14427
14428
14429
14430
14431
14432
14433
14434
14435
14436
14437
14438
14439
14440
14441
14442
14443
14444
14445
14446
14447
14448
14449
14450
14451
14452
14453
14454
14455
14456
14457
14458
14459
14460
14461
14462
14463
14464
14465
14466
14467
14468
14469
14470
14471
14472
14473
14474
14475
14476
14477
14478
14479
14480
14481
14482
14483
14484
14485
14486
14487
14488
14489
14490
14491
14492
14493
14494
14495
14496
14497
14498
14499
14500
14501
14502
14503
14504
14505
14506
14507
14508
14509
14510
14511
14512
14513
14514
14515
14516
14517
14518
14519
14520
14521
14522
14523
14524
14525
14526
14527
14528
14529
14530
14531
14532
14533
14534
14535
14536
14537
14538
14539
14540
14541
14542
14543
14544
14545
14546
14547
14548
14549
14550
14551
14552
14553
14554
14555
14556
14557
14558
14559
14560
14561
14562
14563
14564
14565
14566
14567
14568
14569
14570
14571
14572
14573
14574
14575
14576
14577
14578
14579
14580
14581
14582
14583
14584
14585
14586
14587
14588
14589
14590
14591
14592
14593
14594
14595
14596
14597
14598
14599
14600
14601
14602
14603
14604
14605
14606
14607
14608
14609
14610
14611
14612
14613
14614
14615
14616
14617
14618
14619
14620
14621
14622
14623
14624
14625
14626
14627
14628
14629
14630
14631
14632
14633
14634
14635
14636
14637
14638
14639
14640
14641
14642
14643
14644
14645
14646
14647
14648
14649
14650
14651
14652
14653
14654
14655
14656
14657
14658
14659
14660
14661
14662
14663
14664
14665
14666
14667
14668
14669
14670
14671
14672
14673
14674
14675
14676
14677
14678
14679
14680
14681
14682
14683
14684
14685
14686
14687
14688
14689
14690
14691
14692
14693
14694
14695
14696
14697
14698
14699
14700
14701
14702
14703
14704
14705
14706
14707
14708
14709
14710
14711
14712
14713
14714
14715
14716
14717
14718
14719
14720
14721
14722
14723
14724
14725
14726
14727
14728
14729
14730
14731
14732
14733
14734
14735
14736
14737
14738
14739
14740
14741
14742
14743
14744
14745
14746
14747
14748
14749
14750
14751
14752
14753
14754
14755
14756
14757
14758
14759
14760
14761
14762
14763
14764
14765
14766
14767
14768
14769
14770
14771
14772
14773
14774
14775
14776
14777
14778
14779
14780
14781
14782
14783
14784
14785
14786
14787
14788
14789
14790
14791
14792
14793
14794
14795
14796
14797
14798
14799
14800
14801
14802
14803
14804
14805
14806
14807
14808
14809
14810
14811
14812
14813
14814
14815
14816
14817
14818
14819
14820
14821
14822
14823
14824
14825
14826
14827
14828
14829
14830
14831
14832
14833
14834
14835
14836
14837
14838
14839
14840
14841
14842
14843
14844
14845
14846
14847
14848
14849
14850
14851
14852
14853
14854
14855
14856
14857
14858
14859
14860
14861
14862
14863
14864
14865
14866
14867
14868
14869
14870
14871
14872
14873
14874
14875
14876
14877
14878
14879
14880
14881
14882
14883
14884
14885
14886
14887
14888
14889
14890
14891
14892
14893
14894
14895
14896
14897
14898
14899
14900
14901
14902
14903
14904
14905
14906
14907
14908
14909
14910
14911
14912
14913
14914
14915
14916
14917
14918
14919
14920
14921
14922
14923
14924
14925
14926
14927
14928
14929
14930
14931
14932
14933
14934
14935
14936
14937
14938
14939
14940
14941
14942
14943
14944
14945
14946
14947
14948
14949
14950
14951
14952
14953
14954
14955
14956
14957
14958
14959
14960
14961
14962
14963
14964
14965
14966
14967
14968
14969
14970
14971
14972
14973
14974
14975
14976
14977
14978
14979
14980
14981
14982
14983
14984
14985
14986
14987
14988
14989
14990
14991
14992
14993
14994
14995
14996
14997
14998
14999
15000
15001
15002
15003
15004
15005
15006
15007
15008
15009
15010
15011
15012
15013
15014
15015
15016
15017
15018
15019
15020
15021
15022
15023
15024
15025
15026
15027
15028
15029
15030
15031
15032
15033
15034
15035
15036
15037
15038
15039
15040
15041
15042
15043
15044
15045
15046
15047
15048
15049
15050
15051
15052
15053
15054
15055
15056
15057
15058
15059
15060
15061
15062
15063
15064
15065
15066
15067
15068
15069
15070
15071
15072
15073
15074
15075
15076
15077
15078
15079
15080
15081
15082
15083
15084
15085
15086
15087
15088
15089
15090
15091
15092
15093
15094
15095
15096
15097
15098
15099
15100
15101
15102
15103
15104
15105
15106
15107
15108
15109
15110
15111
15112
15113
15114
15115
15116
15117
15118
15119
15120
15121
15122
15123
15124
15125
15126
15127
15128
15129
15130
15131
15132
15133
15134
15135
15136
15137
15138
15139
15140
15141
15142
15143
15144
15145
15146
15147
15148
15149
15150
15151
15152
15153
15154
15155
15156
15157
15158
15159
15160
15161
15162
15163
15164
15165
15166
15167
15168
15169
15170
15171
15172
15173
15174
15175
15176
15177
15178
15179
15180
15181
15182
15183
15184
15185
15186
15187
15188
15189
15190
15191
15192
15193
15194
15195
15196
15197
15198
15199
15200
15201
15202
15203
15204
15205
15206
15207
15208
15209
15210
15211
15212
15213
15214
15215
15216
15217
15218
15219
15220
15221
15222
15223
15224
15225
15226
15227
15228
15229
15230
15231
15232
15233
15234
15235
15236
15237
15238
15239
15240
15241
15242
15243
15244
15245
15246
15247
15248
15249
15250
15251
15252
15253
15254
15255
15256
15257
15258
15259
15260
15261
15262
15263
15264
15265
15266
15267
15268
15269
15270
15271
15272
15273
15274
15275
15276
15277
15278
15279
15280
15281
15282
15283
15284
15285
15286
15287
15288
15289
15290
15291
15292
15293
15294
15295
15296
15297
15298
15299
15300
15301
15302
15303
15304
15305
15306
15307
15308
15309
15310
15311
15312
15313
15314
15315
15316
15317
15318
15319
15320
15321
15322
15323
15324
15325
15326
15327
15328
15329
15330
15331
15332
15333
15334
15335
15336
15337
15338
15339
15340
15341
15342
15343
15344
15345
15346
15347
15348
15349
15350
15351
15352
15353
15354
15355
15356
15357
15358
15359
15360
15361
15362
15363
15364
15365
15366
15367
15368
15369
15370
15371
15372
15373
15374
15375
15376
15377
15378
15379
15380
15381
15382
15383
15384
15385
15386
15387
15388
15389
15390
15391
15392
15393
15394
15395
15396
15397
15398
15399
15400
15401
15402
15403
15404
15405
15406
15407
15408
15409
15410
15411
15412
15413
15414
15415
15416
15417
15418
15419
15420
15421
15422
15423
15424
15425
15426
15427
15428
15429
15430
15431
15432
15433
15434
15435
15436
15437
15438
15439
15440
15441
15442
15443
15444
15445
15446
15447
15448
15449
15450
15451
15452
15453
15454
15455
15456
15457
15458
15459
15460
15461
15462
15463
15464
15465
15466
15467
15468
15469
15470
15471
15472
15473
15474
15475
15476
15477
15478
15479
15480
15481
15482
15483
15484
15485
15486
15487
15488
15489
15490
15491
15492
15493
15494
15495
15496
15497
15498
15499
15500
15501
15502
15503
15504
15505
15506
15507
15508
15509
15510
15511
15512
15513
15514
15515
15516
15517
15518
15519
15520
15521
15522
15523
15524
15525
15526
15527
15528
15529
15530
15531
15532
15533
15534
15535
15536
15537
15538
15539
15540
15541
15542
15543
15544
15545
15546
15547
15548
15549
15550
15551
15552
15553
15554
15555
15556
15557
15558
15559
15560
15561
15562
15563
15564
15565
15566
15567
15568
15569
15570
15571
15572
15573
15574
15575
15576
15577
15578
15579
15580
15581
15582
15583
15584
15585
15586
15587
15588
15589
15590
15591
15592
15593
15594
15595
15596
15597
15598
15599
15600
15601
15602
15603
15604
15605
15606
15607
15608
15609
15610
15611
15612
15613
15614
15615
15616
15617
15618
15619
15620
15621
15622
15623
15624
15625
15626
15627
15628
15629
15630
15631
15632
15633
15634
15635
15636
15637
15638
15639
15640
15641
15642
15643
15644
15645
15646
15647
15648
15649
15650
15651
15652
15653
15654
15655
15656
15657
15658
15659
15660
15661
15662
15663
15664
15665
15666
15667
15668
15669
15670
15671
15672
15673
15674
15675
15676
15677
15678
15679
15680
15681
15682
15683
15684
15685
15686
15687
15688
15689
15690
15691
15692
15693
15694
15695
15696
15697
15698
15699
15700
15701
15702
15703
15704
15705
15706
15707
15708
15709
15710
15711
15712
15713
15714
15715
15716
15717
15718
15719
15720
15721
15722
15723
15724
15725
15726
15727
15728
15729
15730
15731
15732
15733
15734
15735
15736
15737
15738
15739
15740
15741
15742
15743
15744
15745
15746
15747
15748
15749
15750
15751
15752
15753
15754
15755
15756
15757
15758
15759
15760
15761
15762
15763
15764
15765
15766
15767
15768
15769
15770
15771
15772
15773
15774
15775
15776
15777
15778
15779
15780
15781
15782
15783
15784
15785
15786
15787
15788
15789
15790
15791
15792
15793
15794
15795
15796
15797
15798
15799
15800
15801
15802
15803
15804
15805
15806
15807
15808
15809
15810
15811
15812
15813
15814
15815
15816
15817
15818
15819
15820
15821
15822
15823
15824
15825
15826
15827
15828
15829
15830
15831
15832
15833
15834
15835
15836
15837
15838
15839
15840
15841
15842
15843
15844
15845
15846
15847
15848
15849
15850
15851
15852
15853
15854
15855
15856
15857
15858
15859
15860
15861
15862
15863
15864
15865
15866
15867
15868
15869
15870
15871
15872
15873
15874
15875
15876
15877
15878
15879
15880
15881
15882
15883
15884
15885
15886
15887
15888
15889
15890
15891
15892
15893
15894
15895
15896
15897
15898
15899
15900
15901
15902
15903
15904
15905
15906
15907
15908
15909
15910
15911
15912
15913
15914
15915
15916
15917
15918
15919
15920
15921
15922
15923
15924
15925
15926
15927
15928
15929
15930
15931
15932
15933
15934
15935
15936
15937
15938
15939
15940
15941
15942
15943
15944
15945
15946
15947
15948
15949
15950
15951
15952
15953
15954
15955
15956
15957
15958
15959
15960
15961
15962
15963
15964
15965
15966
15967
15968
15969
15970
15971
15972
15973
15974
15975
15976
15977
15978
15979
15980
15981
15982
15983
15984
15985
15986
15987
15988
15989
15990
15991
15992
15993
15994
15995
15996
15997
15998
15999
16000
16001
16002
16003
16004
16005
16006
16007
16008
16009
16010
16011
16012
16013
16014
16015
16016
16017
16018
16019
16020
16021
16022
16023
16024
16025
16026
16027
16028
16029
16030
16031
16032
16033
16034
16035
16036
16037
16038
16039
16040
16041
16042
16043
16044
16045
16046
16047
16048
16049
16050
16051
16052
16053
16054
16055
16056
16057
16058
16059
16060
16061
16062
16063
16064
16065
16066
16067
16068
16069
16070
16071
16072
16073
16074
16075
16076
16077
16078
16079
16080
16081
16082
16083
16084
16085
16086
16087
16088
16089
16090
16091
16092
16093
16094
16095
16096
16097
16098
16099
16100
16101
16102
16103
16104
16105
16106
16107
16108
16109
16110
16111
16112
16113
16114
16115
16116
16117
16118
16119
16120
16121
16122
16123
16124
16125
16126
16127
16128
16129
16130
16131
16132
16133
16134
16135
16136
16137
16138
16139
16140
16141
16142
16143
16144
16145
16146
16147
16148
16149
16150
16151
16152
16153
16154
16155
16156
16157
16158
16159
16160
16161
16162
16163
16164
16165
16166
16167
16168
16169
16170
16171
16172
16173
16174
16175
16176
16177
16178
16179
16180
16181
16182
16183
16184
16185
16186
16187
16188
16189
16190
16191
16192
16193
16194
16195
16196
16197
16198
16199
16200
16201
16202
16203
16204
16205
16206
16207
16208
16209
16210
16211
16212
16213
16214
16215
16216
16217
16218
16219
16220
16221
16222
16223
16224
16225
16226
16227
16228
16229
16230
16231
16232
16233
16234
16235
16236
16237
16238
16239
16240
16241
16242
16243
16244
16245
16246
16247
16248
16249
16250
16251
16252
16253
16254
16255
16256
16257
16258
16259
16260
16261
16262
16263
16264
16265
16266
16267
16268
16269
16270
16271
16272
16273
16274
16275
16276
16277
16278
16279
16280
16281
16282
16283
16284
16285
16286
16287
16288
16289
16290
16291
16292
16293
16294
16295
16296
16297
16298
16299
16300
16301
16302
16303
16304
16305
16306
16307
16308
16309
16310
16311
16312
16313
16314
16315
16316
16317
16318
16319
16320
16321
16322
16323
16324
16325
16326
16327
16328
16329
16330
16331
16332
16333
16334
16335
16336
16337
16338
16339
16340
16341
16342
16343
16344
16345
16346
16347
16348
16349
16350
16351
16352
16353
16354
16355
16356
16357
16358
16359
16360
16361
16362
16363
16364
16365
16366
16367
16368
16369
16370
16371
16372
16373
16374
16375
16376
16377
16378
16379
16380
16381
16382
16383
16384
16385
16386
16387
16388
16389
16390
16391
16392
16393
16394
16395
16396
16397
16398
16399
16400
16401
16402
16403
16404
16405
16406
16407
16408
16409
16410
16411
16412
16413
16414
16415
16416
16417
16418
16419
16420
16421
16422
16423
16424
16425
16426
16427
16428
16429
16430
16431
16432
16433
16434
16435
16436
16437
16438
16439
16440
16441
16442
16443
16444
16445
16446
16447
16448
16449
16450
16451
16452
16453
16454
16455
16456
16457
16458
16459
16460
16461
16462
16463
16464
16465
16466
16467
16468
16469
16470
16471
16472
16473
16474
16475
16476
16477
16478
16479
16480
16481
16482
16483
16484
16485
16486
16487
16488
16489
16490
16491
16492
16493
16494
16495
16496
16497
16498
16499
16500
16501
16502
16503
16504
16505
16506
16507
16508
16509
16510
16511
16512
16513
16514
16515
16516
16517
16518
16519
16520
16521
16522
16523
16524
16525
16526
16527
16528
16529
16530
16531
16532
16533
16534
16535
16536
16537
16538
16539
16540
16541
16542
16543
16544
16545
16546
16547
16548
16549
16550
16551
16552
16553
16554
16555
16556
16557
16558
16559
16560
16561
16562
16563
16564
16565
16566
16567
16568
16569
16570
16571
16572
16573
16574
16575
16576
16577
16578
16579
16580
16581
16582
16583
16584
16585
16586
16587
16588
16589
16590
16591
16592
16593
16594
16595
16596
16597
16598
16599
16600
16601
16602
16603
16604
16605
16606
16607
16608
16609
16610
16611
16612
16613
16614
16615
16616
16617
16618
16619
16620
16621
16622
16623
16624
16625
16626
16627
16628
16629
16630
16631
16632
16633
16634
16635
16636
16637
16638
16639
16640
16641
16642
16643
16644
16645
16646
16647
16648
16649
16650
16651
16652
16653
16654
16655
16656
16657
16658
16659
16660
16661
16662
16663
16664
16665
16666
16667
16668
16669
16670
16671
16672
16673
16674
16675
16676
16677
16678
16679
16680
16681
16682
16683
16684
16685
16686
16687
16688
16689
16690
16691
16692
16693
16694
16695
16696
16697
16698
16699
16700
16701
16702
16703
16704
16705
16706
16707
16708
16709
16710
16711
16712
16713
16714
16715
16716
16717
16718
16719
16720
16721
16722
16723
16724
16725
16726
16727
16728
16729
16730
16731
16732
16733
16734
16735
16736
16737
16738
16739
16740
16741
16742
16743
16744
16745
16746
16747
16748
16749
16750
16751
16752
16753
16754
16755
16756
16757
16758
16759
16760
16761
16762
16763
16764
16765
16766
16767
16768
16769
16770
16771
16772
16773
16774
16775
16776
16777
16778
16779
16780
16781
16782
16783
16784
16785
16786
16787
16788
16789
16790
16791
16792
16793
16794
16795
16796
16797
16798
16799
16800
16801
16802
16803
16804
16805
16806
16807
16808
16809
16810
16811
16812
16813
16814
16815
16816
16817
16818
16819
16820
16821
16822
16823
16824
16825
16826
16827
16828
16829
16830
16831
16832
16833
16834
16835
16836
16837
16838
16839
16840
16841
16842
16843
16844
16845
16846
16847
16848
16849
16850
16851
16852
16853
16854
16855
16856
16857
16858
16859
16860
16861
16862
16863
16864
16865
16866
16867
16868
16869
16870
16871
16872
16873
16874
16875
16876
16877
16878
16879
16880
16881
16882
16883
16884
16885
16886
16887
16888
16889
16890
16891
16892
16893
16894
16895
16896
16897
16898
16899
16900
16901
16902
16903
16904
16905
16906
16907
16908
16909
16910
16911
16912
16913
16914
16915
16916
16917
16918
16919
16920
16921
16922
16923
16924
16925
16926
16927
16928
16929
16930
16931
16932
16933
16934
16935
16936
16937
16938
16939
16940
16941
16942
16943
16944
16945
16946
16947
16948
16949
16950
16951
16952
16953
16954
16955
16956
16957
16958
16959
16960
16961
16962
16963
16964
16965
16966
16967
16968
16969
16970
16971
16972
16973
16974
16975
16976
16977
16978
16979
16980
16981
16982
16983
16984
16985
16986
16987
16988
16989
16990
16991
16992
16993
16994
16995
16996
16997
16998
16999
17000
17001
17002
17003
17004
17005
17006
17007
17008
17009
17010
17011
17012
17013
17014
17015
17016
17017
17018
17019
17020
17021
17022
17023
17024
17025
17026
17027
17028
17029
17030
17031
17032
17033
17034
17035
17036
17037
17038
17039
17040
17041
17042
17043
17044
17045
17046
17047
17048
17049
17050
17051
17052
17053
17054
17055
17056
17057
17058
17059
17060
17061
17062
17063
17064
17065
17066
17067
17068
17069
17070
17071
17072
17073
17074
17075
17076
17077
17078
17079
17080
17081
17082
17083
17084
17085
17086
17087
17088
17089
17090
17091
17092
17093
17094
17095
17096
17097
17098
17099
17100
17101
17102
17103
17104
17105
17106
17107
17108
17109
17110
17111
17112
17113
17114
17115
17116
17117
17118
17119
17120
17121
17122
17123
17124
17125
17126
17127
17128
17129
17130
17131
17132
17133
17134
17135
17136
17137
17138
17139
17140
17141
17142
17143
17144
17145
17146
17147
17148
17149
17150
17151
17152
17153
17154
17155
17156
17157
17158
17159
17160
17161
17162
17163
17164
17165
17166
17167
17168
17169
17170
17171
17172
17173
17174
17175
17176
17177
17178
17179
17180
17181
17182
17183
17184
17185
17186
17187
17188
17189
17190
17191
17192
17193
17194
17195
17196
17197
17198
17199
17200
17201
17202
17203
17204
17205
17206
17207
17208
17209
17210
17211
17212
17213
17214
17215
17216
17217
17218
17219
17220
17221
17222
17223
17224
17225
17226
17227
17228
17229
17230
17231
17232
17233
17234
17235
17236
17237
17238
17239
17240
17241
17242
17243
17244
17245
17246
17247
17248
17249
17250
17251
17252
17253
17254
17255
17256
17257
17258
17259
17260
17261
17262
17263
17264
17265
17266
17267
17268
17269
17270
17271
17272
17273
17274
17275
17276
17277
17278
17279
17280
17281
17282
17283
17284
17285
17286
17287
17288
17289
17290
17291
17292
17293
17294
17295
17296
17297
17298
17299
17300
17301
17302
17303
17304
17305
17306
17307
17308
17309
17310
17311
17312
17313
17314
17315
17316
17317
17318
17319
17320
17321
17322
17323
17324
17325
17326
17327
17328
17329
17330
17331
17332
17333
17334
17335
17336
17337
17338
17339
17340
17341
17342
17343
17344
17345
17346
17347
17348
17349
17350
17351
17352
17353
17354
17355
17356
17357
17358
17359
17360
17361
17362
17363
17364
17365
17366
17367
17368
17369
17370
17371
17372
17373
17374
17375
17376
17377
17378
17379
17380
17381
17382
17383
17384
17385
17386
17387
17388
17389
17390
17391
17392
17393
17394
17395
17396
17397
17398
17399
17400
17401
17402
17403
17404
17405
17406
17407
17408
17409
17410
17411
17412
17413
17414
17415
17416
17417
17418
17419
17420
17421
17422
17423
17424
17425
17426
17427
17428
17429
17430
17431
17432
17433
17434
17435
17436
17437
17438
17439
17440
17441
17442
17443
17444
17445
17446
17447
17448
17449
17450
17451
17452
17453
17454
17455
17456
17457
17458
17459
17460
17461
17462
17463
17464
17465
17466
17467
17468
17469
17470
17471
17472
17473
17474
17475
17476
17477
17478
17479
17480
17481
17482
17483
17484
17485
17486
17487
17488
17489
17490
17491
17492
17493
17494
17495
17496
17497
17498
17499
17500
17501
17502
17503
17504
17505
17506
17507
17508
17509
17510
17511
17512
17513
17514
17515
17516
17517
17518
17519
17520
17521
17522
17523
17524
17525
17526
17527
17528
17529
17530
17531
17532
17533
17534
17535
17536
17537
17538
17539
17540
17541
17542
17543
17544
17545
17546
17547
17548
17549
17550
17551
17552
17553
17554
17555
17556
17557
17558
17559
17560
17561
17562
17563
17564
17565
17566
17567
17568
17569
17570
17571
17572
17573
17574
17575
17576
17577
17578
17579
17580
17581
17582
17583
17584
17585
17586
17587
17588
17589
17590
17591
17592
17593
17594
17595
17596
17597
17598
17599
17600
17601
17602
17603
17604
17605
17606
17607
17608
17609
17610
17611
17612
17613
17614
17615
17616
17617
17618
17619
17620
17621
17622
17623
17624
17625
17626
17627
17628
17629
17630
17631
17632
17633
17634
17635
17636
17637
17638
17639
17640
17641
17642
17643
17644
17645
17646
17647
17648
17649
17650
17651
17652
17653
17654
17655
17656
17657
17658
17659
17660
17661
17662
17663
17664
17665
17666
17667
17668
17669
17670
17671
17672
17673
17674
17675
17676
17677
17678
17679
17680
17681
17682
17683
17684
17685
17686
17687
17688
17689
17690
17691
17692
17693
17694
17695
17696
17697
17698
17699
17700
17701
17702
17703
17704
17705
17706
17707
17708
17709
17710
17711
17712
17713
17714
17715
17716
17717
17718
17719
17720
17721
17722
17723
17724
17725
17726
17727
17728
17729
17730
17731
17732
17733
17734
17735
17736
17737
17738
17739
17740
17741
17742
17743
17744
17745
17746
17747
17748
17749
17750
17751
17752
17753
17754
17755
17756
17757
17758
17759
17760
17761
17762
17763
17764
17765
17766
17767
17768
17769
17770
17771
17772
17773
17774
17775
17776
17777
17778
17779
17780
17781
17782
17783
17784
17785
17786
17787
17788
17789
17790
17791
17792
17793
17794
17795
17796
17797
17798
17799
17800
17801
17802
17803
17804
17805
17806
17807
17808
17809
17810
17811
17812
17813
17814
17815
17816
17817
17818
17819
17820
17821
17822
17823
17824
17825
17826
17827
17828
17829
17830
17831
17832
17833
17834
17835
17836
17837
17838
17839
17840
17841
17842
17843
17844
17845
17846
17847
17848
17849
17850
17851
17852
17853
17854
17855
17856
17857
17858
17859
17860
17861
17862
17863
17864
17865
17866
17867
17868
17869
17870
17871
17872
17873
17874
17875
17876
17877
17878
17879
17880
17881
17882
17883
17884
17885
17886
17887
17888
17889
17890
17891
17892
17893
17894
17895
17896
17897
17898
17899
17900
17901
17902
17903
17904
17905
17906
17907
17908
17909
17910
17911
17912
17913
17914
17915
17916
17917
17918
17919
17920
17921
17922
17923
17924
17925
17926
17927
17928
17929
17930
17931
17932
17933
17934
17935
17936
17937
17938
17939
17940
17941
17942
17943
17944
17945
17946
17947
17948
17949
17950
17951
17952
17953
17954
17955
17956
17957
17958
17959
17960
17961
17962
17963
17964
17965
17966
17967
17968
17969
17970
17971
17972
17973
17974
17975
17976
17977
17978
17979
17980
17981
17982
17983
17984
17985
17986
17987
17988
17989
17990
17991
17992
17993
17994
17995
17996
17997
17998
17999
18000
18001
18002
18003
18004
18005
18006
18007
18008
18009
18010
18011
18012
18013
18014
18015
18016
18017
18018
18019
18020
18021
18022
18023
18024
18025
18026
18027
18028
18029
18030
18031
18032
18033
18034
18035
18036
18037
18038
18039
18040
18041
18042
18043
18044
18045
18046
18047
18048
18049
18050
18051
18052
18053
18054
18055
18056
18057
18058
18059
18060
18061
18062
18063
18064
18065
18066
18067
18068
18069
18070
18071
18072
18073
18074
18075
18076
18077
18078
18079
18080
18081
18082
18083
18084
18085
18086
18087
18088
18089
18090
18091
18092
18093
18094
18095
18096
18097
18098
18099
18100
18101
18102
18103
18104
18105
18106
18107
18108
18109
18110
18111
18112
18113
18114
18115
18116
18117
18118
18119
18120
18121
18122
18123
18124
18125
18126
18127
18128
18129
18130
18131
18132
18133
18134
18135
18136
18137
18138
18139
18140
18141
18142
18143
18144
18145
18146
18147
18148
18149
18150
18151
18152
18153
18154
18155
18156
18157
18158
18159
18160
18161
18162
18163
18164
18165
18166
18167
18168
18169
18170
18171
18172
18173
18174
18175
18176
18177
18178
18179
18180
18181
18182
18183
18184
18185
18186
18187
18188
18189
18190
18191
18192
18193
18194
18195
18196
18197
18198
18199
18200
18201
18202
18203
18204
18205
18206
18207
18208
18209
18210
18211
18212
18213
18214
18215
18216
18217
18218
18219
18220
18221
18222
18223
18224
18225
18226
18227
18228
18229
18230
18231
18232
18233
18234
18235
18236
18237
18238
18239
18240
18241
18242
18243
18244
18245
18246
18247
18248
18249
18250
18251
18252
18253
18254
18255
18256
18257
18258
18259
18260
18261
18262
18263
18264
18265
18266
18267
18268
18269
18270
18271
18272
18273
18274
18275
18276
18277
18278
18279
18280
18281
18282
18283
18284
18285
18286
18287
18288
18289
18290
18291
18292
18293
18294
18295
18296
18297
18298
18299
18300
18301
18302
18303
18304
18305
18306
18307
18308
18309
18310
18311
18312
18313
18314
18315
18316
18317
18318
18319
18320
18321
18322
18323
18324
18325
18326
18327
18328
18329
18330
18331
18332
18333
18334
18335
18336
18337
18338
18339
18340
18341
18342
18343
18344
18345
18346
18347
18348
18349
18350
18351
18352
18353
18354
18355
18356
18357
18358
18359
18360
18361
18362
18363
18364
18365
18366
18367
18368
18369
18370
18371
18372
18373
18374
18375
18376
18377
18378
18379
18380
18381
18382
18383
18384
18385
18386
18387
18388
18389
18390
18391
18392
18393
18394
18395
18396
18397
18398
18399
18400
18401
18402
18403
18404
18405
18406
18407
18408
18409
18410
18411
18412
18413
18414
18415
18416
18417
18418
18419
18420
18421
18422
18423
18424
18425
18426
18427
18428
18429
18430
18431
18432
18433
18434
18435
18436
18437
18438
18439
18440
18441
18442
18443
18444
18445
18446
18447
18448
18449
18450
18451
18452
18453
18454
18455
18456
18457
18458
18459
18460
18461
18462
18463
18464
18465
18466
18467
18468
18469
18470
18471
18472
18473
18474
18475
18476
18477
18478
18479
18480
18481
18482
18483
18484
18485
18486
18487
18488
18489
18490
18491
18492
18493
18494
18495
18496
18497
18498
18499
18500
18501
18502
18503
18504
18505
18506
18507
18508
18509
18510
18511
18512
18513
18514
18515
18516
18517
18518
18519
18520
18521
18522
18523
18524
18525
18526
18527
18528
18529
18530
18531
18532
18533
18534
18535
18536
18537
18538
18539
18540
18541
18542
18543
18544
18545
18546
18547
18548
18549
18550
18551
18552
18553
18554
18555
18556
18557
18558
18559
18560
18561
18562
18563
18564
18565
18566
18567
18568
18569
18570
18571
18572
18573
18574
18575
18576
18577
18578
18579
18580
18581
18582
18583
18584
18585
18586
18587
18588
18589
18590
18591
18592
18593
18594
18595
18596
18597
18598
18599
18600
18601
18602
18603
18604
18605
18606
18607
18608
18609
18610
18611
18612
18613
18614
18615
18616
18617
18618
18619
18620
18621
18622
18623
18624
18625
18626
18627
18628
18629
18630
18631
18632
18633
18634
18635
18636
18637
18638
18639
18640
18641
18642
18643
18644
18645
18646
18647
18648
18649
18650
18651
18652
18653
18654
18655
18656
18657
18658
18659
18660
18661
18662
18663
18664
18665
18666
18667
18668
18669
18670
18671
18672
18673
18674
18675
18676
18677
18678
18679
18680
18681
18682
18683
18684
18685
18686
18687
18688
18689
18690
18691
18692
18693
18694
18695
18696
18697
18698
18699
18700
18701
18702
18703
18704
18705
18706
18707
18708
18709
18710
18711
18712
18713
18714
18715
18716
18717
18718
18719
18720
18721
18722
18723
18724
18725
18726
18727
18728
18729
18730
18731
18732
18733
18734
18735
18736
18737
18738
18739
18740
18741
18742
18743
18744
18745
18746
18747
18748
18749
18750
18751
18752
18753
18754
18755
18756
18757
18758
18759
18760
18761
18762
18763
18764
18765
18766
18767
18768
18769
18770
18771
18772
18773
18774
18775
18776
18777
18778
18779
18780
18781
18782
18783
18784
18785
18786
18787
18788
18789
18790
18791
18792
18793
18794
18795
18796
18797
18798
18799
18800
18801
18802
18803
18804
18805
18806
18807
18808
18809
18810
18811
18812
18813
18814
18815
18816
18817
18818
18819
18820
18821
18822
18823
18824
18825
18826
18827
18828
18829
18830
18831
18832
18833
18834
18835
18836
18837
18838
18839
18840
18841
18842
18843
18844
18845
18846
18847
18848
18849
18850
18851
18852
18853
18854
18855
18856
18857
18858
18859
18860
18861
18862
18863
18864
18865
18866
18867
18868
18869
18870
18871
18872
18873
18874
18875
18876
18877
18878
18879
18880
18881
18882
18883
18884
18885
18886
18887
18888
18889
18890
18891
18892
18893
18894
18895
18896
18897
18898
18899
18900
18901
18902
18903
18904
18905
18906
18907
18908
18909
18910
18911
18912
18913
18914
18915
18916
18917
18918
18919
18920
18921
18922
18923
18924
18925
18926
18927
18928
18929
18930
18931
18932
18933
18934
18935
18936
18937
18938
18939
18940
18941
18942
18943
18944
18945
18946
18947
18948
18949
18950
18951
18952
18953
18954
18955
18956
18957
18958
18959
18960
18961
18962
18963
18964
18965
18966
18967
18968
18969
18970
18971
18972
18973
18974
18975
18976
18977
18978
18979
18980
18981
18982
18983
18984
18985
18986
18987
18988
18989
18990
18991
18992
18993
18994
18995
18996
18997
18998
18999
19000
19001
19002
19003
19004
19005
19006
19007
19008
19009
19010
19011
19012
19013
19014
19015
19016
19017
19018
19019
19020
19021
19022
19023
19024
19025
19026
19027
19028
19029
19030
19031
19032
19033
19034
19035
19036
19037
19038
19039
19040
19041
19042
19043
19044
19045
19046
19047
19048
19049
19050
19051
19052
19053
19054
19055
19056
19057
19058
19059
19060
19061
19062
19063
19064
19065
19066
19067
19068
19069
19070
19071
19072
19073
19074
19075
19076
19077
19078
19079
19080
19081
19082
19083
19084
19085
19086
19087
19088
19089
19090
19091
19092
19093
19094
19095
19096
19097
19098
19099
19100
19101
19102
19103
19104
19105
19106
19107
19108
19109
19110
19111
19112
19113
19114
19115
19116
19117
19118
19119
19120
19121
19122
19123
19124
19125
19126
19127
19128
19129
19130
19131
19132
19133
19134
19135
19136
19137
19138
19139
19140
19141
19142
19143
19144
19145
19146
19147
19148
19149
19150
19151
19152
19153
19154
19155
19156
19157
19158
19159
19160
19161
19162
19163
19164
19165
19166
19167
19168
19169
19170
19171
19172
19173
19174
19175
19176
19177
19178
19179
19180
19181
19182
19183
19184
19185
19186
19187
19188
19189
19190
19191
19192
19193
19194
19195
19196
19197
19198
19199
19200
19201
19202
19203
19204
19205
19206
19207
19208
19209
19210
19211
19212
19213
19214
19215
19216
19217
19218
19219
19220
19221
19222
19223
19224
19225
19226
19227
19228
19229
19230
19231
19232
19233
19234
19235
19236
19237
19238
19239
19240
19241
19242
19243
19244
19245
19246
19247
19248
19249
19250
19251
19252
19253
19254
19255
19256
19257
19258
19259
19260
19261
19262
19263
19264
19265
19266
19267
19268
19269
19270
19271
19272
19273
19274
19275
19276
19277
19278
19279
19280
19281
19282
19283
19284
19285
19286
19287
19288
19289
19290
19291
19292
19293
19294
19295
19296
19297
19298
19299
19300
19301
19302
19303
19304
19305
19306
19307
19308
19309
19310
19311
19312
19313
19314
19315
19316
19317
19318
19319
19320
19321
19322
19323
19324
19325
19326
19327
19328
19329
19330
19331
19332
19333
19334
19335
19336
19337
19338
19339
19340
19341
19342
19343
19344
19345
19346
19347
19348
19349
19350
19351
19352
19353
19354
19355
19356
19357
19358
19359
19360
19361
19362
19363
19364
19365
19366
19367
19368
19369
19370
19371
19372
19373
19374
19375
19376
19377
19378
19379
19380
19381
19382
19383
19384
19385
19386
19387
19388
19389
19390
19391
19392
19393
19394
19395
19396
19397
19398
19399
19400
19401
19402
19403
19404
19405
19406
19407
19408
19409
19410
19411
19412
19413
19414
19415
19416
19417
19418
19419
19420
19421
19422
19423
19424
19425
19426
19427
19428
19429
19430
19431
19432
19433
19434
19435
19436
19437
19438
19439
19440
19441
19442
19443
19444
19445
19446
19447
19448
19449
19450
19451
19452
19453
19454
19455
19456
19457
19458
19459
19460
19461
19462
19463
19464
19465
19466
19467
19468
19469
19470
19471
19472
19473
19474
19475
19476
19477
19478
19479
19480
19481
19482
19483
19484
19485
19486
19487
19488
19489
19490
19491
19492
19493
19494
19495
19496
19497
19498
19499
19500
19501
19502
19503
19504
19505
19506
19507
19508
19509
19510
19511
19512
19513
19514
19515
19516
19517
19518
19519
19520
19521
19522
19523
19524
19525
19526
19527
19528
19529
19530
19531
19532
19533
19534
19535
19536
19537
19538
19539
19540
19541
19542
19543
19544
19545
19546
19547
19548
19549
19550
19551
19552
19553
19554
19555
19556
19557
19558
19559
19560
19561
19562
19563
19564
19565
19566
19567
19568
19569
19570
19571
19572
19573
19574
19575
19576
19577
19578
19579
19580
19581
19582
19583
19584
19585
19586
19587
19588
19589
19590
19591
19592
19593
19594
19595
19596
19597
19598
19599
19600
19601
19602
19603
19604
19605
19606
19607
19608
19609
19610
19611
19612
19613
19614
19615
19616
19617
19618
19619
19620
19621
19622
19623
19624
19625
19626
19627
19628
19629
19630
19631
19632
19633
19634
19635
19636
19637
19638
19639
19640
19641
19642
19643
19644
19645
19646
19647
19648
19649
19650
19651
19652
19653
19654
19655
19656
19657
19658
19659
19660
19661
19662
19663
19664
19665
19666
19667
19668
19669
19670
19671
19672
19673
19674
19675
19676
19677
19678
19679
19680
19681
19682
19683
19684
19685
19686
19687
19688
19689
19690
19691
19692
19693
19694
19695
19696
19697
19698
19699
19700
19701
19702
19703
19704
19705
19706
19707
19708
19709
19710
19711
19712
19713
19714
19715
19716
19717
19718
19719
19720
19721
19722
19723
19724
19725
19726
19727
19728
19729
19730
19731
19732
19733
19734
19735
19736
19737
19738
19739
19740
19741
19742
19743
19744
19745
19746
19747
19748
19749
19750
19751
19752
19753
19754
19755
19756
19757
19758
19759
19760
19761
19762
19763
19764
19765
19766
19767
19768
19769
19770
19771
19772
19773
19774
19775
19776
19777
19778
19779
19780
19781
19782
19783
19784
19785
19786
19787
19788
19789
19790
19791
19792
19793
19794
19795
19796
19797
19798
19799
19800
19801
19802
19803
19804
19805
19806
19807
19808
19809
19810
19811
19812
19813
19814
19815
19816
19817
19818
19819
19820
19821
19822
19823
19824
19825
19826
19827
19828
19829
19830
19831
19832
19833
19834
19835
19836
19837
19838
19839
19840
19841
19842
19843
19844
19845
19846
19847
19848
19849
19850
19851
19852
19853
19854
19855
19856
19857
19858
19859
19860
19861
19862
19863
19864
19865
19866
19867
19868
19869
19870
19871
19872
19873
19874
19875
19876
19877
19878
19879
19880
19881
19882
19883
19884
19885
19886
19887
19888
19889
19890
19891
19892
19893
19894
19895
19896
19897
19898
19899
19900
19901
19902
19903
19904
19905
19906
19907
19908
19909
19910
19911
19912
19913
19914
19915
19916
19917
19918
19919
19920
19921
19922
19923
19924
19925
19926
19927
19928
19929
19930
19931
19932
19933
19934
19935
19936
19937
19938
19939
19940
19941
19942
19943
19944
19945
19946
19947
19948
19949
19950
19951
19952
19953
19954
19955
19956
19957
19958
19959
19960
19961
19962
19963
19964
19965
19966
19967
19968
19969
19970
19971
19972
19973
19974
19975
19976
19977
19978
19979
19980
19981
19982
19983
19984
19985
19986
19987
19988
19989
19990
19991
19992
19993
19994
19995
19996
19997
19998
19999
20000
20001
20002
20003
20004
20005
20006
20007
20008
20009
20010
20011
20012
20013
20014
20015
20016
20017
20018
20019
20020
20021
20022
20023
20024
20025
20026
20027
20028
20029
20030
20031
20032
20033
20034
20035
20036
20037
20038
20039
20040
20041
20042
20043
20044
20045
20046
20047
20048
20049
20050
20051
20052
20053
20054
20055
20056
20057
20058
20059
20060
20061
20062
20063
20064
20065
20066
20067
20068
20069
20070
20071
20072
20073
20074
20075
20076
20077
20078
20079
20080
20081
20082
20083
20084
20085
20086
20087
20088
20089
20090
20091
20092
20093
20094
20095
20096
20097
20098
20099
20100
20101
20102
20103
20104
20105
20106
20107
20108
20109
20110
20111
20112
20113
20114
20115
20116
20117
20118
20119
20120
20121
20122
20123
20124
20125
20126
20127
20128
20129
20130
20131
20132
20133
20134
20135
20136
20137
20138
20139
20140
20141
20142
20143
20144
20145
20146
20147
20148
20149
20150
20151
20152
20153
20154
20155
20156
20157
20158
20159
20160
20161
20162
20163
20164
20165
20166
20167
20168
20169
20170
20171
20172
20173
20174
20175
20176
20177
20178
20179
20180
20181
20182
20183
20184
20185
20186
20187
20188
20189
20190
20191
20192
20193
20194
20195
20196
20197
20198
20199
20200
20201
20202
20203
20204
20205
20206
20207
20208
20209
20210
20211
20212
20213
20214
20215
20216
20217
20218
20219
20220
20221
20222
20223
20224
20225
20226
20227
20228
20229
20230
20231
20232
20233
20234
20235
20236
20237
20238
20239
20240
20241
20242
20243
20244
20245
20246
20247
20248
20249
20250
20251
20252
20253
20254
20255
20256
20257
20258
20259
20260
20261
20262
20263
20264
20265
20266
20267
20268
20269
20270
20271
20272
20273
20274
20275
20276
20277
20278
20279
20280
20281
20282
20283
20284
20285
20286
20287
20288
20289
20290
20291
20292
20293
20294
20295
20296
20297
20298
20299
20300
20301
20302
20303
20304
20305
20306
20307
20308
20309
20310
20311
20312
20313
20314
20315
20316
20317
20318
20319
20320
20321
20322
20323
20324
20325
20326
20327
20328
20329
20330
20331
20332
20333
20334
20335
20336
20337
20338
20339
20340
20341
20342
20343
20344
20345
20346
20347
20348
20349
20350
20351
20352
20353
20354
20355
20356
20357
20358
20359
20360
20361
20362
20363
20364
20365
20366
20367
20368
20369
20370
20371
20372
20373
20374
20375
20376
20377
20378
20379
20380
20381
20382
20383
20384
20385
20386
20387
20388
20389
20390
20391
20392
20393
20394
20395
20396
20397
20398
20399
20400
20401
20402
20403
20404
20405
20406
20407
20408
20409
20410
20411
20412
20413
20414
20415
20416
20417
20418
20419
20420
20421
20422
20423
20424
20425
20426
20427
20428
20429
20430
20431
20432
20433
20434
20435
20436
20437
20438
20439
20440
20441
20442
20443
20444
20445
20446
20447
20448
20449
20450
20451
20452
20453
20454
20455
20456
20457
20458
20459
20460
20461
20462
20463
20464
20465
20466
20467
20468
20469
20470
20471
20472
20473
20474
20475
20476
20477
20478
20479
20480
20481
20482
20483
20484
20485
20486
20487
20488
20489
20490
20491
20492
20493
20494
20495
20496
20497
20498
20499
20500
20501
20502
20503
20504
20505
20506
20507
20508
20509
20510
20511
20512
20513
20514
20515
20516
20517
20518
20519
20520
20521
20522
20523
20524
20525
20526
20527
20528
20529
20530
20531
20532
20533
20534
20535
20536
20537
20538
20539
20540
20541
20542
20543
20544
20545
20546
20547
20548
20549
20550
20551
20552
20553
20554
20555
20556
20557
20558
20559
20560
20561
20562
20563
20564
20565
20566
20567
20568
20569
20570
20571
20572
20573
20574
20575
20576
20577
20578
20579
20580
20581
20582
20583
20584
20585
20586
20587
20588
20589
20590
20591
20592
20593
20594
20595
20596
20597
20598
20599
20600
20601
20602
20603
20604
20605
20606
20607
20608
20609
20610
20611
20612
20613
20614
20615
20616
20617
20618
20619
20620
20621
20622
20623
20624
20625
20626
20627
20628
20629
20630
20631
20632
20633
20634
20635
20636
20637
20638
20639
20640
20641
20642
20643
20644
20645
20646
20647
20648
20649
20650
20651
20652
20653
20654
20655
20656
20657
20658
20659
20660
20661
20662
20663
20664
20665
20666
20667
20668
20669
20670
20671
20672
20673
20674
20675
20676
20677
20678
20679
20680
20681
20682
20683
20684
20685
20686
20687
20688
20689
20690
20691
20692
20693
20694
20695
20696
20697
20698
20699
20700
20701
20702
20703
20704
20705
20706
20707
20708
20709
20710
20711
20712
20713
20714
20715
20716
20717
20718
20719
20720
20721
20722
20723
20724
20725
20726
20727
20728
20729
20730
20731
20732
20733
20734
20735
20736
20737
20738
20739
20740
20741
20742
20743
20744
20745
20746
20747
20748
20749
20750
20751
20752
20753
20754
20755
20756
20757
20758
20759
20760
20761
20762
20763
20764
20765
20766
20767
20768
20769
20770
20771
20772
20773
20774
20775
20776
20777
20778
20779
20780
20781
20782
20783
20784
20785
20786
20787
20788
20789
20790
20791
20792
20793
20794
20795
20796
20797
20798
20799
20800
20801
20802
20803
20804
20805
20806
20807
20808
20809
20810
20811
20812
20813
20814
20815
20816
20817
20818
20819
20820
20821
20822
20823
20824
20825
20826
20827
20828
20829
20830
20831
20832
20833
20834
20835
20836
20837
20838
20839
20840
20841
20842
20843
20844
20845
20846
20847
20848
20849
20850
20851
20852
20853
20854
20855
20856
20857
20858
20859
20860
20861
20862
20863
20864
20865
20866
20867
20868
20869
20870
20871
20872
20873
20874
20875
20876
20877
20878
20879
20880
20881
20882
20883
20884
20885
20886
20887
20888
20889
20890
20891
20892
20893
20894
20895
20896
20897
20898
20899
20900
20901
20902
20903
20904
20905
20906
20907
20908
20909
20910
20911
20912
20913
20914
20915
20916
20917
20918
20919
20920
20921
20922
20923
20924
20925
20926
20927
20928
20929
20930
20931
20932
20933
20934
20935
20936
20937
20938
20939
20940
20941
20942
20943
20944
20945
20946
20947
20948
20949
20950
20951
20952
20953
20954
20955
20956
20957
20958
20959
20960
20961
20962
20963
20964
20965
20966
20967
20968
20969
20970
20971
20972
20973
20974
20975
20976
20977
20978
20979
20980
20981
20982
20983
20984
20985
20986
20987
20988
20989
20990
20991
20992
20993
20994
20995
20996
20997
20998
20999
21000
21001
21002
21003
21004
21005
21006
21007
21008
21009
21010
21011
21012
21013
21014
21015
21016
21017
21018
21019
21020
21021
21022
21023
21024
21025
21026
21027
21028
21029
21030
21031
21032
21033
21034
21035
21036
21037
21038
21039
21040
21041
21042
21043
21044
21045
21046
21047
21048
21049
21050
21051
21052
21053
21054
21055
21056
21057
21058
21059
21060
21061
21062
21063
21064
21065
21066
21067
21068
21069
21070
21071
21072
21073
21074
21075
21076
21077
21078
21079
21080
21081
21082
21083
21084
21085
21086
21087
21088
21089
21090
21091
21092
21093
21094
21095
21096
21097
21098
21099
21100
21101
21102
21103
21104
21105
21106
21107
21108
21109
21110
21111
21112
21113
21114
21115
21116
21117
21118
21119
21120
21121
21122
21123
21124
21125
21126
21127
21128
21129
21130
21131
21132
21133
21134
21135
21136
21137
21138
21139
21140
21141
21142
21143
21144
21145
21146
21147
21148
21149
21150
21151
21152
21153
21154
21155
21156
21157
21158
21159
21160
21161
21162
21163
21164
21165
21166
21167
21168
21169
21170
21171
21172
21173
21174
21175
21176
21177
21178
21179
21180
21181
21182
21183
21184
21185
21186
21187
21188
21189
21190
21191
21192
21193
21194
21195
21196
21197
21198
21199
21200
21201
21202
21203
21204
21205
21206
21207
21208
21209
21210
21211
21212
21213
21214
21215
21216
21217
21218
21219
21220
21221
21222
21223
21224
21225
21226
21227
21228
21229
21230
21231
21232
21233
21234
21235
21236
21237
21238
21239
21240
21241
21242
21243
21244
21245
21246
21247
21248
21249
21250
21251
21252
21253
21254
21255
21256
21257
21258
21259
21260
21261
21262
21263
21264
21265
21266
21267
21268
21269
21270
21271
21272
21273
21274
21275
21276
21277
21278
21279
21280
21281
21282
21283
21284
21285
21286
21287
21288
21289
21290
21291
21292
21293
21294
21295
21296
21297
21298
21299
21300
21301
21302
21303
21304
21305
21306
21307
21308
21309
21310
21311
21312
21313
21314
21315
21316
21317
21318
21319
21320
21321
21322
21323
21324
21325
21326
21327
21328
21329
21330
21331
21332
21333
21334
21335

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
    "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">

 <html xmlns="http://www.w3.org/1999/xhtml"
 xml:lang="en" lang="en">

<head>
 <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />

 <!--The following viewport code is important.-->
 <meta name="viewport" content="width=device-width,
 initial-scale=1" /><!--Helps display html correctly
 in mobile devices. Chrome android and Foxfire android
 both malfunction without it.-->

 <meta http-equiv="Content-Style-Type" content="text/css" />

 <title>
 Passages from the Life of a Philosopher;
 by Charles Babbage;
 a Project Gutenberg ebook.
 </title>

 <link rel="coverpage" href="images/cover.jpg" />

 <style type="text/css">

/*== CSS VERSION 20180615 ==*/

body {
 margin: 0.5em 2.5em 0.5em 0.5em;
 padding: 0;
 line-height: 1.5;
 font-size: 120%;
}

/*== resets and basics ==*/
a,
div,
h1,
h2,
img,
p,
span {
 margin: 0;
 padding: 0;
 text-indent: 0;
}
.section,
h1,
h2 {
 page-break-before: always;
}
.section {
 margin: 0 auto;
 max-width: 32em;
 clear: both;
}
#dcoverpage {
 max-width: 28em;
 margin: 0 auto;
}
div,
p {
 max-height: 100%;
}
p {
 text-indent: 1.5em;
 text-align: justify;
}
.pfirst,
.pcenter,
.pcontinue,
.pright,
.psignature,
.pcompclose {
 text-indent: 0;
}
.fsz3 {
 font-size: 1.5em;
}
.fsz4 {
 font-size: 1.28em;
}
.fsz6 {
 font-size: 0.94em;
}
.fsz7 {
 font-size: 0.78em;
}
.fsz8 {
 font-size: 0.68em;
}
.fsz9 {
 font-size: 0.57em;
}
div {
 text-align: center;
}
#dtransnote {
 padding: 0.2em;
 margin: 3em auto;
 max-width: 41.7em;
 border: #865 medium solid;
 background-color: #fffcf2;
 font-size: 0.76em;
 page-break-before: always;
}
.phanga {
 padding-left: 1.5em;
 text-indent: -1.5em;
 text-align: justify;
}
.psignature {
 padding-right: 1em;
}
.pcompclose {
 padding-right: 3em;
}
.padtopa {
 padding-top: 1.50em;
}
.padtopb {
 padding-top: 0.75em;
}
.padtopc {
 padding-top: 0.38em;
}
.pcompclose,
.pright,
.psignature {
 text-align: right;
}
.dftnt {  /*== footnotes ==*/
 font-size: 0.76em;
 margin: 0.48em 0 0.68em 4.05em;
 padding: 0.2em;
 border-top: medium #ccc solid;
 line-height: 1.25;
 page-break-before: auto;
 page-break-inside: avoid;
}
#h1herein {
 font-size: 1em;
 font-weight: normal;
 max-width: 16em;
 min-width:  5em;
 text-align: left;
 letter-spacing: 0.20em;
 page-break-before: avoid;
 margin: 5em auto 2em auto;
}
.h2herein {
 font-size: 1.32em;
 text-align: center;
 font-weight: normal;
 padding: 3em 0 0.5em 0;
 letter-spacing: 0.05em;
 page-break-before: avoid;
}
.hsmall,
.hsmaller {
 font-size: 0.76em;
 display: block;
 text-align: center;
}
.hsmaller {
 font-size: 0.56em;
}
.h3herein {
 margin: 1em 9.4% 0 9.4%;
 padding: 0;
 font-size: 1em;
 text-align: center;
 font-weight: normal;
 page-break-before: avoid;
}
.pcenter {
 text-align: center;
}

/* === images === */
img {
 width: 100%;
 height: auto;
}
.iglyph-a {
 height: 1.15em;
 width: auto;
 vertical-align: -0.25em;
}
.dctr01,
#dctr02 {
 clear: both;
 page-break-inside: avoid;
 page-break-before: auto;
}
.dctr01 {
 margin: 0.2em 0;
}
#dctr02 {
 margin: 0 7%;
}

/*===floats===*/
.dfloatright {
 float: right;
}
.dfloatright {
 margin: 0 0 0 0.5em;
 clear: both;
}
.clearfix {
 clear: both;
}

/* === links === */
a {
 color: #20c;
 font-weight: normal;
 text-decoration: underline;
}
.afnanc,
.afnlabel {
 text-decoration: none;
}
.afnanc {
 vertical-align: top;
 font-size: 0.76em;
 line-height: 1;
}

/* === lists === */
ul {
 list-style-type: none;
 margin: 0.5em 0 0.5em 1.5em;
 padding: 0;
 text-align: left;
}
li {
 margin: 0;
 padding: 0 0 0 1.5em;
 text-indent: -1.5em;
 text-align: left;
}
.ulindenta {
 margin: 0.5em 0 0.5em 3em;
}
.li0 {
 padding: 0;
 text-indent: 0;
}
#ulp276 {
 margin: -1em 0 0.5em -1.72em;
 font-size: 0.87em;
}
.ullha {
 line-height: 1.1;
 margin: 0 0 0 1.5em;
}
.ulp338a {
 line-height: 1.1;
 margin: 0.5em 0;
 page-break-before: auto;
 page-break-inside: avoid;
}
#ulp338b {
 margin-top: 0;
}
#ulp416 {
 margin-left: 0;
}

/* === tables === */
table {
 padding: 0;
 margin: 0;
 border-collapse: separate; /*workaround for ADE bug*/
 border-spacing: 0;
 line-height: 1.1;
}
th {
 text-align: center;
 vertical-align: top;
 padding: 0.2em 0.3em;
 font-weight: normal;
}
td {
 vertical-align: bottom;
 padding: 0.2em 0.5em;
}
.tdleft {
 text-align: left;
 padding-left: 1.5em;
 text-indent: -1em;
}
.tdleftina {
 text-align: left;
 padding-left: 2em;
 text-indent: -1em;
}
.tdpright {
 text-align: right;
 text-indent: 0;
}
.dkeeptgth {
 page-break-before: auto;
 page-break-inside: avoid;
}
.tdcntr {
 text-align: center;
}
.dtablebox {
 margin: 0.5em 0 0.5em 3em;
 page-break-before: auto;
 page-break-inside: avoid;
}
.thcntr {
 border: thin gray solid;
 width: 20%;
}
.borall {
 border: thin gray solid;
}
.borbblk {
 border-bottom: medium black solid;
}
.tdmid {
 vertical-align: middle;
}
.bor13 {
 border-top: thin gray solid;
 border-bottom: thin gray solid;
}
.bor10 {
 border-top: thin gray solid;
}

/*== small caps ==*/
.smcap {
 display: inline-block;
}
.smcap,
.smmaj {
 font-style: normal;
 text-transform: uppercase;
 letter-spacing: 0.05em;
}
b {
 font-weight: normal;
 margin: 0;
 padding: 0;
 text-indent: 0;
}
b,
.smmaj {
 font-size: 0.72em;
}

/* ==poetry== */
.dpoemctr {
 margin: 0.38em 0;
}
.dstanzactr,
.dstanzalft {
 page-break-inside: avoid;
 page-break-before: auto;
}
.dstanzactr {
 display: inline-block;
 margin: 0.5em 0;
}
.dpp00,
.dpp01,
.dpp08 {
 display: block;
 text-align: left;
 padding-left: 3em;
 margin-left: 0.6em; /*==to allow for quotation mark outdents==*/
}
.dquoteverse {
 display: block;
 padding-left: 3.6em;
 text-indent: -3.6em;
 text-align: left;
 margin-left: 0;
}
.dquoteverse1 {
 display: block;
 padding-left: 3.6em;
 text-indent: -2.6em;
 text-align: left;
 margin-left: 0;
}
.spquotebox {
 display: inline-block;
 width: 0.6em;
 text-align: right;
}
.dpp00 {
 text-indent: -3em;
}
.dpp01 {
 text-indent: -2em;
}
.dpp08 {
 text-indent: 5em;
}
.dpoemcite {
 display: block;
 padding-right: 5em;
 text-align: right;
 margin-top: -0.2em;
}

/* === miscellaneous === */
sub,
sup {
 margin: 0;
 padding: 0;
 text-indent: 0;
 line-height: 1;
 font-size: 0.87em;
}
sup {
 vertical-align: super;
}
sub {
 vertical-align: sub;
}
i {
 font-style: italic;
}
.dblockquote {
 line-height: 1.25;
 margin: 0.5em 0 0.5em 0;
 border-left: medium #aaa solid;
 padding-left: 0.5em;
}
.depigram {
 margin: 0.5em 0 0.5em 0.22em;
 font-size: 0.87em;
 line-height: 1.1;
 margin: 0 1.5em;
}
.nowrap {
 display: inline-block;
}
.xxpn {
 position: absolute;
 right: 0;
 line-height: 1.81; /*assumes lh of container is 1.3*/
}
.xxpn {
 font-size: 0.68em;
 font-style: normal;
 font-weight: normal;
 color: #aaa;
 text-decoration: none;
}
.hrblk {
 margin: 0.7em 50%;
 border: thin white solid;
}
.hr10 {
 margin: 0.7em 45%;
 border: thin black solid;
}
.hr20 {
 margin: 0.25em 40%;
 border: thin black solid;
}
#idp-ii {
 margin: 0 8%;
 font-size: 0.76em;
 line-height: 1.1;
}
#idul-ii {
 display: inline-block;
 font-size: 0.76em;
 line-height: 1.1;
}
#p-iiia {
 display: block;
 line-height: 1;
 text-align: justify;
 font-size: 0.56em;
 max-width: 90%;
 margin: 0.5em auto 0 auto;
 letter-spacing: 0.1em;
}
#p-iiic {
 line-height: 1.1;
 max-width: 90%;
 margin: 0 auto 0 auto;
 font-size: 0.66em;
}
#idp-v {
 text-align: right;
 padding-right: 3em;
}
#ulp-ix {
 max-width: 26em;
 min-width: 5em;
 margin: 0 auto;
 font-size: 0.87em;
}
.ptoc {
 text-align: right;
 margin: 0.33em 0;
 line-height: 1.2;
 text-indent: 0;
}
.dsynopsis {
 font-size: 0.76em;
 text-align: justify;
 margin: 0.5em 1.97em;
}
.dsdnote {
 font-size:   0.76em;
 text-align:  right;
 clear:       left;
 line-height: 1.97;
}
.sppla {
 padding-left: 2em;
}
#idth-52 {
 text-align: justify;
}
#spp58 {
 color: white;
 background-color: white;
 visibility: hidden;
}
.tafmono {
 font-family: monospace;
}
#pp131 {
 font-size: 0.76em;
 text-indent: 0;
 line-height: 1;
 margin-left: -1em;
}
.pina {
 padding-left: 1.5em;
}
.pinb {
 padding-left: 3em;
}
.dp139 {
 display: inline-block;
 max-width: 16em;
 text-align: right;
 line-height: 1.1;
 margin-top: 0.2em;
 margin-bottom: 0.2em;
}
.pscenea {
 margin: 1em 0 0.5em 0;
 padding-left: 1.5em;
 text-indent: -1.5em;
 line-height: 1.1;
}
.psceneb {
 margin: 1em 0 0.5em 0;
 line-height: 1.1;
 text-align: center;
}
.stgdira {
 float: right;
}
.sppunlist {
 display: inline-block;
 line-height: 1.1;
 vertical-align: middle;
 text-align: left;
 padding-left: 0.3em;
 padding-right: 0.3em;
}
.spblk {
 display: block;
}
#p493 {
 font-size: 0.87em;
 max-width: 36.8em;
}
#dp493a {
 font-size: 0.87em;
 margin-left: 5.2em;
 text-indent: -1.7em;
 text-align: left;
}
.pp494a {
 font-size: 0.87em;
 text-indent: -1.72em;
 line-height: 1.72;
 margin-left: 1.72em;
 padding-left: 1.72em;
}

/* === handheld === */
@media handheld {
 .xxpn {
  position: static;
  padding-top: 0.72em;
  padding-left: 0.5em;
  line-height: inherit;
  font-size: 0.57em;
 }
 body {
   margin: 0.5em;
   padding: 0;
   font-size: 100%;
 }
 div,
 p {
   max-height: none;
 }
 .dfloatright,
 .stgdira,
 .xxpn {
   float: right;
 }
}
</style>
</head>
<body>


<div>*** START OF THE PROJECT GUTENBERG EBOOK 57532 ***</div>


<div id="dcoverpage"><img id="coverpage" src="images/cover.jpg"
width="600" height="800" alt="" /></div>

<div class="section">
<h1 id="h1herein">PASSAGES
FROM THE LIFE OF A PHILOSOPHER, by Charles Babbage</h1>
</div>

<div class="section">
<div id="dctr02"><img src="images/i-ii.jpg"
width="800" height="1058" alt="" />
<div class="fsz9 pright"><i>B. H. Babbage, del.</i></div>

<p id="idp-ii">Impression from a woodcut of a small portion of Mr. Babbage’s Difference
Engine No. 1, the property of Government, at present deposited in the Museum
at South Kensington.</p>

<ul id="idul-ii">
<li>It was commenced 1823.</li>
<li>This portion put together 1833.</li>
<li>The construction abandoned 1842.</li>
<li>This plate was printed June, 1853.</li>
<li>This portion was in the Exhibition 1862.</li>
</ul></div><!--dctr02--></div><!--section-->

<div class="section padtopa">
<div class="fsz4">PASSAGES<br />

<span class="fsz9">FROM</span><br />

<span class="fsz3">THE LIFE OF A PHILOSOPHER.</span><br />
<span class="fsz9">BY</span><br />
<span class="fsz4">CHARLES BABBAGE, ESQ., M.A.,</span><br />

<span id="p-iiia">F.R.S., F.R.S.E., F.R.A.S., F. STAT. S., HON.
M.R.I.A., M.C.P.S.,
<span class="fsz4">COMMANDER OF THE ITALIAN ORDER OF ST. MAURICE AND
ST. LAZARUS,</span>
INST. IMP. (ACAD. MORAL.) PARIS CORR., ACAD. AMER. ART.
ET SC. BOSTON, REG. ŒCON. BORUSS., PHYS. HIST. NAT. GENEV., ACAD. REG.
MONAC., HAFN., MASSIL., ET DIVION., SOCIUS. ACAD. IMP. ET REG. PETROP.,
NEAP., BRUX., PATAV., GEORG. FLOREN, LYNCEI ROM., MUT., PHILOMATH.
PARIS, SOC. CORR., ETC.</span></div>

<div class="dpoemctr padtopa fsz7"><div class="dstanzactr">
<div class="dquoteverse"><span class="spquotebox">“</span>I’m
 a phi­los­o­pher. Confound them all—</div>
<div class="dpp00">Birds, beasts, and men; but no, not
womankind.”—<i>Don Juan.</i></div></div></div>

<p id="p-iiic">“I now gave my mind to philosophy: the great object of my ambition
was to make out a complete system of the universe, including and
comprehending the origin, causes, consequences, and termination of all
things. Instead of countenance, encouragement, and applause, which
I should have received from every one who has the true dignity of
an oyster at heart, I was exposed to calumny and misrep­re­sen­ta­tion.
While engaged in my great work on the universe, some even went
so far as to accuse me of infidelity;—such is the malignity of
oysters.”—<i>“Autobiography of an Oyster” deciphered by the aid of
photography in the shell of a phi­los­o­pher of that race,—recently
scolloped.</i></p>

<div class="fsz6 padtopa">LONDON:</div>

<div class="fsz6">LONGMAN, GREEN, LONGMAN, ROBERTS, &amp; GREEN.</div>

<div class="fsz6">1864.</div>

<div class="fsz9 padtopa">[<i>The right of Translation is reserved.</i>]</div>
</div><!--section-->

<div class="section">
<h2 class="h2herein">DEDICATION.</h2>

<hr class="hr20" />

<div class="padtopb">TO VICTOR EMMANUEL II., KING OF ITALY.</div>

<p class="pfirst"><span class="smcap">S<b>IRE</b>,</span></p>

<p><span class="smcap">I<b>N</b></span>
dedicating this volume to your Majesty, I am also
doing an act of justice to the memory of your illustrious
father.</p>

<p>In 1840, the King, Charles Albert, invited the learned of
Italy to assemble in his capital. At the request of her most
gifted Analyst, I brought with me the drawings and explanations
of the Analytical Engine. These were thoroughly
examined and their truth acknowledged by Italy’s choicest
sons.</p>

<p>To the King, your father, I am indebted for the first public
and official acknowledgment of this invention.</p>

<p>I am happy in thus expressing my deep sense of that obligation
to his son, the Sovereign of united Italy, the country
of Archimedes and of Galileo.</p>

<div class="padtopc">
I am, Sire,<br />
With the highest respect,</div>
<div id="idp-v">Your Majesty’s faithful Servant,</div>

<div class="psignature padtopc">CHARLES BABBAGE.</div>
</div><!--section-->

<div class="section">
<h2 class="h2herein">PREFACE.</h2>

<hr class="hr10" />

<p class="pfirst padtopb"><span class="smcap">S<b>OME</b></span>
men write their lives to save themselves from <i>ennui</i>,
careless of the amount they inflict on their readers.</p>

<p>Others write their personal history, lest some kind friend
should survive them, and, in showing off his own talent, unwittingly
show them up.</p>

<p>Others, again, write their own life from a different motive—from
fear that the vampires of literature might make it
their prey.</p>

<p>I have frequently had applications to write my life, both
from my countrymen and from foreigners. Some caterers
for the public offered to pay me for it. Others required that
I should pay them for its insertion; others offered to insert
it without charge. One proposed to give me a quarter of a
column gratis, and as many additional lines of eloge as I
chose to write and pay for at ten-pence per line. To many
of these I sent a list of my works, with the remark that
they formed the best life of an author; but nobody cared to
insert them.</p>

<p>I have no desire to write my own biography, as long as I
have strength and means to do better work.</p>

<p>The remarkable circumstances attending those Calculating
Machines, on which I have spent so large a portion of my
life, make me wish to place on record some account of their
past history. As, however, such a work would be utterly
uninteresting to the greater part of my countrymen, I thought
it might be rendered less unpalatable by relating some of my
experience amongst various classes of society, widely differing
from each other, in which I have oc­ca­sion­al­ly mixed.</p>

<p>This volume does not aspire to the name of an autobiography.
It relates a variety of isolated circumstances in
which I have taken part—some of them arranged in the
order of time, and others grouped together in separate chapters,
from similarity of subject.</p>

<p>The selection has been made in some cases from the importance
of the matter. In others, from the celebrity of the
persons concerned; whilst several of them furnish interesting
illustrations of human character.</p>
</div><!--section-->

<div class="section">
<h2 class="h2herein">CONTENTS.</h2>

<ul id="ulp-ix">
<li class="li0">
<p class="ptoc">I. • My Ancestors&nbsp;•&nbsp;&#x2007;&#x2007;<a
href="#p001" title="go to pag&#x65; 1">1</a></p></li>

<li class="li0">
<p class="ptoc">II. • Childhood&nbsp;•&nbsp;&#x2007;&#x2007;<a
href="#p007" title="go to pag&#x65; 7">7</a></p></li>

<li class="li0">
<p class="ptoc">III. • Boyhood&nbsp;•&nbsp;&#x2007;<a
href="#p017" title="go to pag&#x65; 17">17</a></p></li>

<li class="li0">
<p class="ptoc">IV. • Cambridge&nbsp;•&nbsp;&#x2007;<a
href="#p025" title="go to pag&#x65; 25">25</a></p></li>

<li class="li0">
<p class="ptoc">V. • Difference Engine No. 1&nbsp;•&nbsp;&#x2007;<a
href="#p041" title="go to pag&#x65; 41">41</a></p></li>

<li class="li0">
<p class="ptoc">VI. • Statement relative to the Difference
Engine, drawn up by the late Sir H. Nicolas
from the Author’s Papers&nbsp;•&nbsp;&#x2007;<a
href="#p068" title="go to pag&#x65; 68">68</a></p></li>

<li class="li0">
<p class="ptoc">VII. • Difference Engine No. 2&nbsp;•&nbsp;&#x2007;<a
href="#p097" title="go to pag&#x65; 97">97</a></p></li>

<li class="li0">
<p class="ptoc">VIII. • Of the Analytical Engine&nbsp;•&nbsp;<a
href="#p112" title="go to pag&#x65; 112">112</a></p></li>

<li class="li0">
<p class="ptoc">IX. • Of the Mechanical Notation&nbsp;•&nbsp;<a
href="#p142" title="go to pag&#x65; 142">142</a></p></li>

<li class="li0">
<p class="ptoc">X. • The Exhibition of 1862&nbsp;•&nbsp;<a
href="#p147" title="go to pag&#x65; 147">147</a></p></li>

<li class="li0">
<p class="ptoc">XI. • The late Prince Consort&nbsp;•&nbsp;<a
href="#p168" title="go to pag&#x65; 168">168</a></p></li>

<li class="li0">
<p class="ptoc">XII. • Recollections of the Duke of
Wellington&nbsp;•&nbsp;<a
href="#p173" title="go to pag&#x65; 173">173</a></p></li>

<li class="li0">
<p class="ptoc">XIII. • Recollections of Wollaston, Davy,
and Rogers&nbsp;•&nbsp;<a
href="#p186" title="go to pag&#x65; 186">186</a></p></li>

<li class="li0">
<p class="ptoc">XIV. • Recollections of Laplace, Biot, and
Humboldt&nbsp;•&nbsp;<a
href="#p195" title="go to pag&#x65; 195">195</a></p></li>

<li class="li0">
<p class="ptoc">XV. • Experience by Water&nbsp;•&nbsp;<a
href="#p205" title="go to pag&#x65; 205">205</a></p></li>

<li class="li0">
<p class="ptoc">XVI. • Experience by Fire&nbsp;•&nbsp;<a
href="#p213" title="go to pag&#x65; 213">213</a></p></li>

<li class="li0">
<p class="ptoc">XVII. • Experience amongst Workmen&nbsp;•&nbsp;<a
href="#p228" title="go to pag&#x65; 228">228</a></p></li>

<li class="li0">
<p class="ptoc">XVIII. • Picking Locks and Deciphering&nbsp;•&nbsp;<a
href="#p233" title="go to pag&#x65; 233">233</a></p></li>

<li class="li0">
<p class="ptoc">XIX. • Experience in St. Giles’s&nbsp;•&nbsp;<a
href="#p242" title="go to pag&#x65; 242">242</a></p></li>

<li class="li0">
<p class="ptoc">XX. • Theatrical Experience&nbsp;•&nbsp;<a
href="#p251" title="go to pag&#x65; 251">251</a></p></li>

<li class="li0">
<p class="ptoc">XXI. • Electioneering Experience&nbsp;•&nbsp;<a
href="#p259" title="go to pag&#x65; 259">259</a></p></li>

<li class="li0">
<p class="ptoc">XXII. • Scene from a New After-Piece&nbsp;•&nbsp;<a
href="#p276" title="go to pag&#x65; 276">276</a></p></li>

<li class="li0">
<p class="ptoc">XXIII. • Experience at Courts&nbsp;•&nbsp;<a
href="#p292" title="go to pag&#x65; 292">292</a></p></li>

<li class="li0">
<p class="ptoc">XXIV. • Experience at Courts&nbsp;•&nbsp;<a
href="#p298" title="go to pag&#x65; 298">298</a></p></li>

<li class="li0">
<p class="ptoc">XXV. • Railways&nbsp;•&nbsp;<a
href="#p313" title="go to pag&#x65; 313">313</a></p></li>

<li class="li0">
<p class="ptoc">XXVI. • Street Nuisances&nbsp;•&nbsp;<a
href="#p337" title="go to pag&#x65; 337">337</a></p></li>

<li class="li0">
<p class="ptoc">XXVII. • Wit&nbsp;•&nbsp;<a
href="#p363" title="go to pag&#x65; 363">363</a></p></li>

<li class="li0">
<p class="ptoc">XXVIII. • Hints for Travellers&nbsp;•&nbsp;<a
href="#p371" title="go to pag&#x65; 371">371</a></p></li>

<li class="li0">
<p class="ptoc">XXIX. • Miracles&nbsp;•&nbsp;<a
href="#p387" title="go to pag&#x65; 387">387</a></p></li>

<li class="li0">
<p class="ptoc">XXX. • Religion&nbsp;•&nbsp;<a
href="#p396" title="go to pag&#x65; 396">396</a></p></li>

<li class="li0">
<p class="ptoc">XXXI. • A Vision&nbsp;•&nbsp;<a
href="#p406" title="go to pag&#x65; 406">406</a></p></li>

<li class="li0">
<p class="ptoc">XXXII. • Various Reminiscences&nbsp;•&nbsp;<a
href="#p421" title="go to pag&#x65; 421">421</a></p></li>

<li class="li0">
<p class="ptoc">XXXIII. • The Author’s Cont­ri­bu­tions to
Human Knowledge&nbsp;•&nbsp;<a
href="#p430" title="go to pag&#x65; 430">430</a></p></li>

<li class="li0">
<p class="ptoc">XXXIV. • The Author’s further Cont­ri­bu­tions
to Human Knowledge&nbsp;•&nbsp;<a
href="#p441" title="go to pag&#x65; 441">441</a></p></li>

<li class="li0">
<p class="ptoc">XXXV. • Results of Science&nbsp;•&nbsp;<a
href="#p473" title="go to pag&#x65; 473">473</a></p></li>

<li class="li0">
<p class="ptoc">
XXXVI. • Agreeable Recollections&nbsp;•&nbsp;<a
href="#p482" title="go to pag&#x65; 482">482</a></p>
<hr class="hr10" /></li>

<li class="li0">
<p class="ptoc">
Appendix&nbsp;•&nbsp;<a
href="#p487" title="go to pag&#x65; 487">487</a></p></li>
</ul></div><!--section-->

<div class="section" id="p001">
<div class="padtopa">PASSAGES FROM THE LIFE OF A PHILOSOPHER.</div>

<h2 class="h2herein">CHAPTER I.
<span class="hsmall">MY ANCESTORS.</span></h2>

<hr class="hr20" />

<div class="dpoemctr fsz7"><div class="dstanzactr">
<div class="dpp00">Traced his descent, through ages dark,</div>
<div class="dpp00">From cats that caterwauled in Noah’s ark.</div></div>
<div class="dpoemcite"><span class="smcap">S<b>ALMAGUNDI</b>,</span>
 4to, 1793.</div></div>
<hr class="hr20" />

<div class="dsynopsis">
Value of a celebrated Name&#x200a;—&#x200a;My
Ancestors&#x200a;—&#x200a;Their Ante-Mosaic
origin&#x200a;—&#x200a;Flint-workers&#x200a;—&#x200a;Tool-makers&#x200a;—&#x200a;Not
descended from Cain&#x200a;—&#x200a;Ought a Phi­los­o­pher
to avow it if he were?&#x200a;—&#x200a;Probability of
Descent from Tubal Cain&#x200a;—&#x200a;Argument in favour,
he worked in Iron&#x200a;—&#x200a;On the other side, he
invented Organs&#x200a;—&#x200a;Possible origin of my
Name&#x200a;—&#x200a;Family History in very recent times.</div>

<p class="pfirst"><span class="smcap">W<b>HAT</b></span>
is there in a name? It is merely an empty basket,
until you put something into it. My earliest visit to the
Continent taught me the value of such a basket, filled with
the name of my venerable friend the first Herschel, ere yet
my younger friend his son, had adorned his distinguished
patronymic with the additional laurels of his own well-earned
fame.</p>

<p>The inheritance of a celebrated name is not, however,
without its disadvantages. This truth I never found more
fully appreciated, nor more admirably expressed, than in a
conversation with the son of Filangieri, the
author of the <span class="xxpn" id="p002">{2}</span>
celebrated Treatise on Legislation, with whom I became acquainted
at Naples, and in whose company I visited several
of the most interesting institutions of that capital.</p>

<p>In the course of one of our drives, I alluded to the advantages
of inheriting a distinguished name, as in the case of
the second Herschel. His remark was, “For my own part,
I think it a great disadvantage. Such a man must feel in
the position of one inheriting a vast estate, so deeply
mortgaged that he can never hope, by any efforts of his
own, to redeem it.”</p>

<p>Without reverting to the philosophic, but unromantic,
views of our origin taken by Darwin, I shall pass over the
long history of our progress from a monad up to man, and
commence tracing my ancestry as the world generally do:
namely, as soon as there is the slightest ground for conjecture.
Although I have contended for the Mosaic date of the
creation of man as long as I decently could, and have even
endeavoured to explain away<a class="afnanc" href="#fn1" id="fnanc1">1</a>
some of the facts relied upon
to prove man’s long anterior origin; yet I must admit that the
continual accumulation of evidence probably will, at last,
compel me to acknowledge that, in this single instance,
the writings of Moses may have been misapprehended.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc1" id="fn1">1</a>
On the remains of human art, mixed with the bones of
extinct races of animals. Proceedings of the Royal Society, 26th May,
1859.</p></div>

<div class="dsdnote">〈DESCENT FROM FLINT-WORKERS.〉</div>

<p>Let us, therefore, take for granted that man and certain
extinct races of animals lived together, thousands of years
before Adam. We find, at that period, a race who formed
knives, and hammers, and arrow-heads out of flint. Now,
considering my own inveterate habit of contriving <i>tools</i>, it is
more probable that I should derive my passion by hereditary
transmission from these original tool-makers, than from any
other inferior race existing
at that period. <span class="xxpn" id="p003">{3}</span></p>

<p>Many years ago I met a very agreeable party at Mr. Rogers’
table. Somebody introduced the subject of ancestry. I remarked
that most people are reluctant to acknowledge as
their father or grandfather, any person who had committed a
dishonest action or a crime. But that no one ever scrupled
to be proud of a remote ancestor, even though he might have
been a thief or a murderer. Various remarks were made,
and reasons assigned, for this tendency of the educated mind.
I then turned to my next neighbour, Sir Robert H. Inglis, and
asked him what he would do, supposing he possessed undoubted
documents, that he was lineally descended from Cain.</p>

<p>Sir Robert said he was at that moment proposing to himself
the very same question. After some consideration, he
said he should burn them; and then inquired what I should
do in the same circumstances. My reply was, that I should
preserve them: but simply because I thought the preservation
of any <i>fact</i> might ultimately be useful.</p>

<div class="dsdnote">〈NOT THROUGH CAIN.〉</div>

<p>I possess no evidence that I am descended from Cain. If
any herald suppose that there may be such a presumption, I
think it must arise from his confounding Cain with Tubal
Cain, who was a great worker in iron. Still, however he
might argue that, the probabilities are in favour of his
opinion: for I, too, work in iron. But a friend of mine, to
whose kind criticisms I am much indebted, suggests that as
Tubal Cain invented the <i>Organ</i>, this probability is opposed
to the former one.</p>

<p>The next step in my pedigree is to determine whence the
origin of my modern family name.</p>

<p>Some have supposed it to be derived from the cry of sheep.
If so, that would point to a descent from the Shepherd Kings.
Others have supposed it is derived from the name of a place
called Bab or Babb, as we have, in the West
of England, Bab <span class="xxpn" id="p004">{4}</span>
Tor, Babbacombe, &amp;c. But this is evidently erroneous; for,
when a people took possession of a desert country, its various
localities could possess no names; consequently, the colonists
could not take names from the country to which they
migrated, but would very naturally give their own names to
the several lands they appropriated: “<i>mais revenons à nos
moutons</i>.”</p>

<p>How my blood was trans­mit­ted to me through more
modern races, is quite immaterial, seeing the admitted antiquity
of the flint-workers.</p>

<div class="dsdnote">〈SAD OMISSION.〉</div>

<p>In recent times, that is, since the Conquest, my knowledge
of the history of my family is limited by the unfortunate
omission of my name from the roll of William’s followers.
Those who are curious about the subject, and are idlers, may,
if they think it worth while, search all the parish registers
in the West of England and elsewhere.</p>

<p>The light I can throw upon it is not great, and rests on a
few documents, and on family tradition. During the past
four generations I have no surviving collateral relatives of
my own name.</p>

<p>The name of Babbage is not uncommon in the West of
England. One day during my boyhood, I observed it over a
small grocer’s shop, whilst riding through the town of Chudley.
I dismounted, went into the shop, purchased some figs, and
found a very old man of whom I made inquiry as to his
family. He had not a good memory himself, but his wife
told me that his name was Babb when she married him, and
that it was only during the last twenty years he had adopted
the name of Babbage, which, the old man thought, sounded
better. Of course I told his wife that I entirely agreed with
her husband, and thought him a very sensible fellow.</p>

<p>The craft most frequently practised by
my ancestors seems <span class="xxpn" id="p005">{5}</span>
to have been that of a goldsmith, although several are believed
to have practised less dignified trades.</p>

<p>In the time of Henry the Eighth one of my ancestors, together
with a hundred men, were taken prisoners at the
siege of Calais.</p>

<p>When William the Third landed in Torbay, another ancestor
of mine, a yeoman possessing some small estate, undertook
to distribute his proclamations. For this bit of high
treason he was rewarded with a silver medal, which I well
remember seeing, when I was a boy. It had descended to a
very venerable and truthful old lady, an unmarried aunt, the
historian of our family, on whose authority the identity of
the medal I saw with that given by King William must rest.</p>

<p>Another ancestor married one of two daughters, the
only children of a wealthy physician, Dr. Burthogge, an intimate
friend and cor­res­pon­dent of John Locke.</p>

<div class="dsdnote">〈A WILD ANCESTOR.〉</div>

<p>Somewhere about 1700 a member of my family, one
Richard Babbage, who appears to have been a very wild
fellow, having tried his hand at various trades, and given
them all up, offended a wealthy relative.</p>

<p>To punish this idleness, his relative entailed all his large
estates upon eleven different people, after whom he gave it to
this Richard Babbage, who, had there been no entail, would
have taken them as heir-at-law.</p>

<p>Ten of these lives had dropped, and the eleventh was in a
consumption, when Richard Babbage took it into his head to
go off to America with Bamfylde Moore Carew, the King of
the Beggars.</p>

<p>The last only of the eleven lives existed when he embarked,
and that life expired within twelve months after
Richard Babbage sailed. The estates remained in possession
of the rep­re­sen­ta­tives of the eleventh
in the entail. <span class="xxpn" id="p006">{6}</span></p>

<p>If it could have been proved that Richard Babbage had
survived twelve months after his voyage to America, these
estates would have remained in my own branch of the
family.</p>

<p>I possess a letter from Richard Babbage, dated on board
the ship in which he sailed for America.</p>

<div class="dsdnote">〈ACT OF PARLIAMENT.〉</div>

<p>In the year 1773 it became necessary to sell a portion of
this property, for the purpose of building a church at Ashbrenton.
A private Act of Parliament was passed for that
purpose, in which the rights of the true
heir were reserved.</p>
</div><!--section-->

<div class="section" id="p007">
<h2 class="h2herein">CHAPTER II.
<span class="hsmall">CHILDHOOD.</span></h2>

<hr class="hr20" />
<div class="dpoemctr fsz7"><div class="dstanzactr">
<div class="dpp00">“The Prince of Darkness is a gentleman.”—<i>Hamlet.</i></div>
</div></div>
<hr class="hr20" />

<div class="dsynopsis">
Early Passion for inquiry and inquisition into
Toys&#x200a;—&#x200a;Lost on London Bridge&#x200a;—&#x200a;Supposed
value of the young Phi­los­o­pher&#x200a;—&#x200a;Found
again&#x200a;—&#x200a;Strange Coincidence in
after-years&#x200a;—&#x200a;Poisoned&#x200a;—&#x200a;Frightened a
Schoolfellow by a Ghost&#x200a;—&#x200a;Frightened himself by trying
to raise the Devil&#x200a;—&#x200a;Effect of Want of Occupation for
the Mind&#x200a;—&#x200a;Treasure-trove&#x200a;—&#x200a;Death and
Non-appearance of a Schoolfellow.</div>

<p class="pfirst"><span class="smcap">F<b>ROM</b></span>
my earliest years I had a great desire to inquire into
the causes of all those little things and events which astonish
the childish mind. At a later period I commenced the still
more important inquiry into those laws of thought and those
aids which assist the human mind in passing from received
knowledge to that other knowledge then unknown to our race.
I now think it fit to record some of those views to which, at
various periods of my life, my reasoning has led me. Truth
only has been the object of my search, and I am not conscious
of ever having turned aside in my inquiries from any fear
of the conclusions to which they might lead.</p>

<p>As it may be interesting to some of those who will
hereafter read these lines, I shall briefly mention a few
events of my earliest, and even of my childish years. My
parents being born at a certain period of history, and in a
certain latitude and longitude, of course
followed the religion <span class="xxpn" id="p008">{8}</span>
of their country. They brought me up in the Protestant form
of the Christian faith. My excellent mother taught me the
usual forms of my daily and nightly prayer; and neither in
my father nor my mother was there any mixture of bigotry
and intolerance on the one hand, nor on the other of that
unbecoming and familiar mode of addressing the Almighty
which afterwards so much disgusted me in my youthful years.</p>

<p>My invariable question on receiving any new toy, was
“Mamma, what is inside of it?” Until this information was
obtained those around me had no repose, and the toy itself,
I have been told, was generally broken open if the answer
did not satisfy my own little ideas of the “fitness of things.”</p>
</div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Earliest Recollections.</i></h3>

<p>Two events which impressed themselves forcibly on my
memory happened, I think, previously to my eighth year.</p>

<div class="dsdnote">〈THE YOUNG PHI­LOS­O­PHER LOST.〉</div>

<p>When about five years old, I was walking with my nurse,
who had in her arms an infant brother of mine, across London
Bridge, holding, as I thought, by her apron. I was looking
at the ships in the river. On turning round to speak to her,
I found that my nurse was not there, and that I was alone
upon London Bridge. My mother had always impressed upon
me the necessity of great caution in passing any street-crossing:
I went on, therefore, quietly until I reached Tooley Street,
where I remained watching the passing vehicles, in order to
find a safe opportunity of crossing that very busy street.</p>

<div class="dsdnote">〈THE CRI­ER OF­FERS A RE­WARD.〉</div>

<p>In the mean time the nurse, having lost one of her charges,
had gone to the crier, who proceeded immediately to call, by
the ringing of his bell, the attention of the public to the fact
that a young phi­los­o­pher was lost, and to the still more important
fact that five shillings would be the reward of his
fortunate discoverer. I well remember sitting on
the steps of <span class="xxpn" id="p009">{9}</span>
the door of the linendraper’s shop on the opposite corner of
Tooley Street, when the gold-laced crier was making proclamation
of my loss; but I was too much occupied with eating
some pears to attend to what he was saying.</p>

<p>The fact was, that one of the men in the linendraper’s
shop, observing a little child by itself, went over to it, and
asked what it wanted. Finding that it had lost its nurse,
he brought it across the street, gave it some pears, and
placed it on the steps at the door: having asked my name,
the shopkeeper found it to be that of one of his own customers.
He accordingly sent off a messenger, who announced to my
mother the finding of young Pickle before she was aware of
his loss.</p>

<p>Those who delight in observing coincidences may perhaps
account for the following singular one. Several years ago
when the houses in Tooley Street were being pulled down,
I believe to make room for the new railway terminus, I happened
to pass along the very spot on which I had been lost
in my infancy. A slate of the largest size, called a
Duchess,<a class="afnanc" href="#fn2" id="fnanc2">2</a>
was thrown from the roof of one of the houses, and penetrated
into the earth close to my feet.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc2" id="fn2">2</a>
There exists an aristocracy even amongst slates, perhaps
from their occupying the most <i>elevated</i> position in every house. Small
ones are called Ladies, a larger size Countesses, and the biggest of
all are Duchesses.</p></div>

<p>The other event, which I believe happened some time after
the one just related, is as follows. I give it from memory,
as I have always repeated it.</p>

<div class="dsdnote">〈YOUNG PHI­LOS­O­PHER POISONED.〉</div>

<p>I was walking with my nurse and my brother in a public
garden, called Mont­pel­ier Gar­dens, in Wal­worth. On returning
through the private road leading to the gardens, I
gathered and swallowed some dark berries very like black
currants:—these were poisonous. <span class="xxpn" id="p010">{10}</span></p>

<p>On my return home, I recollect being placed between my
father’s knees, and his giving me a glass of castor oil, which I
took from his hand.</p>

<p>My father at that time possessed a collection of pictures.
He sat on a chair on the right hand side of the chimney-piece
in the breakfast room, under a fine picture of our
Saviour taken down from the cross. On the opposite wall
was a still-celebrated “Interior of Antwerp Cathedral.”</p>

<p>In after-life I several times mentioned the subject both to
my father and to my mother; but neither of them had the
slightest recollection of the matter.</p>

<p>Having suffered in health at the age of five years, and
again at that of ten by violent fevers, from which I was with
difficulty saved, I was sent into Devonshire and placed under
the care of a clergyman (who kept a school at Alphington,
near Exeter), with in­struc­tions to attend to my health; but, not
to press too much knowledge upon me: a mission which he
faithfully accomplished. Perhaps great idleness may have
led to some of my childish reasonings.</p>

<p>Relations of ghost stories often circulate amongst children,
and also of visitations from the devil in a <i>personal</i> form.
Of course I shared the belief of my comrades, but still had
some doubts of the existence of these personages, although I
greatly feared their appearance. Once, in conjunction with
a companion, I frightened another boy, bigger than myself,
with some pretended ghost; how prepared or how represented
by natural objects I do not now remember: I believe
it was by the accidental passing shadows of some external
objects upon the walls of our common bedroom.</p>

<div class="dsdnote">〈DELUDES A BOY WITH A GHOST.〉</div>

<p>The effect of this on my playfellow was painful; he was
much frightened for several days; and it naturally occurred
to me, after some time, that as I had deluded
him with ghosts, <span class="xxpn" id="p011">{11}</span>
I might myself have been deluded by older persons, and that,
after all, it might be a doubtful point whether ghost or devil
ever really existed. I gathered all the information I could
on the subject from the other boys, and was soon informed
that there was a peculiar process by which the devil might
be raised and become personally visible. I carefully collected
from the traditions of different boys the visible forms in
which the Prince of Darkness had been recorded to have
appeared. Amongst them <span class="nowrap">were—</span></p>

<ul>
<li>A rabbit,</li>
<li>An owl,</li>
<li>A black cat, very frequently,</li>
<li>A raven,</li>
<li>A man with a cloven foot, also frequent.</li>
</ul>

<p>After long thinking over the subject, although checked by
a belief that the inquiry was wicked, my curiosity at length
over-balanced my fears, and I resolved to attempt to raise
the devil. Naughty people, I was told, had made written
compacts with the devil, and had signed them with their
names written in their own blood. These had become very
rich and great men during their life, a fact which might be
well known. But, after death, they were described as
having suffered and continuing to suffer physical torments
throughout eternity, another fact which, to my uninstructed
mind, it seemed difficult to prove.</p>

<p>As I only desired an interview with the gentleman in
black simply to convince my senses of his existence, I declined
adopting the legal forms of a bond, and preferred
one more resembling that of leaving a visiting card, when, if
not at home, I might expect the sat­is­fac­tion of a return of the
visit by the devil in person. <span class="xxpn" id="p012">{12}</span></p>

<div class="dsdnote">〈TRIES TO RAISE THE DEVIL.〉</div>

<p>Accordingly, having selected a promising locality, I went
one evening towards dusk up into a deserted garret. Having
closed the door, and I believe opened the window, I proceeded
to cut my finger and draw a circle on the floor with the blood
which flowed from the incision.</p>

<p>I then placed myself in the centre of the circle, and either
said or read the Lord’s Prayer backwards. This I accomplished
at first with some trepidation and in great fear
towards the close of the scene. I then stood still in the
centre of that magic and superstitious circle, looking with
intense anxiety in all directions, especially at the window and
at the chimney. Fortunately for myself, and for the reader
also, if he is interested in this narrative, no owl or black cat
or unlucky raven came into the room.</p>

<p>In either case my then weakened frame might have expiated
this foolish experiment by its own extinction, or by
the alienation of that too curious spirit which controlled its
feeble powers.</p>

<div class="dsdnote">〈EXPERIMENTAL RELIGION.〉</div>

<p>After waiting some time for my expected but dreaded
visitor, I, in some degree, recovered my self-possession, and
leaving the circle of my incantation, I gradually opened the
door and gently closing it, descended the stairs, at first
slowly, and by degrees much more quickly. I then rejoined
my companions, but said nothing whatever of my recent
attempt. After supper the boys retired to bed. When we
were in bed and the candle removed, I proceeded as usual
to repeat my prayers silently to myself. After the few first
sentences of the Lord’s Prayer, I found that I had forgotten a
sentence, and could not go on to the conclusion. This
alarmed me very much, and having repeated another prayer
or hymn, I remained long awake, and very unhappy. I
thought that this forgetfulness was
a punishment inflicted <span class="xxpn" id="p013">{13}</span>
upon me by the Almighty, and that I was a wicked little
boy for having attempted to satisfy myself about the existence
of a devil. The next night my memory was more
faithful, and my prayers went on as usual. Still, however, I
was unhappy, and continued to brood over the inquiry. My
uninstructed faculties led me from doubts of the existence of
a devil to doubts of the book and the religion which asserted
him to be a living being. My sense of justice (whether it be
innate or acquired) led me to believe that it was impossible
that an almighty and all-merciful God could punish me, a
poor little boy, with eternal torments because I had anxiously
taken the only means I knew of to verify the truth or falsehood
of the religion I had been taught. I thought over
these things for a long time, and, in my own childish mind,
wished and prayed that God would tell me what was true.
After long meditation, I resolved to make an experiment
to settle the question. I thought, if it was really of such
immense importance to me here and hereafter to believe
rightly, that the Almighty would not consign me to eternal
misery because, after trying all means that I could devise, I
was unable to know the truth. I took an odd mode of
making the experiment; I resolved that at a certain hour of
a certain day I would go to a certain room in the house, and
that if I found the door open, I would believe the Bible; but
that if it were closed, I should conclude that it was not true.
I remember well that the ob­ser­va­tion was made, but I have
no recollection as to the state of the door. I presume it was
found open from the circumstance that, for many years after,
I was no longer troubled by doubts, and indeed went through
the usual religious forms with very little thought about their
origin.</p>

<div class="dsdnote">〈DISCOVERY OF GOLD.〉</div>

<p>At length, as time went on, my bodily
health was restored <span class="xxpn" id="p014">{14}</span>
by my native air: my mind, however, receiving but little in­struc­tion,
began, I imagine, to prey upon itself—such at least
I infer to have been the case from the following circumstance.
One day, when uninterested in the sports of my little companions,
I had retired into the shrubbery and was leaning my
head, supported by my left arm, upon the lower branch of a
thorn-tree. Listless and unoccupied, I <i>imagined</i> I had a
head-ache. After a time I perceived, lying on the ground
just under me, a small bright bit of metal. I instantly seized
the precious discovery, and turning it over, examined both
sides. I immediately concluded that I had discovered some
valuable treasure, and running away to my deserted companions,
showed them my golden coin. The little company
became greatly excited, and declared that it must be gold,
and that it was a piece of money of great value. We ran off
to get the opinion of the usher; but whether he partook of
the delusion, or we acquired our knowledge from the higher
authority of the master, I know not. I only recollect the
entire dissipation of my head-ache, and then my ultimate
great disappointment when it was pronounced, upon the undoubted
authority of the village doctor, that the square piece
of brass I had found was a half-dram weight which had
escaped from the box of a pair of medical scales. This little
incident had an important effect upon my after-life. I reflected
upon the extraordinary fact, that my head-ache had
been entirely cured by the discovery of the piece of brass.
Although I may not have put into words the principle,
<i>that occupation of the mind is such a source of pleasure that
it can relieve even the pain of a head-ache</i>; yet I am sure it
practically gave an additional stimulus to me in many a
difficult inquiry. Some few years after, when suffering
under a form of tooth-ache, not
acute though tediously <span class="xxpn" id="p015">{15}</span>
wearing, I often had recourse to a volume of Don Quixote,
and still more frequently to one of Robinson Crusoe. Although
at first it required a painful effort of attention, yet
it almost always happened, after a time, that I had forgotten
the moderate pain in the overpowering interest of the novel.</p>

<div class="dsdnote">〈COMPACT TO APPEAR AFTER DEATH.〉</div>

<p>My most intimate companion and friend was a boy named
Dacres, the son of Admiral Richard Dacres. We had often
talked over such questions as those I have mentioned in
this chapter, and we had made an agreement that whichever
died first should, if possible, appear to the other after death,
in order to satisfy the survivor about their solution.</p>

<p>After a year or two my young friend entered the navy,
but we kept up our friendship, and when he was ashore I saw
him frequently. He was in a ship of eighty guns at the
passage of the Dardanelles, under the command of Sir
Thomas Duckworth. Ultimately he was sent home in
charge of a prize-ship, in which he suffered the severest
hardships during a long and tempestuous voyage, and then
died of consumption.</p>

<p>I saw him a few days before his death, at the age of about
eighteen. We talked of former times, but neither of us mentioned
the compact. I believe it occurred to his mind: it
was certainly strongly present to my own.</p>

<div class="dsdnote">〈DID NOT APPEAR.〉</div>

<p>He died a few days after. On the evening of that day I
retired to my own room, which was partially detached from
the house by an intervening conservatory. I sat up until
after midnight, endeavouring to read, but found it impossible
to fix my attention on any subject, except the overpowering
feeling of curiosity, which absorbed my mind. I then undressed
and went into bed; but sleep was entirely banished.
I had previously carefully examined whether any cat, bird,
or living animal might be accidentally concealed
in my room, <span class="xxpn" id="p016">{16}</span>
and I had studied the forms of the furniture lest they should
in the darkness mislead me.</p>

<p>I passed a night of perfect sleeplessness. The distant clock
and a faithful dog, just outside my own door, produced the
only sounds which disturbed the intense silence of that
anxious night.</p></div><!--section-->

<div class="section" id="p017">
<h2 class="h2herein">CHAPTER III.
<span class="hsmall">BOYHOOD.</span></h2>

<div class="dsynopsis">
Taken to an Exhibition of Mechanism&#x200a;—&#x200a;Silver
Ladies&#x200a;—&#x200a;School near London&#x200a;—&#x200a;Unjustly
punished&#x200a;—&#x200a;Injurious Effect&#x200a;—&#x200a;Ward’s
Young Mathematician’s Guide&#x200a;—&#x200a;Got up in
the Night to Study&#x200a;—&#x200a;Frederick Marryat
interrupts&#x200a;—&#x200a;Treaty of Peace&#x200a;—&#x200a;Found
out&#x200a;—&#x200a;Strange Effect of Treacle and Cognac on
Boys&#x200a;—&#x200a;Taught to write Sermons under the Rev. Charles
Simeon.</div>

<p class="pfirst"><span class="smcap">D<b>URING</b></span>
my boyhood my mother took me to several exhibitions
of machinery. I well remember one of them in
Hanover Square, by a man who called himself Merlin. I
was so greatly interested in it, that the Exhibitor remarked
the circumstance, and after explaining some of the objects
to which the public had access, proposed to my mother to
take me up to his workshop, where I should see still more
wonderful automata. We accordingly ascended to the
attic. There were two uncovered female figures of silver,
about twelve inches high.</p>

<p>One of these walked or rather glided along a space of
about four feet, when she turned round and went back to her
original place. She used an eye-glass oc­ca­sion­al­ly, and
bowed frequently, as if recognizing her acquaintances. The
motions of her limbs were singularly graceful.</p>

<p>The other silver figure was an admirable <i>danseuse</i>, with a
bird on the fore finger of her right hand, which wagged its
tail, flapped its wings, and opened its beak. This lady attitudinized
in a most fascinating manner. Her eyes were full
of
imagination, and irresistible. <span class="xxpn" id="p018">{18}</span></p>

<p>These silver figures were the chef-d’œuvres of the artist:
they had cost him years of unwearied labour, and were not
even then finished.</p>

<p>After I left Devonshire I was placed at a school in the
neighbourhood of London, in which there were about thirty
boys.</p>

<div class="dsdnote">〈UNJUST PUNISHMENT.〉</div>

<p>My first experience was unfortunate, and prob­a­bly gave an
un­fa­vour­a­ble turn to my whole career during my residence of
three years.</p>

<p>After I had been at school a few weeks, I went with one of
my companions into the play-ground in the dusk of the evening.
We heard a noise, as of people talking in an orchard
at some distance, which belonged to our master. As the
orchard had recently been robbed, we thought that thieves
were again at work. We accordingly climbed over the
boundary wall, ran across the field, and saw in the orchard
beyond a couple of fellows evidently running away. We
pursued as fast as our legs could carry us, and just got up to
the supposed thieves at the ditch on the opposite side of the
orchard.</p>

<p>A roar of laughter then greeted us from two of our own
companions, who had entered the orchard for the purpose of
getting some manure for their flowers out of a rotten mulberry-tree.
These boys were aware of our mistake, and had
humoured it.</p>

<p>We now returned all together towards the play-ground,
when we met our master, who immediately pronounced that
we were each fined one shilling for being out of bounds.
We two boys who had gone out of bounds to protect
our master’s property, and who if thieves had really
been there would probably have been half-killed by them,
attempted to remonstrate and explain the
case; but all <span class="xxpn" id="p019">{19}</span>
remonstrance was vain, and we were accordingly fined. I
never forgot that injustice.</p>

<p>The school-room adjoined the house, but was not directly
connected with it. It contained a library of about three
hundred volumes on various subjects, generally very well
selected; it also contained one or two works on subjects which
do not usually attract at that period of life. I derived much
advantage from this library; and I now mention it because
I think it of great importance that a library should exist in
every school-room.</p>

<div class="dsdnote">〈NIGHT WORK.〉</div>

<p>Amongst the books was a treatise on Algebra, called
“Ward’s Young Mathematician’s Guide.” I was always
partial to my arithmetical lessons, but this book attracted
my particular attention. After I had been at this school for
about a twelvemonth, I proposed to one of my school-fellows,
who was of a studious habit, that we should get up every
morning at three o’clock, light a fire in the school-room, and
work until five or half-past five. We accomplished this
pretty regularly for several months. Our plan had, however,
become partially known to a few of our companions. One
of these, a tall boy, bigger than ourselves, having heard
of it, asked me to allow him to get up with us, urging that
his sole object was to study, and that it would be of great
importance to him in after-life. I had the cruelty to refuse
this very reasonable request. The subject has often recurred
to my memory, but never without regret.</p>

<div class="dsdnote">〈RIVAL COMPETITORS.〉</div>

<p>Another of my young companions, Frederick
Marryat,<a class="afnanc" href="#fn3" id="fnanc3">3</a>
made the same request, but not with the same motive. I
told him we got up in order to work; that he would only
play, and that we should then be found out. After some time,
having exhausted all his arguments, Marryat told me he was
<span class="xxpn" id="p020">{20}</span>
determined to get up, and would do it whether I liked it or
not.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc3" id="fn3">3</a>
Afterwards Captain Marryat.</p></div>

<p>Marryat slept in the same room as myself: it contained
five beds. Our room opened upon a landing, and its door
was exactly opposite that of the master. A flight of stairs
led up to a passage just over the room in which the master
and mistress slept. Passing along this passage, another flight
of stairs led down, on the other side of the master’s bed-room,
to another landing, from which another flight of stairs led
down to the external door of the house, leading by a long
passage to the school-room.</p>

<p>Through this devious course I had cautiously threaded my
way, calling up my companion in his room at the top of the
last flight of stairs, almost every night for several months.</p>

<p>One night on trying to open the door of my own bed-room,
I found Marryat’s bed projecting a little before the door, so
that I could not open it. I perceived that this was done
purposely, in order that I might awaken him. I therefore
cautiously, and by degrees, pushed his bed back without
awaking him, and went as usual to my work. This occurred
two or three nights successively.</p>

<p>One night, however, I found a piece of pack-thread tied to
the door lock, which I traced to Marryat’s bed, and concluded
it was tied to his arm or hand. I merely untied the cord
from the lock, and passed on.</p>

<p>A few nights after I found it impossible to untie the cord,
so I cut it with my pocket-knife. The cord then became
thicker and thicker for several nights, but still my pen-knife
did its work.</p>

<div class="dsdnote">〈VARIOUS STRATAGEMS.〉</div>

<p>One night I found a small chain fixed to the lock, and
passing thence into Marryat’s bed. This defeated my efforts
for that night, and I retired to my own bed.
The next night <span class="xxpn" id="p021">{21}</span>
I was provided with a pair of plyers, and unbent one of the
links, leaving the two portions attached to Marryat’s arm
and to the lock of the door. This occurred several times,
varying by stouter chains, and by having a padlock which I
could not pick in the dark.</p>

<p>At last one morning I found a chain too strong for the
tools I possessed; so I retired to my own bed, defeated. The
next night, however, I provided myself with a ball of packthread.
As soon as I heard by his breathing that Marryat
was asleep, I crept over to the door, drew one end of my
ball of packthread through a link of the too-powerful chain,
and bringing it back with me to bed, gave it a sudden jerk
by pulling both ends of the packthread passing through the
link of the chain.</p>

<p>Marryat jumped up, put out his hand to the door, found
his chain all right, and then lay down. As soon as he was
asleep again, I repeated the operation. Having awakened
him for the third time, I let go one end of the string, and
drew it back by the other, so that he was unable at daylight
to detect the cause.</p>

<p>At last, however, I found it expedient to enter into a treaty
of peace, the basis of which was that I should allow Marryat to
join the night party; but that nobody else should be admitted.
This continued for a short time; but, one by one, three or
four other boys, friends of Marryat, joined our party, and, as
I had anticipated, no work was done. We all got to play;
we let off fire-works in the play-ground, and were of course
discovered.</p>

<div class="dsdnote">〈FOUND OUT.〉</div>

<p>Our master read us a very grave lecture at breakfast upon
the impropriety of this irregular system of turning night into
day, and pointed out its injurious effects upon the health.
This, he said, was so remarkable that he
could distinguish by <span class="xxpn" id="p022">{22}</span>
their pallid countenances those who had taken part in it.
Now he certainly did point out every boy who had been up
on the night we were detected. But it appeared to me very odd
that the same means of judging had not enabled him long
before to discover the two boys who had for several months
habitually practised this system of turning night into day.</p>

<p>Another of our pranks never received its solution in our
master’s mind; indeed I myself scarcely knew its early history.
Somehow or other, a Russian young gentleman, who
was a parlour-boarder, had I believe, expatiated to Marryat
on the virtues of Cognac.</p>

<p>One evening my friend came to me with a quart bottle of
what he called excellent stuff. A council was held amongst
a few of us boys to decide how we should dispose of this
treasure. I did not myself much admire the liquid, but suggested
that it might be very good when mixed up with a lot
of treacle. This thought was unanimously adopted, and a
subscription made to purchase the treacle. Having no vessel
sufficiently large to hold the intended mixture, I proposed
to take one of our garden-pots, stopping up the hole in its
bottom with a cork.</p>

<p>A good big earthen vessel, thus extemporised, was then
filled with this wonderful mixture. A spoon or two, an oyster-shell,
and various other contrivances delivered it to its numerous
consumers, and all the boys got a greater or less
share, according to their taste for this extraordinary liqueur.</p>

<p>The feast was over, the garden-pot was restored to its
owner, and the treacled lips of the boys had been wiped with
their handkerchiefs or on their coat-sleeves, when the bell announced
that it was prayer-time. We all knelt in silence at
our respective desks. As soon as the prayers were over, one
of the oddest scenes occurred. <span class="xxpn" id="p023">{23}</span></p>

<div class="dsdnote">〈EFFECT OF COGNAC.〉</div>

<p>Many boys rose up from their knees—but some fell down
again. Some turned round several times, and then fell.
Some turned round so often that they resembled spinning
dervishes. Others were only more stupid than usual; some
complained of being sick; many were very sleepy; others
were sound asleep, and had to be carried to bed; some
talked fast and heroically, two attempted psalmody, but none
listened.</p>

<p>All investigation at the time was useless: we were sent off
to bed as quickly as possible. It was only known that Count
Cognac had married the sweet Miss Treacle, whom all the
boys knew and loved, and who lodged at the grocer’s, in the
neighbouring village. But I believe neither the pedigree of
the bridegroom nor his domicile were ever discovered. It is
probable that he was of French origin, and dwelt in a cellar.</p>

<p>After I left this school I was for a few years under the
care of an excellent clergyman in the neighbourhood of
Cambridge. There were only six boys; but I fear I did not
derive from it all the advantage that I might have done. I
came into frequent contact with the Rev. Charles Simeon,
and with many of his enthusiastic disciples. Every Sunday
I had to write from memory an abstract of the sermon he
preached in our village. Even at that period of my life
I had a taste for generalization. Accordingly, having generalized
some of Mr. Simeon’s sermons up to a kind of skeleton
form, I tried, by way of experiment, to fill up such a form in
a sermon of my own composing from the text of “Alexander
the coppersmith hath done us much harm.” As well as I
remember, there were in my sermon some queer deductions
from this text; but then they fulfilled all the usual conditions
of our sermons: so thought also two of my companions to
whom I communicated <i>in confidence</i>
this new man­u­fac­ture. <span class="xxpn" id="p024">{24}</span></p>

<div class="dsdnote">〈COMPOSES SERMONS.〉</div>

<p>By some unexplained circumstance my sermon relating to
copper being isomorphous with Simeon’s own productions,
got by substitution into the hands of our master as the
recollections of one of the other boys. Thereupon arose an
awful explosion which I decline to paint.</p>

<p>I did, however, learn something at this school, for I observed
a striking illustration of the Economy of Man­u­fac­tures.
Mr. Simeon had the cure of a very wicked parish in Cambridge,
whilst my instructor held that of a tolerably decent
country village. If each minister had stuck to the in­struc­tion
of his own parish, it would have necessitated the man­u­fac­ture
of four sermons per week, whilst, by this beneficial
interchange of duties, only two were required.</p>

<p>Each congregation enjoyed also another advantage from
this arrangement—the advantage of variety, which, when
moderately indulged in,
excites the appetite.</p>
</div><!--section-->

<div class="section" id="p025">
<h2 class="h2herein">CHAPTER IV.
<span class="hsmall">CAMBRIDGE.</span></h2>

<div class="dsynopsis">
Universal Language&#x200a;—&#x200a;Purchase Lacroix’s Quarto Work on
the Integral Calculus&#x200a;—&#x200a;Disappointment on getting no
explanation of my Math­e­mat­i­cal Difficulties&#x200a;—&#x200a;Origin
of the Analytical Society&#x200a;—&#x200a;The Ghost
Club&#x200a;—&#x200a;Chess&#x200a;—&#x200a;Sixpenny Whist and Guinea
Whist&#x200a;—&#x200a;Boating&#x200a;—&#x200a;Chemistry&#x200a;—&#x200a;Elected
Lucasian Professor of Mathematics in 1828.</div>

<p class="pfirst"><span class="smcap">M<b>Y</b></span>
father, with a view of acquiring some information
which might be of use to me at Cambridge, had consulted a
tutor of one of the colleges, who was passing his long vacation
at the neighbouring watering-place, Teignmouth. He
dined with us frequently. The advice of the Rev. Doctor
was quite sound, but very limited. It might be summed up
in one short sentence: “Advise your son not to purchase his
wine in Cambridge.”</p>

<p>Previously to my entrance at Trinity College, Cambridge,
I resided for a time at Totnes, under the guidance of an
Oxford tutor, who undertook to superintend my classical
studies only.</p>

<p>During my residence at this place I accidentally heard, for
the first time, of an idea of forming a universal language. I
was much fascinated by it, and, soon after, proceeded to
write a kind of grammar, and then to devise a dictionary.
Some trace of the former, I think, I still possess: but I was
stopped in my idea of making a universal dictionary by the
apparent impossibility of arranging signs
in any consecutive <span class="xxpn" id="p026">{26}</span>
order, so as to find, as in a dictionary, the meaning of each
when wanted. It was only after I had been some time at
Cambridge that I became acquainted with the work of
“Bishop Wilkins on Universal Language.”</p>

<p>Being passionately fond of algebra, I had instructed myself
by means of Ward’s “Young Mathematician’s Guide,”
which had casually fallen into my hands at school. I now
employed all my leisure in studying such math­e­mat­i­cal
works as accident brought to my knowledge. Amongst these
were Humphrey Ditton’s “Fluxions,” of which I could make
nothing; Madame Agnesi’s “Analytical Institutions,” from
which I acquired some knowledge; Woodhouse’s “Principles
of Analytical Calculation,” from which I learned the notation
of Leibnitz; and Lagrange’s “Théorie des Fonctions.” I
possessed also the Fluxions of Maclaurin and of Simpson.</p>

<p>Thus it happened that when I went to Cambridge I could
work out such questions as the very moderate amount of
mathematics which I then possessed admitted, with equal
facility, in the dots of Newton, the d’s of Leibnitz, or the
dashes of Lagrange. I had, however, met with many difficulties,
and looked forward with intense delight to the
certainty of having them all removed on my arrival at Cambridge.
I had in my imagination formed a plan for the
institution amongst my future friends of a chess club, and
also of another club for the discussion of math­e­mat­i­cal
subjects.</p>

<div class="dsdnote">〈PURCHASE THE WORK OF LACROIX.〉</div>

<p>In 1811, during the war, it was very difficult to procure
foreign books. I had heard of the great work of Lacroix,
on the “Differential and Integral Calculus,” which I longed
to possess, and being misinformed that its price was two
guineas, I resolved to purchase it in London on my passage
to Cambridge. As soon as I arrived I went
to the French <span class="xxpn" id="p027">{27}</span>
bookseller, Dulau, and to my great surprise found that the
price of the book was seven guineas. After much thought
I made the costly purchase, went on immediately to Cambridge,
saw my tutor, Hudson, got lodgings, and then spent
the greater part of the night in turning over the pages of my
newly-acquired purchase. After a few days, I went to my
public tutor Hudson, to ask the explanation of one of my
math­e­mat­i­cal difficulties. He listened to my question, said it
would not be asked in the Senate House, and was of no sort
of consequence, and advised me to get up the earlier subjects
of the university studies.</p>

<div class="dsdnote">〈DIFFICULTIES NOT ANSWERED.〉</div>

<p>After some little while I went to ask the explanation of
another difficulty from one of the lecturers. He treated the
question just in the same way. I made a third effort to be
enlightened about what was really a doubtful question, and
felt satisfied that the person I addressed knew nothing of
the matter, although he took some pains to disguise his
ignorance.</p>

<p>I thus acquired a distaste for the routine of the studies of
the place, and devoured the papers of Euler and other
mathematicians, scattered through innumerable volumes of
the academies of Petersburgh, Berlin, and Paris, which the
libraries I had recourse to contained.</p>

<p>Under these circumstances it was not surprising that I
should perceive and be penetrated with the superior power
of the notation of Leibnitz.</p>

<p>At an early period, probably at the commencement of the
second year of my residence at Cambridge, a friend of mine,
Michael Slegg, of Trinity, was taking wine with me, discussing
math­e­mat­i­cal subjects, to which he also was enthusiastically
attached. Hearing the chapel bell ring, he took
leave of me, promising to return for a
cup of coffee. <span class="xxpn" id="p028">{28}</span></p>

<div class="dsdnote">〈RESULT OF BIBLE SOCIETY.〉</div>

<p>At this period Cambridge was agitated by a fierce controversy.
Societies had been formed for printing and circulating
the Bible. One party proposed to circulate it with
notes, in order to make it intelligible; whilst the other
scornfully rejected all explanations of the word of God as
profane attempts to mend that which was perfect.</p>

<p>The walls of the town were placarded with broadsides, and
posters were sent from house to house. One of the latter
form of advertisement was lying upon my table when Slegg
left me. Taking up the paper, and looking through it, I
thought it, from its exaggerated tone, a good subject for a
parody.</p>

<p>I then drew up the sketch of a society to be instituted for
translating the small work of Lacroix on the Differential and
Integral Lacroix. It proposed that we should have periodical
meetings for the propagation of d’s; and consigned to
perdition all who supported the heresy of dots. It maintained
that the work of Lacroix was so perfect that any comment
was unnecessary.</p>

<p>On Slegg’s return from chapel I put the parody into his
hands. My friend enjoyed the joke heartily, and at parting
asked my permission to show the parody to a math­e­mat­i­cal
friend of his, Mr. Bromhead.<a class="afnanc" href="#fn4" id="fnanc4">4</a></p>

<p>The next day Slegg called on me, and said that he had
put the joke into the hand of his friend, who, after laughing
heartily, remarked that it was too good a joke to be lost,
and proposed seriously that we should form a society for the
cultivation of mathematics.</p>

<div class="dsdnote">〈ANALYTICAL SOCIETY.〉</div>

<p>The next day Bromhead called on me. We talked the
subject over, and agreed to hold a meeting at
his lodgings
<span class="xxpn" id="p029">{29}</span>
for the purpose of forming a society for the promotion of
analysis.</p>

<p>At that meeting, besides the projectors, there were present
Herschel, Peacock, D’Arblay,<a class="afnanc" href="#fn5" id="fnanc5">5</a>
Ryan,<a class="afnanc" href="#fn6" id="fnanc6">6</a>
Robinson,<a class="afnanc" href="#fn7" id="fnanc7">7</a>
Frederick
Maule,<a class="afnanc" href="#fn8" id="fnanc8">8</a>
and several others. We constituted ourselves “The
Analytical Society;” hired a meeting-room, open daily; held
meetings, read papers, and discussed them. Of course we
were much ridiculed by the Dons; and, not being put down,
it was darkly hinted that we were young infidels, and that no
good would come of us.</p>

<p>In the meantime we quietly pursued our course, and at
last resolved to publish a volume of our Transactions. Owing
to the illness of one of the number, and to various other
circumstances, the volume which was published was entirely
contributed by Herschel and myself.</p>

<p>At last our work was printed, and it became necessary to
decide upon a title. Recalling the slight imputation which
had been made upon our faith, I suggested that the most
appropriate title would <span class="nowrap">be—</span></p>

<p>The Principles of pure D-ism in opposition to the Dot-age
of the University.<a class="afnanc" href="#fn9" id="fnanc9">9</a></p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc4" id="fn4">4</a>
Afterwards Sir Edward Ffrench Bromhead,
Bart., the author of an interesting paper in the Transactions of the
Royal Society.</p>

<p class="pfirst padtopc"><a class="afnlabel" href="#fnanc5" id="fn5">5</a>
The only son of Madame D’Arblay.</p>

<p class="pfirst padtopc"><a class="afnlabel" href="#fnanc6" id="fn6">6</a>
Now the Right Honourable Sir Edward Ryan.</p>

<p class="pfirst padtopc"><a class="afnlabel" href="#fnanc7" id="fn7">7</a>
The Rev. Dr. Robinson, Master of the Temple.</p>

<p class="pfirst padtopc"><a class="afnlabel" href="#fnanc8" id="fn8">8</a>
A younger brother of the late Mr. Justice Maule.</p>

<p class="pfirst padtopc"><a class="afnlabel" href="#fnanc9" id="fn9">9</a>
Leibnitz indicated fluxions by a <i>d</i>, Newton by a dot.</p></div>

<div class="dsdnote">〈ELECTED LUCASIAN PROFESSOR.〉</div>

<p>In thus reviving this wicked pun, I ought at the same
time to record an instance of forgiveness unparalleled in
history. Fourteen years after, being then at Rome, I accidentally
read in Galignani’s newspaper the following paragraph,
dated Cambridge:—“Yesterday the bells of St. Mary
rang on the election of Mr. Babbage as Lucasian Professor
of Mathematics.” <span class="xxpn" id="p030">{30}</span></p>

<p>If this event had happened during the lifetime of my
father, it would have been most gratifying to myself, because,
whilst it would have given him much pleasure, it would then
also have afforded intense delight to my mother.</p>

<p>I concluded that the next post would bring me the official
confirmation of this report, and after some consideration I
sketched the draft of a letter, in which I proposed to thank
the University sincerely for the honour they had done me,
but to decline it.</p>

<p>This sketch of a letter was hardly dry when two of my
intimate friends, the Rev. Mr. Lunn and Mr. Beilby Thompson,<a class="afnanc" href="#fn10" id="fnanc10">10</a>
who resided close to me in the Piazza del Populo, came
over to congratulate me on the appointment. I showed them
my proposed reply, against which they earnestly protested.
Their first, and as they believed their strongest, reason was
that it would give so much pleasure to my mother. To this
I answered that my mother’s opinion of her son had been
confirmed by the reception he had met with in every foreign
country he had visited, and that this, in her estimation, would
add but little to it. To their next argument I had no sat­is­fac­tory
answer. It was that this election could not have
occurred unless some friends of mine in England had taken
active measures to promote it; that some of these might have
been personal friends, but that many others might have
exerted themselves entirely upon principle, and that it would
be harsh to disappoint such friends, and reject such a compliment.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc10" id="fn10">10</a>
Afterwards Lord Wenlock.</p></div>

<p>My own feelings were of a mixed nature. I saw the vast
field that the Difference Engine had opened out; for, before
I left England in the previous year, I had extended its
mechanism to the tabulation of functions having no constant
<span class="xxpn" id="p031">{31}</span>
difference, and more par­tic­u­lar­ly I had arrived at the knowledge
of the entire command it would have over the computation
of the most important classes of tables, those of astronomy
and of navigation. I was also most anxious to give
my whole time to the completion of the mechanism of the
Difference Engine No. 1 which I had then in hand. Small
as the admitted duties of the Lucasian Chair were, I felt that
they would absorb time which I thought better devoted to
the completion of the Difference Engine. If I had then been
aware that the lapse of a few years would have thrown upon
me the enormous labour which the Analytical Engine absorbed,
no motive short of absolute necessity would have
induced me to accept any office which might, in the slightest
degree, withdraw my attention from its contrivance.</p>

<p>The result of this consultation with my two friends was,
that I determined to accept the Chair of Newton, and to hold
it for a few years. In 1839 the demands of the Analytical
Engine upon my attention had become so incessant and so
exhausting, that even the few duties of the Lucasian Chair
had a sensible effect in impairing my bodily strength. I
therefore sent in my resignation.</p>

<div class="dsdnote">〈FIRST EXAMINATION.〉</div>

<p>In January, 1829, I visited Cambridge, to fulfil one of the
first duties of my new office, the examination for Dr. Smith’s
prizes.</p>

<p>These two prizes, of twenty-five pounds each, exercise a
very curious and important influence. Usually three or four
hundred young men are examined previously to taking their
degree. The University officers examine and place them
in the order of their math­e­mat­i­cal merit. The class called
Wranglers is the highest; of these the first is called the
senior wrangler, the others the second and third, &amp;c.,
wranglers. <span class="xxpn" id="p032">{32}</span></p>

<p>All the young men who have just taken their degree, whether
with or without honours, are qualified to compete for the
Smith’s prizes by sending in notice to the electors, who consist
of the three Professors of Geometry, Astronomy, and
Physics, assisted oc­ca­sion­al­ly by two official electors, the Vice-Chancellor
and the Master of Trinity College. However, in
point of fact, generally three, and rarely above six young men
compete.</p>

<div class="dsdnote">〈COURT OF APPEAL.〉</div>

<p>It is manifest that the University officers, who examine
several hundred young men, cannot bestow the same minute
attention upon each as those who, at the utmost, only examine
six. Nor is this of any importance, except to the few first
wranglers, who usually are candidates for these prizes. The
consequence is that the examiners of the Smith’s prizes constitute,
as it were, a court of appeal from the decision of the
University officers. The decision of the latter is thus therefore,
necessarily appealed against upon every occasion. Perhaps
in one out of five or six cases the second or third wrangler
obtains the first Smith’s prize. I may add that in the
few cases known to me previously to my becoming an examiner,
the public opinion of the University always approved
those decisions, without implying any censure on the officers
of the University.</p>

<p>In forming my set of questions, I consulted the late Dean
of Ely and another friend, in order that I might not suddenly
deviate too much from the usual style of examinations.</p>

<p>After having examined the young men, I sat up the whole
night, carefully weighing the relative merits of their answers.
I found, with some mortification, that, according to my marks,
the second wrangler ought to have the first prize. I therefore
put aside the papers until the day before the decision.
I then took an unmarked copy of my questions,
and put new <span class="xxpn" id="p033">{33}</span>
numbers for their respective values. After very carefully
going over the whole of the examination-papers again, I
arrived almost exactly at my former conclusion.</p>

<div class="dsdnote">〈REMARKABLE AGREEMENT.〉</div>

<p>On our meeting at the Vice-Chancellor’s, that functionary
asked me, as the senior professor, what was my decision as to
the two prizes. I stated that the result of my examination
obliged me to award the first prize to the second wrangler.
Professor Airy was then asked the same question. He made
the same reply. Professor Lax being then asked, said he
had arrived at the same conclusion as his two colleagues.</p>

<p>The Vice-Chancellor remarked that when we altered the
arrangement of the University Examiners, it was very sat­is­fac­tory
that we should be unanimous. Professor Airy observed
that this sat­is­fac­tion was enhanced by the fact of
the remarkable difference in the tastes of the three examiners.</p>

<p>The Vice-Chancellor, turning to me, asked whether it
might be permitted to inquire the numbers we had respectively
assigned to each candidate.</p>

<p>I and my colleagues immediately mentioned our numbers,
which Professor Airy at once reduced to a common scale.
On this it appeared that the number of marks assigned to each
by Professor Airy and myself very nearly agreed, whilst that
of Professor Lax differed but little.</p>

<p>On this occasion the first Smith’s prize was assigned to the
second wrangler, Mr. Cavendish, now Duke of Devonshire,
the present Chancellor of the University.</p>

<p>The result of the whole of my after-experience showed that
amongst the highest men the peculiar tastes of the examiners
had no effect in disturbing the proper decision.</p>

<p>I held the Chair of Newton for some few years, and still
feel deeply grateful for the honour
the University conferred <span class="xxpn" id="p034">{34}</span>
upon me—the only honour I ever received in my own
country.<a class="afnanc" href="#fn11" id="fnanc11">11</a></p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc11" id="fn11">11</a>
This professorship is not in the gift of the Government.
The electors are the masters of the various colleges. It was founded in
1663 by Henry Lucas, M.P. for the University, and was endowed by him
with a small estate in Bedfordshire. During my tenure of that office my
net receipts were between 80&#x200a;<i>l.</i> and 90&#x200a;<i>l.</i> a year. I am glad to find
that the estate is now improved, and that the University have added an
annual salary to the Chair of Newton.</p></div>

<p>I must now return to my pursuits during my residence at
Cambridge, the account of which has been partially interrupted
by the history of my appointment to the Chair of
Newton.</p>

<p>Whilst I was an undergraduate, I lived probably in a
greater variety of sets than any of my young companions.
But my chief and choicest consisted of some ten or a dozen
friends who usually breakfasted with me every Sunday after
chapel; arriving at about nine, and remaining to between
twelve and one o’clock. We discussed all knowable and
many unknowable things.</p>

<div class="dsdnote">〈GHOST CLUB—EXTRACTORS.〉</div>

<p>At one time we resolved ourselves into a Ghost Club, and
proceeded to collect evidence, and entered into a considerable
correspondence upon the subject. Some of this was
both interesting and instructive.</p>

<p>At another time we resolved ourselves into a Club which
we called The Extractors. Its rules were as
<span class="nowrap">follows,—</span></p>

<ul>
<li>1st. Every member shall communicate his address to the
Secretary once in six months.</li>

<li>2nd. If this communication is delayed beyond twelve
months, it shall be taken for granted that his relatives had
shut him up as insane.</li>

<li>3rd. Every effort legal and illegal shall be made to get
him out of the madhouse. Hence the name of the club—The
Extractors. <span class="xxpn" id="p035">{35}</span></li>

<li>4th. Every candidate for admission as a member shall
produce six certificates. Three that he is sane and three
others that he is insane.</li></ul>

<p>It has often occurred to me to inquire of my legal friends
whether, if the sanity of any member of the club had been
questioned in after-life, he would have adduced the fact of
membership of the Club of Extractors as an indication of
sanity or of insanity.</p>

<div class="dsdnote">〈SHYNESS—CHESS.〉</div>

<p>During the first part of my residence at Cambridge, I
played at chess very frequently, often with D’Arblay and
with several other good players. There was at that period a
fellow-commoner at Trinity named Brande, who devoted
almost his whole time to the study of chess. I was invited to
meet him one evening at the rooms of a common friend for
the purpose of trying our strength.</p>

<p>On arriving at my friend’s rooms, I found a note informing
me that he had gone to Newmarket, and had left coffee and
the chessmen for us. I was myself tormented by great
shyness, and my yet unseen adversary was, I understood,
equally diffident. I was sitting before the chess-board when
Brande entered. I rose, he advanced, sat down, and took a
white and a black pawn from the board, which he held, one in
either hand. I pointed with my finger to the left hand and
won the move.</p>

<p>The game then commenced; it was rather a long one, and
I won it: but not a word was exchanged until the end: when
Brande uttered the first word. “Another?” To this I nodded
assent.</p>

<p>How that game was decided I do not now remember; but
the first sentence pronounced by either of us, was a remark
by Brande, that he had lost the first game by a certain move
of his white bishop. To this I replied, that I
thought he was <span class="xxpn" id="p036">{36}</span>
mistaken, and that the real cause of his losing the game arose
from the use I had made of my knight two moves previously
to his white bishop’s move.</p>

<p>We then immediately began to replace the men on the
board in the positions they occupied at that particular point
of the game when the white bishop’s move was made. Each
took up any piece indiscriminately, and placed it without
hesitation on the exact square on which it had stood. It
then became apparent that the effective move to which I
had referred was that of my knight.</p>

<p>Brande, during his residence at Cambridge, studied chess
regularly several hours each day, and read almost every
treatise on the subject. After he left college he travelled
abroad, took lessons from every celebrated teacher, and
played with all the most eminent players on the Continent.</p>

<p>At intervals of three or four years I oc­ca­sion­al­ly met him
in London. After the usual greeting he always proposed
that we should play a game of chess.</p>

<p>I found on these occasions, that if I played any of the
ordinary openings, such as are found in the books, I was sure
to be beaten. The only way in which I had a chance of
winning, was by making early in the game a move so bad
that it had not been mentioned in any treatise. Brande
possessed, and had read, almost every book upon the
subject.</p>

<div class="dsdnote">〈SIXPENNY WHIST.〉</div>

<p>Another set which I frequently joined were addicted to
sixpenny whist. It consisted of Higman, afterwards Tutor of
Trinity; Follet, afterwards Attorney-General; of a learned
and accomplished Dean still living, and I have no doubt still
playing an excellent rubber, and myself. We not unfrequently
sat from chapel-time in the evening
until the sound <span class="xxpn" id="p037">{37}</span>
of the morning chapel bell again called us to our religious
duties.</p>

<p>I mixed oc­ca­sion­al­ly with a different set of whist players
at Jesus College. They played high: guinea points, and five
guineas on the rubber. I was always a most welcome visitor,
not from my skill at the game; but because I never played
more than shilling points and five shillings on the rubber.
Consequently my partner had what they considered an advantage:
namely, that of playing guinea points with one of
our adversaries and pound points with the other.</p>

<div class="dsdnote">〈EXPEDITIONS TO THE FENS.〉</div>

<p>Totally different in character was another set in which I
mixed. I was very fond of boating, not of the manual labour
of rowing, but the more in­tel­lec­tual art of sailing. I kept a
beautiful light, London-built boat, and oc­ca­sion­al­ly took long
voyages down the river, beyond Ely into the fens. To accomplish
these trips, it was necessary to have two or three
strong fellows to row when the wind failed or was contrary.
These were useful friends upon my aquatic expeditions, but
not being of exactly the same calibre as my friends of the
Ghost Club, were very cruelly and disrespectfully called by
them “my Tom fools.”</p>

<p>The plan of our voyage was thus:—I sent my servant to
the apothecary for a thing called an ægrotat, which I understood,
for I never saw one, meant a certificate that I was indisposed,
and that it would be injurious to my health to
attend chapel, or hall, or lectures. This was forwarded to
the college authorities.</p>

<p>I also directed my servant to order the cook to send me a
large well-seasoned meat pie, a couple of fowls, &amp;c. These
were packed in a hamper with three or four bottles of wine
and one of noyeau. We sailed when the wind was fair, and
rowed when there was none. Whittlesea Mere
was a very <span class="xxpn" id="p038">{38}</span>
favourite resort for sailing, fishing, and shooting. Sometimes
we reached Lynn. After various adventures and five or
six days of hard exercise in the open air, we returned with
our health more renovated than if the best physician had
prescribed for us.</p>

<hr class="hrblk" />

<div class="dsdnote">〈CHEMISTRY.〉</div>

<p>During my residence at Cambridge, Smithson Tennant
was the Professor of Chemistry, and I attended his lectures.
Having a spare room, I turned it into a kind of laboratory,
in which Herschel worked with me, until he set
up a rival one of his own. We both oc­ca­sion­al­ly assisted
the Professor in preparing his experiments. The science of
chemistry had not then assumed the vast development it has
now attained. I gave up its practical pursuit soon after I
resided in London, but I have never regretted the time I
bestowed upon it at the commencement of my career. I
had hoped to have long continued to enjoy the friendship
of my entertaining and valued instructor, and to have
profited by his introducing me to the science of the metropolis,
but his tragical fate deprived me of that advantage.
Whilst riding with General Bulow across a drawbridge at
Boulogne, the bolt having been displaced, Smithson Tennant
was precipitated to the bottom, and killed on the spot. The
General, having an earlier warning, set spurs to his horse,
and just escaped a similar fate.</p>

<div class="dsdnote">〈TRANSLATION OF LACROIX.〉</div>

<p>My views respecting the notation of Leibnitz now (1812)
received confirmation from an extensive course of reading. I
became convinced that the notation of fluxions must ultimately
prove a strong impediment to the progress of English science.
But I knew, also, that it was hopeless for any young and
unknown author to attempt to introduce the notation of
Leibnitz into an elementary work.
This opinion naturally <span class="xxpn" id="p039">{39}</span>
suggested to me the idea of translating the smaller work of
Lacroix. It is possible, although I have no recollection of it,
that the same idea may have occurred to several of my colleagues
of the Analytical Society, but most of them were so
occupied, first with their degree, and then with their examination
for fellowships, that no steps were at that time taken by
any of them on that subject.</p>

<p>Unencumbered by these distractions, I commenced the
task, but at what period of time I do not exactly recollect.
I had finished a portion of the translation, and laid it aside,
when, some years afterwards, Peacock called on me in Devonshire
Street, and stated that both Herschel and himself were
convinced that the change from the dots to the d’s would not
be accomplished until some foreign work of eminence should
be translated into English. Peacock then proposed that I
should either finish the translation which I had commenced,
or that Herschel and himself should complete the remainder
of my translation. I suggested that we should toss up which
alternative to take. It was determined by lot that we should
make a joint translation. Some months after, the translation
of the small work of Lacroix was published.</p>

<p>For several years after, the progress of the notation of
Leibnitz at Cambridge was slow. It is true that the tutors
of the two largest colleges had adopted it, but it was taught
at none of the other colleges.</p>

<div class="dsdnote">〈COLLECTION OF EXAMPLES.〉</div>

<p>It is always difficult to think and reason in a new language,
and this difficulty discouraged all but men of energetic minds.
I saw, however, that, by making it their interest to do so, the
change might be accomplished. I therefore proposed to
make a large collection of examples of the differential and
integral calculus, consisting merely of the statement of each
problem and its final solution. I foresaw that
if such a <span class="xxpn" id="p040">{40}</span>
publication existed, all those tutors who did not approve of the
change of the Newtonian notation would yet, in order to
save their own time and trouble, go to this collection of
examples to find problems to set to their pupils. After a
short time the use of the new signs would become familiar,
and I anticipated their general adoption at Cambridge as a
matter of course.</p>

<p>I commenced by copying out a large portion of the work
of Hirsch. I then communicated to Peacock and Herschel
my view, and proposed that they should each contribute a
portion.</p>

<p>Peacock considerably modified my plan by giving the process
of solution to a large number of the questions. Herschel
prepared the questions in finite differences, and I supplied the
examples to the calculus of functions. In a very few years
the change was completely established; and thus at last the
English cultivators of math­e­mat­i­cal science, untrammelled by
a limited and imperfect system of signs, entered on equal
terms into competition with
their continental rivals.</p>
</div><!--section-->

<div class="section" id="p041">
<h2 class="h2herein">CHAPTER V.
<span class="hsmall">DIFFERENCE ENGINE NO. 1.</span></h2>

<hr class="hr20" />
<div class="dpoemctr fsz7"><div class="dstanzactr">
<div class="dquoteverse"><span class="spquotebox">“</span>Oh
 no! we never mention it,</div>
<div class="dpp00">Its name is never heard.”</div>
</div></div><hr class="hr20" />

<div class="dsynopsis">
Difference Engine No. 1&#x200a;—&#x200a;First Idea at
Cambridge, 1812&#x200a;—&#x200a;Plan for Dividing Astronomical
Instruments&#x200a;—&#x200a;Idea of a Machine to calculate
Tables by Differences&#x200a;—&#x200a;Illustrations by Piles of
Cannon-balls.</div>

<p class="pfirst"><span class="smcap">C<b>ALCULATING</b> M<b>ACHINES</b></span>
comprise various pieces of mechanism
for assisting the human mind in executing the operations
of arithmetic. Some few of these perform the whole
operation without any mental attention when once the given
numbers have been put into the machine.</p>

<p>Others require a moderate portion of mental attention:
these latter are generally of much simpler construction than
the former, and it may also be added, are less useful.</p>

<p>The simplest way of deciding to which of these two classes
any calculating machine belongs is to ask its maker—Whether,
when the numbers on which it is to operate are placed in the
instrument, it is capable of arriving at its result by the mere
motion of a spring, a descending weight, or any other constant
force? If the answer be in the affirmative, the machine is
really automatic; if otherwise, it is not self-acting.</p>

<p>Of the various machines I have had occasion to examine,
many of those for Addition and Subtraction
have been found <span class="xxpn" id="p042">{42}</span>
to be automatic. Of machines for Multiplication and Division,
which have fully come under my examination, I cannot
at present recall one to my memory as absolutely fulfilling
this condition.</p>

<div class="dsdnote">〈ORIGIN OF DIFFERENCE ENGINE.〉</div>

<p>The earliest idea that I can trace in my own mind of
calculating arithmetical Tables by machinery arose in this
<span class="nowrap">manner:—</span></p>

<p>One evening I was sitting in the rooms of the Analytical
Society, at Cambridge, my head leaning forward on the Table
in a kind of dreamy mood, with a Table of logarithms lying
open before me. Another member, coming into the room, and
seeing me half asleep, called out, “Well, Babbage, what are
you dreaming about?” to which I replied, “I am thinking
that all these Tables (pointing to the logarithms) might be
calculated by machinery.”</p>

<p>I am indebted to my friend, the Rev. Dr. Robinson, the
Master of the Temple, for this anecdote. The event must
have happened either in 1812 or 1813.</p>

<p>About 1819 I was occupied with devising means for accurately
dividing astronomical instruments, and had arrived
at a plan which I thought was likely to succeed perfectly. I
had also at that time been speculating about making
machinery to compute arithmetical Tables.</p>

<p>One morning I called upon the late Dr. Wollaston, to
consult him about my plan for dividing instruments. On
talking over the matter, it turned out that my system was
exactly that which had been described by the Duke de
Chaulnes, in the Memoirs of the French Academy of Sciences,
about fifty or sixty years before. I then mentioned my other
idea of computing Tables by machinery, which Dr. Wollaston
thought a more promising subject.</p>

<p>I considered that a machine to execute
the mere isolated <span class="xxpn" id="p043">{43}</span>
operations of arithmetic, would be comparatively of little
value, unless it were very easily set to do its work, and
unless it executed not only accurately, but with great rapidity,
whatever it was required to do.</p>

<div class="dsdnote">〈ADDITION AND CARRIAGE.〉</div>

<p>On the other hand, the method of differences supplied a
general principle by which <i>all</i> Tables might be computed
through limited intervals, by one uniform process. Again,
the method of differences required the use of mechanism for
Addition only. In order, however, to insure accuracy in the
printed Tables, it was necessary that the machine which computed
Tables should also set them up in type, or else supply
a mould in which stereotype plates of those Tables could
be cast.</p>

<p>I now began to sketch out arrangements for accomplishing
the several partial processes which were required. The
arithmetical part must consist of two distinct processes—the
power of adding one digit to another, and also of carrying the
tens to the next digit, if it should be necessary.</p>

<p>The first idea was, naturally, to add each digit successively.
This, however, would occupy much time if the numbers added
together consisted of many places of figures.</p>

<p>The next step was to add all the digits of the two numbers
each to each at the same instant, but reserving a certain
mechanical memorandum, wherever a carriage became due.
These carriages were then to be executed successively.</p>

<p>Having made various drawings, I now began to make
models of some portions of the machine, to see how they
would act. Each number was to be expressed upon wheels
placed upon an axis; there being one wheel for each figure in
the number operated upon.</p>

<p>Having arrived at a certain point in my progress, it became
necessary to have teeth of a peculiar form
cut upon these <span class="xxpn" id="p044">{44}</span>
wheels. As my own lathe was not fit for this job, I took the
wheels to a wheel-cutter at Lambeth, to whom I carefully
conveyed my in­struc­tions, leaving with him a drawing as his
guide.</p>

<div class="dsdnote">〈UNEXPECTED DIFFICULTY EXPLAINED.〉</div>

<p>These wheels arrived late one night, and the next morning
I began putting them in action with my other mechanism,
when, to my utter astonishment, I found they were quite
unfit for their task. I examined the shape of their teeth,
compared them with those in the drawings, and found they
agreed perfectly; yet they could not perform their intended
work. I had been so certain of the truth of my previous
reasoning, that I now began to be somewhat uneasy. I
reflected that, if the reasoning about which I had been so
certain should prove to have been really fallacious, I could
then no longer trust the power of my own reason. I therefore
went over with my wheels to the artist who had formed the
teeth, in order that I might arrive at some explanation of
this extraordinary contradiction.</p>

<p>On conferring with him, it turned out that, when he had
understood fully the peculiar form of the teeth of wheels, he
discovered that his wheel-cutting engine had not got amongst
its divisions that precise number which I had required. He
therefore had asked me whether another number, which his
machine possessed, would not equally answer my object. I
had inadvertently replied in the affirmative. He then made
arrangements for the precise number of teeth I required; and
the new wheels performed their expected duty perfectly.</p>

<p>The next step was to devise means for printing the tables
to be computed by this machine. My first plan was to make
it put together moveable type. I proposed to make metal
boxes, each containing 3,000 types of one of the ten digits.
These types were to be made to pass out one by
one from the <span class="xxpn" id="p045">{45}</span>
bottom of their boxes, when required by the computing part
of the machine.</p>

<div class="dsdnote">〈VERIFICATION OF TYPE.〉</div>

<p>But here a new difficulty arose. The attendant who put
the types into the boxes might, by mistake, put a wrong type
in one or more of them. This cause of error I removed in
the following manner:—There are usually certain notches in
the side of the type. I caused these notches to be so placed
that all the types of any given digit possessed the same char­ac­ter­is­tic
notches, which no other type had. Thus, when the
boxes were filled, by passing a small wire down these peculiar
notches, it would be impeded in its passage, if there were
included in the row a single wrong figure. Also, if any digit
were accidentally turned upside down, it would be indicated
by the stoppage of the testing wire.</p>

<p>One notch was reserved as common to every species of
type. The object of this was that, before the types which
the Difference Engine had used for its computation were removed
from the iron platform on which they were placed, a
steel wire should be passed through this common notch, and
remain there. The tables, composed of moveable types, thus
interlocked, could never have any of their figures drawn out
by adhesion to the inking-roller, and then by possibility be
restored in an inverted order. A small block of such figures
tied together by a bit of string, remained unbroken for several
years, although it was rather roughly used as a plaything by
my children. One such box was finished, and delivered its
type satisfactorily.</p>

<p>Another plan for printing the tables, was to place the ordinary
printing type round the edges of wheels. Then, as
each successive number was produced by the arithmetical
part, the type-wheels would move down upon a plate of soft
composition, upon which the tabular
number would be <span class="xxpn" id="p046">{46}</span>
impressed. This mould was formed of a mixture of plaster-of-Paris
with other materials, so as to become hard in the
course of a few hours.</p>

<div class="dsdnote">〈MOULDS AND COPPER-PLATE.〉</div>

<p>The first difficulty arose from the impression of one tabular
number on the mould being distorted by the succeeding one.</p>

<p>I was not then aware that a very slight depth of impression
from the type would be quite sufficient. I surmounted the
difficulty by previously passing a roller, having longitudinal
wedge-shaped projections, over the plastic material. This
formed a series of small depressions in the matrix between
each line. Thus the expansion arising from the impression
of one line partially filled up the small depression or ditch
which occurred between each successive line.</p>

<p>The various minute difficulties of this kind were successively
overcome; but subsequent experience has proved that
the depth necessary for stereotype moulds is very small, and
that even thick paper, prepared in a peculiar manner, is quite
sufficient for the purpose.</p>

<p>Another series of experiments were, however, made for the
purpose of punching the computed numbers upon copper
plate. A special machine was contrived and constructed,
which might be called a co-ordinate machine, because it
moved the copper plate and steel punches in the direction of
three rectangular co-ordinates. This machine was afterwards
found very useful for many other purposes. It was, in fact, a
general shaping machine, upon which many parts of the Difference
Engine were formed.</p>

<p>Several specimens of surface and copper-plate printing, as
well as of the copper plates, produced by these means, were
exhibited at the Exhibition of 1862.</p>

<p>I have proposed and drawn various machines for the
purpose of calculating a series of
numbers forming Tables <span class="xxpn" id="p047">{47}</span>
by means of a certain system called “The Method of Differences,”
which it is the object of this sketch to explain.</p>

<p>The first Difference Engine with which I am acquainted
comprised a few figures, and was made by myself, between
1820 and June 1822. It consisted of from six to eight
figures. A much larger and more perfect engine was sub­se­quent­ly
commenced in 1823 for the Government.</p>

<p>It was proposed that this latter Difference Engine should
have six orders of differences, each consisting of about
twenty places of figures, and also that it should print the
Tables it computed.</p>

<p>The small portion of it which was placed in the International
Exhibition of 1862 was put together nearly thirty
years ago. It was accompanied by various parts intended to
enable it to print the results it calculated, either as a single
copy on paper—or by putting together moveable types—or by
stereotype plates taken from moulds punched by the machine—or
from copper plates impressed by it. The parts necessary
for the execution of each of these processes were made,
but these were not at that time attached to the calculating
part of the machine.</p>

<p>A considerable number of the parts by which the printing
was to be accomplished, as also several specimens of portions
of tables punched on copper, and of stereotype moulds, were
exhibited in a glass case adjacent to the Engine.</p>

<div class="dsdnote">〈‘EDINBURGH REVIEW.’〉</div>

<p>In 1834 Dr. Lardner published, in the ‘Edinburgh Review,’<a class="afnanc" href="#fn12" id="fnanc12">12</a>
a very elaborate description of this portion of the machine,
in which he explained clearly the method of Differences.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc12" id="fn12">12</a>
‘Edinburgh Review,’ No. cxx., July, 1834.</p></div>

<p>It is very singular that two persons, one resident in London,
the other in Sweden, should both have been struck, on reading
this review, with the simplicity of the math­e­mat­i­cal principle
<span class="xxpn" id="p048">{48}</span>
of differences as applied to the calculation of Tables, and
should have been so fascinated with it as to have undertaken
to construct a machine of the kind.</p>

<div class="dsdnote">〈MR. DEACON—MR. SCHEUTZ.〉</div>

<p>Mr. Deacon, of Beaufort House, Strand, whose mechanical
skill is well known, made, for his own sat­is­fac­tion, a small
model of the calculating part of such a machine, which was
shown only to a few friends, and of the existence of which I
was not aware until after the Swedish machine was brought
to London.</p>

<p>Mr. Scheutz, an eminent printer at Stockholm, had far
greater difficulties to encounter. The construction of mechanism,
as well as the math­e­mat­i­cal part of the question,
was entirely new to him. He, however, undertook to make
a machine having four differences, and fourteen places of
figures, and capable of printing its own Tables.</p>

<p>After many years’ indefatigable labour, and an almost
ruinous expense, aided by grants from his Government, by
the constant assistance of his son, and by the support of
many enlightened members of the Swedish Academy, he
completed his Difference Engine. It was brought to London,
and some time afterwards exhibited at the great Exhibition
at Paris. It was then purchased for the Dudley Observatory
at Albany by an enlightened and public-spirited merchant of
that city, John F. Rathbone, Esq.</p>

<p>An exact copy of this machine was made by Messrs.
Donkin and Co., for the English Government, and is now in
use in the Registrar-General’s Department at Somerset House.
It is very much to be regretted that this specimen of English
workmanship was not exhibited in
the International Exhibition.</p>
</div><!--section-->

<div class="section">
<div class="xxpn" id="p049">{49}</div>
<h3 class="h3herein"><i>Explanation of the Difference Engine.</i></h3>

<p>Those who are only familiar with ordinary arithmetic may,
by following out with the pen some of the examples which
will be given, easily make themselves acquainted with the
simple principles on which the Difference Engine acts.</p>

<div class="dsdnote">〈ARITHMETICAL TABLES.〉</div>

<p>It is necessary to state distinctly at the outset, that the Difference
Engine is not intended to answer special questions. Its object is to
calculate and print a <i>series</i> of results formed according to given
laws. These are called Tables—many such are in use in various trades.
For example—there are collections of Tables of the amount of any
number of pounds from 1 to 100 lbs. of butchers’ meat at various prices
per lb. Let us examine one of these Tables: viz.—the price of meat
5&#x200a;<i>d.</i> per lb., we find</p>

<div class="dtablebox">
<table summary="">
<tr>
 <th class="tdcntr" rowspan="2" scope="col">Number.<br />Lbs.</th>
 <th class="tdcntr" colspan="2" scope="colgroup">Table.<br />Price.</th></tr>
<tr>
 <th class="tdcntr" scope="col"><i>s.</i></th>
 <th class="tdcntr" scope="col"><i>d.</i></th></tr>
<tr>
 <td class="tdcntr">1</td>
 <td class="tdcntr">0</td>
 <td class="tdcntr">&#x2007;5</td></tr>
<tr>
 <td class="tdcntr">2</td>
 <td class="tdcntr">0</td>
 <td class="tdcntr">10</td></tr>
<tr>
 <td class="tdcntr">3</td>
 <td class="tdcntr">1</td>
 <td class="tdcntr">&#x2007;3</td></tr>
<tr>
 <td class="tdcntr">4</td>
 <td class="tdcntr">1</td>
 <td class="tdcntr">&#x2007;8</td></tr>
<tr>
 <td class="tdcntr">5</td>
 <td class="tdcntr">2</td>
 <td class="tdcntr">&#x2007;1</td></tr>
</table></div>

<p>There are two ways of computing this <span class="nowrap">Table:—</span></p>

<ul><li>1st. We might have multiplied the number of lbs. in each line
by 5, the price per lb., and have put down the result in <i>l.</i> <i>s.</i>
<i>d.</i>, as in the 2nd column: or,</li>

<li>2nd. We might have put down the price of 1 lb., which is
5&#x200a;<i>d.</i>, and have added five pence for each succeeding
lb.</li></ul>

<p>Let us now examine the relative advantages of each plan.
We shall find that if we had multiplied each number
of lbs. in <span class="xxpn" id="p050">{50}</span>
the Table by 5, and put down the resulting amount, then
every number in the Table would have been computed independently.
If, therefore, an error had been committed, it
would not have affected any but the single tabular number at
which it had been made. On the other hand, if a single
error had occurred in the system of computing by adding five
at each step, any such error would have rendered the whole
of the rest of the Table untrue.</p>

<div class="dsdnote">〈DIFFERENCES.〉</div>

<p>Thus the system of calculating by differences, which is the
easiest, is much more liable to error. It has, on the other
hand, this great advantage: viz., that when the Table has
been so computed, if we calculate its last term directly, and
if it agree with the last term found by the continual addition
of 5, we shall then be quite certain that every term throughout
is correct. In the system of computing each term
directly, we possess no such check upon our accuracy.</p>

<p>Now the Table we have been considering is, in fact, merely
a Table whose first difference is constant and equal to five.
If we express it in pence it <span class="nowrap">becomes—</span></p>

<div class="dtablebox">
<table summary="">
<tr>
 <th class="tdcntr" scope="col" title="number of lbs."></th>
 <th class="tdcntr" scope="col">Table.</th>
 <th class="tdcntr" scope="col">1st&nbsp;Dif-<br />ference.</th></tr>
<tr>
 <td class="tdcntr">1</td>
 <td class="tdcntr">&#x2007;5</td>
 <td class="tdcntr">5</td></tr>
<tr>
 <td class="tdcntr">2</td>
 <td class="tdcntr">10</td>
 <td class="tdcntr">5</td></tr>
<tr>
 <td class="tdcntr">3</td>
 <td class="tdcntr">15</td>
 <td class="tdcntr">5</td></tr>
<tr>
 <td class="tdcntr">4</td>
 <td class="tdcntr">20</td>
 <td class="tdcntr">5</td></tr>
<tr>
 <td class="tdcntr">5</td>
 <td class="tdcntr">25</td>
 <td class="tdcntr"></td></tr>
</table></div>

<p class="pcontinue">Any machine, therefore, which could add one number to
another, and at the same time retain the original number
called the first difference for the next operation, would be
able to compute all such Tables.</p>
</div><!--section-->

<div class="section">
<div class="dsdnote">〈GROUPS OF MARBLES.〉</div>

<p>Let us now consider another form of Table which might readily occur
to a boy playing with his marbles, or to a young lady with the balls of
her solitaire board. <span class="xxpn" id="p051">{51}</span></p>

<p>The boy may place a row of his marbles on the sand, at
equal distances from each other, <span class="nowrap">thus—</span></p>

<div class="dctr01"><img src="images/i051a.jpg"
width="600" height="19" alt="" /></div>

<p class="pcontinue">He might then, beginning with the second, place two other
marbles under each, <span class="nowrap">thus—</span></p>

<div class="dctr01"><img src="images/i051b.jpg"
width="600" height="34" alt="" /></div>

<p class="pcontinue">He might then, beginning with the third, place three other
marbles under each group, and so on; commencing always
one group later, and making the addition one marble more
each time. The several groups would stand thus
<span class="nowrap">arranged—</span></p>

<div class="dctr01"><img src="images/i051c.jpg"
width="600" height="74" alt="" /></div>

<p>He will not fail to observe that he has thus formed a series
of triangular groups, every group having an equal number of
marbles in each of its three sides. Also that the side of each
successive group contains one more marble than that of its
preceding group.</p>

<p>Now an inquisitive boy would naturally count the numbers
in each group and he would find them <span class="nowrap">thus—</span></p>

<div>1 <span class="sppla">3</span>
<span class="sppla">6</span>
<span class="sppla">10</span>
<span class="sppla">15</span>
<span class="sppla">21</span>
</div>

<p>He might also want to know how many marbles the thirtieth or any
other distant group might contain. Perhaps he might go to papa to
obtain this information; but I much fear papa would snub him, and would
tell him that it was nonsense—that it was useless—that nobody knew the
number, and so forth. If the boy is told by papa, that he is not able
to answer the question, then I recommend him to pay careful attention
to whatever that father may at any time say, for he has overcome
two of the greatest obstacles to the acquisition <span class="xxpn"
id="p052">{52}</span> of knowledge—inasmuch as he possesses the
consciousness that he does not know—and he has the moral courage to
avow it.<a class="afnanc" href="#fn13" id="fnanc13">13</a></p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel"
href="#fnanc13" id="fn13">13</a> The most remarkable instance I ever
met with of the distinctness with which any individual perceived
the exact boundary of his own knowledge, was that of the late Dr.
Wollaston.</p></div>

<p>If papa fail to inform him, let him go to mamma, who will
not fail to find means to satisfy her darling’s curiosity. In the
meantime the author of this sketch will endeavour to lead his
young friend to make use of his own common sense for the
purpose of becoming better acquainted with the triangular
figures he has formed with his marbles.</p>

<div class="dsdnote">〈SECOND DIFFERENCE CONSTANT.〉</div>

<p>In the case of the Table of the price of butchers’ meat, it
was obvious that it could be formed by adding the same <i>constant</i>
difference continually to the first term. Now suppose
we place the numbers of our groups of marbles in a column,
as we did our prices of various weights of meat. Instead of
adding a certain difference, as we did in the former case, let
us subtract the figures representing each group of marbles
from the figures of the succeeding group in the Table. The
process will stand <span class="nowrap">thus:—</span></p>

<div class="dtablebox">
<table class="fsz7 borall" summary="">
<tr>
 <th class="thcntr" scope="col" rowspan="2">Number of the Group.</th>
 <th class="thcntr" scope="col">Table.</th>
 <th class="thcntr" scope="col">1st Difference.</th>
 <th class="thcntr" scope="col" rowspan="2">2nd Difference.</th></tr>
<tr>
 <th class="thcntr" scope="col">Number of Marbles in each Group.</th>
 <th class="thcntr" id="idth-52" scope="col">Dif­fer­ence
 be­tween the num­ber of Mar­bles in each
 Group and that in the next.</th></tr>
<tr>
 <td class="tdcntr">1</td>
 <td class="tdcntr">&#x2007;1</td>
 <td class="tdcntr">1</td>
 <td class="tdcntr">1</td></tr>
<tr>
 <td class="tdcntr">2</td>
 <td class="tdcntr">&#x2007;3</td>
 <td class="tdcntr">2</td>
 <td class="tdcntr">1</td></tr>
<tr>
 <td class="tdcntr">3</td>
 <td class="tdcntr">&#x2007;6</td>
 <td class="tdcntr">3</td>
 <td class="tdcntr">1</td></tr>
<tr>
 <td class="tdcntr">4</td>
 <td class="tdcntr">10</td>
 <td class="tdcntr">4</td>
 <td class="tdcntr">1</td></tr>
<tr>
 <td class="tdcntr">5</td>
 <td class="tdcntr">15</td>
 <td class="tdcntr">5</td>
 <td class="tdcntr">1</td></tr>
<tr>
 <td class="tdcntr">6</td>
 <td class="tdcntr">21</td>
 <td class="tdcntr">6</td>
 <td class="tdcntr"></td></tr>
<tr>
 <td class="tdcntr">7</td>
 <td class="tdcntr">28</td>
 <td class="tdcntr">7</td>
 <td class="tdcntr"></td></tr>
</table></div>

<p class="pcontinue">It is usual to call the third column thus formed
<i>the column of</i> <span class="xxpn" id="p053">{53}</span> <i>first
dif­fer­ences</i>. It is evident in the present instance that that column
represents the natural numbers. But we already know that the first
difference of the natural numbers is constant and equal to unity.
It appears, therefore, that a Table of these numbers, representing
the group of marbles, might be constructed to any extent by mere
addition—using the number 1 as the first number of the Table, the
number 1 as the first Difference, and also the number 1 as the second
Difference, which last always remains constant.</p>

<p>Now as we could find the value of any given number of
pounds of meat directly, without going through all the previous
part of the Table, so by a somewhat different rule we
can find at once the value of any group whose number is
given.</p>

<p>Thus, if we require the number of marbles in the fifth
group, proceed <span class="nowrap">thus:—</span></p>

<div class="dtablebox">
<table summary="">
<tr>
 <th class="tdleft" scope="row">Take the number of the group</th>
 <td><p class="tdpright">5</p></td></tr>
<tr>
 <th class="tdleft" scope="row">Add 1 to this number, it becomes</th>
 <td><p class="tdpright">6</p></td></tr>
<tr>
 <th class="tdleft" scope="row">Multiply these numbers together</th>
 <td class="bor13"><p class="tdpright">2)30</p></td></tr>
<tr>
 <th class="tdleft" scope="row">Divide the product by 2</th>
 <td><p class="tdpright">15</p></td></tr>
<tr>
 <th class="tdleft" colspan="2" scope="row">This gives 15, the number of
 marbles<br /> in the 5th group.</th></tr>
</table></div>

<p>If the reader will take the trouble to calculate with his
pencil the five groups given above, he will soon perceive
the general truth of this rule.</p>

<p>We have now arrived at the fact that this Table—like that
of the price of butchers’ meat—can be calculated by two
different methods. By the first, each number of the Table is
calculated independently: by the second, the truth of each
number depends upon the truth of all the previous numbers.</p>

<div class="dsdnote">〈TRIANGULAR NUMBERS.〉</div>

<p>Perhaps my young friend may now ask me, What is the
use of such Tables? Until he has advanced
further in his <span class="xxpn" id="p054">{54}</span>
arithmetical studies, he must take for granted that they are
of some use. The very Table about which he has been reasoning
possesses a special name—it is called a Table of Triangular
Numbers. Almost every general collection of Tables
hitherto published contains portions of it of more or less extent.</p>

<p>Above a century ago, a volume in small quarto, containing the
first 20,000 triangular numbers, was published at the Hague by E.
De Joncourt, A.M., and Professor of Philosophy.<a class="afnanc"
href="#fn14" id="fnanc14">14</a> I cannot resist quoting the author’s
enthusiastic expression of the happiness he enjoyed in composing his
celebrated work:</p>

<div class="dblockquote">
<p>“The Trigonals here to be found, and nowhere else, are
exactly elaborate. Let the candid reader make the best
of these numbers, and feel (if possible) in perusing my work
the pleasure I had in composing it.</p>

<p>“That sweet joy may arise from such contemplations
cannot be denied. Numbers and lines have many charms,
unseen by vulgar eyes, and only discovered to the unwearied
and respectful sons of Art. In features the serpentine line
(who starts not at the name) produces beauty and love; and
in numbers, high powers, and humble roots, give soft delight.</p>

<p>“Lo! the raptured arithmetician! Easily satisfied, he
asks no Brussels lace, nor a coach and six. To calculate,
contents his liveliest desires, and obedient numbers are
within his reach.”</p></div>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc14" id="fn14">14</a>
‘On the Nature and Notable Use of the most Simple Trigonal
Numbers.’ By E. De Joncourt, at the Hague. 1762.</p></div>

<div class="dsdnote">〈SQUARE NUMBERS.〉</div>

<p>I hope my young friend is acquainted with the fact—that
the product of any number multiplied by itself is called the
square of that number. Thus 36 is the product of 6 multiplied
by 6, and 36 is called the square of 6. I would now
recommend him to examine the series of square numbers</p>

<div>1, 4, 9, 16, 25, 36, 49, 64, &amp;c.,</div>

<p class="pcontinue"><span class="xxpn" id="p055">{55}</span> and to
make, for his own in­struc­tion, the series of their first and second
differences, and then to apply to it the same reasoning which has been
already applied to the Table of Triangular Numbers.</p>

<div class="dsdnote">〈CANNON BALLS.〉</div>

<p>When he feels that he has mastered that Table, I shall be
happy to accompany mamma’s darling to Woolwich or to
Portsmouth, where he will find some practical illustrations of
the use of his newly-acquired numbers. He will find scattered
about in the Arsenal various heaps of cannon balls,
some of them triangular, others square or oblong pyramids.</p>

<p>Looking on the simplest form—the triangular pyramid—he
will observe that it exactly represents his own heaps of
marbles placed each successively above one another until the
top of the pyramid contains only a single ball.</p>

<p>The new series thus formed by the addition of his own
triangular numbers <span class="nowrap">is—</span></p>

<div class="dtablebox">
<table summary="">
<tr>
 <th scope="col">Number.</th>
 <th scope="col">Table.</th>
 <th scope="col">1st Dif-<br />ference.</th>
 <th scope="col">2nd Dif-<br />ference.</th>
 <th scope="col">3rd Dif-<br />ference.</th></tr>
<tr>
 <td class="tdcntr">1</td>
 <td class="tdcntr">&#x2007;1</td>
 <td class="tdcntr">&#x2007;3</td>
 <td class="tdcntr">3</td>
 <td class="tdcntr">1</td></tr>
<tr>
 <td class="tdcntr">2</td>
 <td class="tdcntr">&#x2007;4</td>
 <td class="tdcntr">&#x2007;6</td>
 <td class="tdcntr">4</td>
 <td class="tdcntr">1</td></tr>
<tr>
 <td class="tdcntr">3</td>
 <td class="tdcntr">10</td>
 <td class="tdcntr">10</td>
 <td class="tdcntr">5</td>
 <td class="tdcntr">1</td></tr>
<tr>
 <td class="tdcntr">4</td>
 <td class="tdcntr">20</td>
 <td class="tdcntr">15</td>
 <td class="tdcntr">6</td>
 <td></td></tr>
<tr>
 <td class="tdcntr">5</td>
 <td class="tdcntr">35</td>
 <td class="tdcntr">21</td>
 <td></td>
 <td></td></tr>
<tr>
 <td class="tdcntr">6</td>
 <td class="tdcntr">56</td>
 <td></td>
 <td></td>
 <td></td></tr>
</table></div>

<p>He will at once perceive that this Table of the number of
cannon balls contained in a triangular pyramid can be carried
to any extent by simply adding successive differences,
the third of which is constant.</p>

<p>The next step will naturally be to inquire how any number
in this Table can be calculated by itself. A little consideration
will lead him to a fair guess; a little industry will
enable him to confirm his conjecture.</p>

<div class="dsdnote">〈NUMBER IN EACH PILE.〉</div>

<p>It will be observed at p. 49 that in
order to find <span class="xxpn" id="p056">{56}</span>
independently any number of the Table of the price of butchers’
meat, the following rule was <span class="nowrap">observed:—</span></p>

<p>Take the number whose tabular number is required.</p>

<p>Multiply it by the first difference.</p>

<p>This product is equal to the required tabular number.</p>

<p>Again, at p. 53, the rule for finding any triangular number
<span class="nowrap">was:—</span></p>

<div class="dtablebox">
<table summary="">
<tr>
 <th class="tdleft" scope="row">Take the number of the group</th>
 <td><p class="tdpright">5</p></td></tr>
<tr>
 <th class="tdleft" scope="row">Add 1 to this number, it becomes</th>
 <td><p class="tdpright">6</p></td></tr>
<tr>
 <th class="tdleft" scope="row">Multiply these numbers together</th>
 <td class="bor13"><p class="tdpright">2)30</p></td></tr>
<tr>
 <th class="tdleft" scope="row">Divide the product by 2</th>
 <td><p class="tdpright">15</p></td></tr>
</table></div>

<p>This is the number of marbles
 in the 5th group.</p>

<p>Now let us make a bold conjecture respecting the Table of
cannon balls, and try this <span class="nowrap">rule:—</span></p>

<div class="dtablebox">
<table summary="">
<tr>
 <th class="tdleft" scope="row">Take the number whose
 tabular<br /> number is required, say</th>
 <td><p class="tdpright">5</p></td></tr>
<tr>
 <th class="tdleft" scope="row">Add 1 to that number</th>
 <td><p class="tdpright">6</p></td></tr>
<tr>
 <th class="tdleft" scope="row">Add 1 more to that number</th>
 <td><p class="tdpright">7</p></td></tr>
<tr>
 <th class="tdleft" scope="row">Multiply all three numbers together</th>
 <td class="bor13"><p class="tdpright">2)210</p></td></tr>
<tr>
 <th class="tdleft" scope="row">Divide by 2</th>
 <td class="borbblk"><p class="tdpright">105</p></td></tr>
</table></div>

<p>The real number in the 5th pyramid is 35. But the
number 105 at which we have arrived is exactly three times
as great. If, therefore, instead of dividing by 2 we had
divided by 2 and also by 3, we should have arrived at a true
result in this instance.</p>

<p>The amended
rule is <span class="nowrap">therefore—</span>
<span class="xxpn" id="p057">{57}</span></p>

<div class="dtablebox">
<table summary="">
<tr>
 <th class="tdleft" scope="row">Take the number whose<br /> tabular
 number is<br /> required, say</th>
 <td><p class="tdpright"><i>n</i></p></td></tr>
<tr>
 <th class="tdleft" scope="row">Add 1 to it</th>
 <td><p class="tdpright"><i>n</i>&#x2009;+&#x202f;1</p></td></tr>
<tr>
 <th class="tdleft" scope="row">Add 1 to this</th>
 <td><p class="tdpright"><i>n</i>&#x2009;+&#x202f;2</p></td></tr>
<tr>
 <th class="tdleft" scope="row">Multiply
 these three<br /> numbers together</th>
 <td><p class="tdpright"><i>n</i>&#x2009;×&#x202f;(<i>n</i>&#x2009;+&#x202f;1)&#x2009;×&#x202f;(<i>n</i>&#x2009;+&#x202f;2)</p></td></tr>
<tr>
 <th class="tdleft" scope="row">Divide by
 1&#x2009;×&#x202f;2&#x2009;×&#x202f;3.<br />
 The result is</th>
 <td><p class="tdpright">(<i>n</i>(<i>n</i>&#x2009;+&#x202f;1)(<i>n</i>&#x2009;+&#x202f;2))/6</p></td></tr>
</table></div>

<p>This rule will, upon trial, be found to give correctly every
tabular number.</p>

<p>By similar reasoning we might arrive at the knowledge of
the number of cannon balls in square and rectangular
pyramids. But it is presumed that enough has been stated
to enable the reader to form some general notion of the
method of calculating arithmetical Tables by differences
which are constant.</p>

<div class="dsdnote">〈ASTRONOMICAL TABLES.〉</div>

<p>It may now be stated that mathematicians have discovered
that all the Tables most important for practical purposes, such
as those relating to Astronomy and Navigation, can, although
they may not possess any constant differences, still be calculated
in detached portions by that method.</p>

<p>Hence the importance of having machinery to calculate by
differences, which, if well made, cannot err; and which, if carelessly
set, presents in the last term it calculates the power of
verification of every antecedent term.</p>
</div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Of the Mechanical Arrangements necessary for computing
Tables by the Method of Differences.</i></h3>

<p>From the preceding explanation it appears that all Tables
may be calculated, to a greater or less extent, by the method
of Differences. That method requires,
for its successful <span class="xxpn" id="p058">{58}</span>
execution, little beyond mechanical means of performing the
arithmetical operation of Addition. Subtraction can, by the
aid of a well-known artifice, be converted into Addition.</p>

<div class="dsdnote">〈ADDITION.〉</div>

<p>The process of Addition includes two distinct parts—1st.
The first consists of the addition of any one digit to
another digit; 2nd. The second consists in carrying the tens
to the next digit above.</p>

<p>Let us take the case of the addition of the two following
numbers, in which no carriages <span class="nowrap">occur:—</span></p>

<ul class="ulindenta">
<li>6023</li>
<li>1970</li>
<li><span class="bor10">7993</span></li></ul>

<p>It will be observed that, in making this addition, the mind
acts by successive steps. The person adding says to <span
class="nowrap">himself—</span></p>

<ul class="ulindenta">
<li>0 and 3 make three,</li>
<li>7 and 2 make nine,</li>
<li>9 and 0 make nine,</li>
<li>1 and 6 make seven.</li>
</ul>

<div class="dsdnote">〈CARRIAGE.〉</div>

<p>In the following addition there are several
<span class="nowrap">carriages:—</span></p>

<ul class="ulindenta">
<li>2648</li>
<li>4564</li>
<li><span class="bor10">7212</span></li>
</ul>

<p>The person adding says to <span class="nowrap">himself—</span></p>

<div class="nowrap">
<div class="fsz6 pright">4 and 8 make 12: put down 2 and carry
one.</div>

<div class="fsz6 pright">1 and 6 are 7 and 4 make 11: put down 1 and
carry one.</div>

<div class="fsz6 pright">1 and 5 are 6 and 6 make 12: put down 2 and
carry one.</div>

<div class="fsz6 pright">1 and 4 are 5 and 2 make &#x2007;7: put down 7.
<span id="spp58">and carry non</span></div></div><!--nowrap-->

<p>Now, the length of time required for adding one number to
another is mainly dependent upon the number
of figures to <span class="xxpn" id="p059">{59}</span>
be added. If we could tell the average time required by
the mind to add two figures together, the time required for
adding any given number of figures to another equal number
would be found by multiplying that average time by the
number of digits in either number.</p>

<p>When we attempt to perform such additions by machinery
we might follow exactly the usual process of the human mind.
In that case we might take a series of wheels, each having
marked on its edges the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
These wheels might be placed above each other upon an axis.
The lowest would indicate the units’ figure, the next above
the tens, and so on, as in the Difference Engine at the
Exhibition, a woodcut of which faces the title-page.</p>

<p>Several such axes, with their figure wheels, might be
placed around a system of central wheels, with which the
wheels of any one or more axes might at times be made to
gear. Thus the figures on any one axis might, by means of
those central wheels, be added to the figure wheels of any
other axis.</p>

<p>But it may fairly be expected, and it is indeed of great
importance that calculations made by machinery should not
merely be exact, but that they should be done in a much
shorter time than those performed by the human mind. Suppose
there were no tens to carry, as in the first of the two
cases; then, if we possessed mechanism capable of adding any
one digit to any other in the units’ place of figures, a similar
mechanism might be placed above it to add the tens’ figures,
and so on for as many figures as might be required.</p>

<p>But in this case, since there are no carriages, each digit
might be added to its corresponding digit at the same time.
Thus, the time of adding by means of mechanism, any two
numbers, however many figures they might
consist of, would <span class="xxpn" id="p060">{60}</span>
not exceed that of adding a single digit to another digit. If
this could be accomplished it would render additions and
subtractions with numbers having ten, twenty, fifty, or any
number of figures, as rapid as those operations are with single
figures.</p>

<div class="dsdnote">〈SUCCESSIVE CARRIAGE.〉</div>

<p>Let us now examine the case in which there were several
carriages. Its successive stages may be better explained, <span
class="nowrap">thus—</span></p>

<div class="dtablebox">
<table class="tafmono" summary="">
<tr>
 <th scope="col">Stages.</th>
 <th scope="col" title="calculation"></th></tr>
<tr>
 <th class="tdleft" scope="row" title="addend"></th>
 <td>2648</td></tr>
<tr>
 <th class="tdleft" scope="row" title="addend"></th>
 <td>4584</td></tr>
<tr>
 <th class="tdleftina" scope="row">1 Add units’ figure = 4</th>
 <td class="bor10">2642</td></tr>
<tr>
 <th class="tdleftina" scope="row" rowspan="2">2 Carry</th>
 <td>&#x2007;&#x2007;1&#x2007;</td></tr>
<tr>
 <td class="bor10">2652</td></tr>
<tr>
 <th class="tdleftina" scope="row" rowspan="2">3 Add tens’ figure = 8</th>
 <td>&#x2007;&#x2007;8&#x2007;</td></tr>
<tr>
 <td class="bor10">2632</td></tr>
<tr>
 <th class="tdleftina" scope="row" rowspan="2">4 Carry</th>
 <td>&#x2007;1&#x2007;&#x2007;</td></tr>
<tr>
 <td class="bor10">2732</td></tr>
<tr>
 <th class="tdleftina" scope="row" rowspan="2">5 Add hundreds’ figure = 5</th>
 <td>&#x2007;5&#x2007;&#x2007;</td></tr>
<tr>
 <td class="bor10">2232</td></tr>
<tr>
 <th class="tdleftina" scope="row" rowspan="2">6 Carry</th>
 <td>1&#x2007;&#x2007;&#x2007;</td></tr>
<tr>
 <td class="bor10">3232</td></tr>
<tr>
 <th class="tdleftina" scope="row" rowspan="2">7 Add thousands’ figure = 4</th>
 <td>4&#x2007;&#x2007;&#x2007;</td></tr>
<tr>
 <td class="bor10">7232</td></tr>
<tr>
 <th class="tdleftina" scope="row"
 colspan="2">8 Carry 0. There is no carr.</th></tr>
</table></div><!--dtablebox-->

<p>Now if, as in this case, all the carriages were known, it would
then be possible to make all the additions of digits at the same
time, provided we could also record each carriage as it became
due. We might then complete the addition by adding, at the same
instant, each carriage in its proper place. The process would
then stand <span class="nowrap">thus:—</span> <span class="xxpn"
id="p061">{61}</span></p>

<div class="dtablebox">
<table class="tafmono" summary="">
<tr>
 <th class="tdleft" scope="col">Stages</th>
 <th scope="col" title="calculation"></th>
 <th scope="col" title="comment"></th></tr>
<tr>
 <th class="tdleft" scope="col" title="addend"></th>
 <td scope="col">2648</td>
 <td class="tdleft" scope="col"></td></tr>
<tr>
 <th class="tdleft" scope="row" title="addend"></th>
 <td>4564</td>
 <td class="tdleft"></td></tr>
<tr>
 <th class="tdleftina tdmid" rowspan="2" scope="row">1</th>
 <td class="bor10">6102</td>
 <td class="tdleft">Add each digit to the digit above.</td></tr>
<tr>
 <td>111&#x2007;</td>
 <td class="tdleft">Record the carriages.</td></tr>
<tr>
 <th class="tdleftina tdmid" scope="row">2</th>
 <td class="bor10">7212</td>
 <td class="tdleft">Add the above carriages.</td></tr>
</table></div><!--dtablebox-->

<p>Now, whatever mechanism is contrived for adding any one
digit to any other must, of course, be able to add the largest
digit, nine, to that other digit. Supposing, therefore, one
unit of number to be passed over in one second of time, it is
evident that any number of pairs of digits may be added
together in nine seconds, and that, when all the consequent
carriages are known, as in the above case, it will cost one
second more to make those carriages. Thus, addition and
carriage would be completed in ten seconds, even though the
numbers consisted each of a hundred figures.</p>

<p>But, unfortunately, there are multitudes of cases in which
the carriages that become due are only known in successive
periods of time. As an example, add together the two following
<span class="nowrap">numbers:—</span></p>

<div class="dtablebox">
<table class="tafmono" summary="">
<tr>
 <th scope="col">Stages</th>
 <th scope="col"></th></tr>
<tr>
 <th class="tdleft" scope="row" title="addend"></th>
 <td>&#x2007;8473</td></tr>
<tr>
 <th class="tdleft" scope="row" title="addend"></th>
 <td>&#x2007;1528</td></tr>
<tr>
 <th class="tdleftina" scope="row">1 Add all the digits</th>
 <td class="bor10">&#x2007;9991</td></tr>
<tr>
<th class="tdleftina" scope="row" rowspan="2">2 Carry on tens and warn
 next car.</th>
 <td>&#x2007;&#x2007;&#x2007;1&#x2007;</td></tr>
<tr>
 <td class="bor10">&#x2007;9901</td></tr>
<tr>
 <th class="tdleftina" scope="row" rowspan="2">3 Carry on hundreds,
 and ditto</th>
 <td>&#x2007;&#x2007;1&#x2007;&#x2007;</td></tr>
<tr>
 <td class="bor10">&#x2007;9001</td></tr>
<tr>
 <th class="tdleftina" scope="row" rowspan="2">4 Carry on thousands,
 and ditto</th>
 <td>&#x2007;1&#x2007;&#x2007;&#x2007;</td></tr>
<tr>
 <td class="bor10">00001</td></tr>
<tr>
 <th class="tdleftina" scope="row" rowspan="2">5 Carry on ten thousands</th>
 <td>1&#x2007;&#x2007;&#x2007;&#x2007;</td></tr>
<tr>
 <td class="bor10">10001</td></tr>
</table></div><!--dtablebox-->

<div><span class="xxpn" id="p062">{62}</span></div>

<p>In this case the carriages only become known successively,
and they amount to the number of figures to be added; consequently,
the mere addition of two numbers, each of fifty
places of figures, would require only nine seconds of time,
whilst the possible carriages would consume fifty seconds.</p>

<p>The mechanical means I employed to make these carriages
bears some slight analogy to the operation of the faculty of
memory. A toothed wheel had the ten digits marked upon
its edge; between the nine and the zero a projecting tooth
was placed. Whenever any wheel, in receiving addition,
passed from nine to zero, the projecting tooth pushed over a
certain lever. Thus, as soon as the nine seconds of time required
for addition were ended, every carriage which had
<i>become due</i> was indicated by the altered position of its lever.
An arm now went round, which was so contrived that the
act of replacing that lever caused the carriage which its
position indicated to be made to the next figure above.
But this figure might be a nine, in which case, in passing to
zero, it would put over its lever, and so on. By placing the
arms spirally round an axis, these successive carriages were
accomplished.</p>

<p>Multitudes of contrivances were designed, and almost
endless drawings made, for the purpose of economizing the
time and simplifying the mechanism of carriage. In that
portion of the Difference Engine in the Exhibition of 1862
the time of carriage has been reduced to about one-fourth
part of what was at first required.</p>

<div class="dsdnote">〈ANTICIPATING CARRIAGE.〉</div>

<p>At last having exhausted, during years of labour, the
principle of successive carriages, it occurred to me that it
might be possible to teach mechanism to accomplish another
mental process, namely—to foresee. This idea occurred to
me in October, 1834. It cost me much
thought, but the <span class="xxpn" id="p063">{63}</span>
principle was arrived at in a short time. As soon as that was
attained, the next step was to teach the mechanism which
could foresee to act upon that foresight. This was not so
difficult: certain mechanical means were soon devised which,
although very far from simple, were yet sufficient to dem­on­strate
the possibility of constructing such machinery.</p>

<p>The process of simplifying this form of carriage occupied
me, at intervals, during a long series of years. The demands
of the Analytical Engine, for the mechanical execution of
arithmetical operations, were of the most extensive kind.
The multitude of similar parts required by the Analytical
Engine, amounting in some instances to upwards of fifty
thousand, rendered any, even the simplest, improvement of
each part a matter of the highest importance, more especially
as regarded the diminished amount of expenditure for its
construction.</p>
</div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Description of the existing portion of Difference
Engine No. 1.</i></h3>

<p>That portion of Difference Engine, No. 1, which during the
last twenty years has been in the museum of King’s College,
at Somerset House, is represented in the woodcut opposite
the title page.</p>

<p>It consists of three columns; each column contains six
cages; each cage contains one figure-wheel.</p>

<p>The column on the right hand has its lowest figure-wheel
covered by a shade which is never removed, and to which the
reader’s attention need not be directed.</p>

<p>The figure-wheel next above may be placed by hand at any
one of the ten digits. In the woodcut it stands at zero.</p>

<p>The third, fourth, and fifth cages are exactly the same as
the second.</p>

<p>The sixth cage contains exactly the same as
the four just <span class="xxpn" id="p064">{64}</span>
described. It also contains two other figure-wheels, which
with a similar one above the frame, may also be dismissed
from the reader’s attention. Those wheels are entirely unconnected
with the moving part of the engine, and are only
used for memoranda.</p>

<p>It appears, therefore, that there are in the first column on
the right hand five figure-wheels, each of which may be set
by hand to any of the figures 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.</p>

<p>The lowest of these figure-wheels represents the unit’s
figure of any number; the next above the ten’s figure, and so
on. The highest figure-wheel will therefore represent tens
of thousands.</p>

<p>Now, as each of these figure-wheels may be set by hand to
any digit, it is possible to place on the first column any
number up to 99999. It is on these wheels that the Table
to be calculated by the engine is expressed. This column is
called the Table column, and the axis of the wheels the Table
axis.</p>

<p>The second or middle column has also six cages, in each of
which a figure-wheel is placed. It will be observed that in
the lowest cage, the figure on the wheel is concealed by a
shade. It may therefore be dismissed from the attention.
The five other figure-wheels are exactly like the figure-wheels
on the Table axis, and can also represent any number up to
99999.</p>

<p>This column is called the First Difference column, and the
axis is called the First Difference axis.</p>

<p>The third column, which is that on the left hand, has also
six cages, in each of which is a figure-wheel capable of being
set by hand to any digit.</p>

<p>The mechanism is so contrived that whatever may be the
numbers placed respectively on the figure-wheels
of each of <span class="xxpn" id="p065">{65}</span>
the three columns, the following succession of operations will
take place as long as the handle is <span class="nowrap">moved:—</span></p>

<ul><li>1st. Whatever number is found upon the column of first
differences will be added to the number found upon the
Table column.</li>

<li>2nd. The same first difference remaining upon its own
column, the number found upon the column of second differences
will be added to that first difference.</li></ul>

<p>It appears, therefore, that with this small portion of the
Engine any Table may be computed by the method of differences,
provided neither the Table itself, nor its first and second
differences, exceed five places of figures.</p>

<p>If the whole Engine had been completed it would have had
six orders of differences, each of twenty places of figures,
whilst the three first columns would each have had half a
dozen additional figures.</p>

<p>This is the simplest explanation of that portion of the
Difference Engine No. 1, at the Exhibition of 1862. There
are, however, certain modifications in this fragment which
render its exhibition more instructive, and which even give a
mechanical insight into those higher powers with which I had
endowed it in its complete state.</p>

<p>As a matter of convenience in exhibiting it, there is an
arrangement by which the <i>three</i> upper figures of the second
difference are transformed into a small engine which counts
the natural numbers.</p>

<p>By this means it can be set to compute any Table whose
second difference is constant and less than 1000, whilst at the
same time it thus shows the position in the Table of each
tabular number.</p>

<p>In the existing portion there are three bells; they can be
respectively ordered to ring when the Table,
its first difference <span class="xxpn" id="p066">{66}</span>
and its second difference, pass from positive to negative.
Several weeks after the machine had been placed in my drawing-room,
a friend came by appointment to test its power of
calculating Tables. After the Engine had computed several
Tables, I remarked that it was evidently finding the root of a
quadratic equation; I therefore set the bells to watch it.
After some time the proper bell sounded twice, indicating,
and giving the two positive roots to be 28 and 30. The Table
thus calculated related to the barometer and really involved a
quadratic equation, although its maker had not previously
observed it. I afterwards set the Engine to tabulate a formula
containing impossible roots, and of course the other
bell warned me when it had attained those roots. I had
never before used these bells, simply because I did not think
the power it thus possessed to be of any practical utility.</p>

<p>Again, the lowest cages of the Table, and of the first difference,
have been made use of for the purpose of illustrating
three important faculties of the finished engine.</p>

<ul><li>1st. The portion exhibited can calculate any Table whose
third difference is constant and less than 10.</li>

<li>2nd. It can be used to show how much more rapidly astronomical
Tables can be calculated in an engine in which there
is no constant difference.</li>

<li>3rd. It can be employed to illustrate those singular laws
which might continue to be produced through ages, and yet
after an enormous interval of time change into other different
laws; each again to exist for ages, and then to be
superseded by new laws. These views were first proposed in
the “Ninth Bridgewater Treatise.”</li></ul>

<div class="dsdnote">〈CURIOUS QUESTIONS.〉</div>

<p>Amongst the various questions which have been asked
respecting the Difference Engine, I will mention a few of
the most remarkable:—One gentleman
addressed me thus: <span class="xxpn" id="p067">{67}</span>
“Pray, Mr. Babbage, can you explain to me in two words
what is the principle of this machine?” Had the querist
possessed a moderate acquaintance with mathematics I might
in four words have conveyed to him the required information
by answering, “The method of differences.” The question
might indeed have been answered with six characters
<span class="nowrap">thus—</span></p>

<div>
Δ<sup>7</sup>&#x200a;<i>u</i><sub><i>x</i></sub> = 0.
</div>

<p class="pcontinue">but such information would have been
unintelligible to such inquirers.</p>

<p>On two occasions I have been asked,—“Pray, Mr. Babbage,
if you put into the machine wrong figures, will the right
answers come out?” In one case a member of the Upper,
and in the other a member of the Lower, House put this
question. I am not able rightly to apprehend the kind of
confusion of ideas that could provoke such a question. I did,
however, explain the following property, which might in some
measure approach towards an answer to it.</p>

<p>It is possible to construct the Analytical Engine in such a
manner that after the question is once communicated to the
engine, it may be stopped at any turn of the handle and set
on again as often as may be desired. At each stoppage every
figure-wheel throughout the Engine, which is capable of being
moved without breaking, may be moved on to any other
digit. Yet after each of these apparent falsifications the
engine will be found to make the next calculation with
perfect truth.</p>

<p>The explanation is very simple, and the property itself
useless. The whole of the mechanism ought of course to be
enclosed in glass, and kept under lock and key, in which case
the mechanism necessary to give it the property alluded to
would be useless.</p>
</div><!--section-->

<div class="section" id="p068">
<h2 class="h2herein">CHAPTER VI.</h2>

<div class="fsz7">Statement relative to the Difference Engine, drawn up
by the late Sir H. Nicolas from the Author’s Papers.</div>

<p class="pfirst"><span class="smcap">T<b>HE</b></span>
following statement was drawn up by the late Sir
Harris Nicolas, G.S.M.&#x202f;&amp;&#x202f;G., from papers and documents in
my possession relating to the Difference Engine. I believe
every paper I possessed at all bearing on the subject was in
his hands for several months.</p>

<hr class="hrblk" />

<p>For
some time previous to 1822, Mr. Babbage had been
engaged in contriving machinery for the execution of extensive
arithmetical operations, and in devising mechanism by
which the machine that made the calculations might also
print the results.</p>

<p>On the 3rd of July, 1822, he published a letter to Sir
Humphry Davy, President of the Royal Society, containing
a statement of his views on that subject; and more par­tic­u­lar­ly
describing an Engine for calculating astronomical, nautical,
and other Tables, by means of the “method of differences.”
In that letter it is stated that a small Model, consisting
of six figures, and capable of working two orders of
differences, had been constructed; and that it performed its
work in a sat­is­fac­tory manner.</p>

<p>The concluding paragraph of that letter is as <span class="nowrap">follows:—</span></p>

<div class="dblockquote">
<p>“Whether I shall construct a larger Engine of this kind,
and bring to <span class="xxpn" id="p069">{69}</span>
perfection the others I have described, will, in a great measure, depend on
the nature of the encouragement I may receive.</p>

<p>“Induced, by a conviction of the great utility of such Engines, to withdraw,
for some time, my attention from a subject on which it has been
engaged during several years, and which possesses charms of a higher order,
I have now arrived at a point where success is no longer doubtful. It
must, however, be attained at a very considerable expense, which would not
probably be replaced, by the works it might produce, for a long period of
time; and which is an undertaking I should feel unwilling to commence,
as altogether foreign to my habits and pursuits.”</p></div>

<p>The Model alluded to had been shown to a large number
of Mr. Babbage’s acquaintances, and to many other persons;
and copies of his letter having been given to several of his
friends, it is probable that one of the copies was sent to the
Treasury.</p>

<p>On the 1st of April, 1823, the Lords of the Treasury referred
that Letter to the Royal Society, <span class="nowrap">requesting—</span></p>

<div class="dblockquote">
<p>“The opinion of the Royal Society on the merits and utility of this
invention.”</p></div>

<p>On the 1st of May the Royal Society reported to the Treasury,
<span class="nowrap">that—</span></p>

<div class="dblockquote">
<p>“Mr. Babbage has displayed great talent and ingenuity in the construction
of his Machine for Computation, which the Committee think fully
adequate to the attainment of the objects proposed by the inventor; and
they consider Mr. Babbage as highly deserving of public encouragement,
in the prosecution of his arduous undertaking.”<a class="afnanc" href="#fn15" id="fnanc15">15</a></p></div>

<p>On the 21st of May these papers were ordered to be printed
by the House of Commons.</p>

<p>In July, 1823, Mr. Babbage had an interview with the
Chancellor of the Exchequer (Mr.
Robinson<a class="afnanc" href="#fn16" id="fnanc16">16</a>&#x202f;), to ascertain if
it was the wish of the Government that he should construct a
large Engine of the kind, which would also print the results
it calculated. <span class="xxpn" id="p070">{70}</span></p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc15" id="fn15">15</a>
Parliamentary Paper, No. 370, printed 22nd May, 1823.</p>

<p class="pfirst padtopc"><a class="afnlabel" href="#fnanc16" id="fn16">16</a>
Afterwards Lord Goderich, now Earl of Ripon.</p></div>

<p>From the conversation which took place on that occasion,
Mr. Babbage apprehended that such was the wish of the Government.
The Chancellor of the Exchequer remarked that
the Government were in general unwilling to make grants of
money for any inventions, however meritorious; because, if
they really possessed the merit claimed for them, the sale of
the article produced would be the best, as well as largest
reward of the inventor: but that the present case was an
<i>exception</i>; it being apparent that the construction of such a
Machine could not be undertaken with a view to profit from
the sale of its produce; and that, as math­e­mat­i­cal Tables
were peculiarly valuable for nautical purposes, it was deemed
a fit object of encouragement by the Government.</p>

<p>The Chancellor of the Exchequer mentioned two modes of
advancing money for the construction:—either through the
recommendation of a Committee of the House of Commons,
or by taking a sum from the Civil Contingencies: and he observed
that, as the Session of Parliament was near its termination,
the latter course might, perhaps, be the most convenient.</p>

<p>Mr. Babbage thinks the Chancellor of the Exchequer also
made some ob­ser­va­tion, indicating that the amount of money
taken from the Civil Contingencies would be smaller than
that which might be had by means of a Committee of the
House of Commons: and he then proposed to take 1,000&#x200a;<i>l.</i> as
a commencement from the Civil Contingencies Fund. To this
Mr. Babbage replied, in words which he distinctly remembers,
“Would it be too much, in the first instance, to take 1,500&#x200a;<i>l.</i>?”
The Chancellor of the Exchequer immediately answered, that
1,500&#x200a;<i>l.</i> should be advanced.</p>

<p>Mr. Babbage’s opinion at that time was, that the Engine
would be completed in two, or at the most in three years;
and that by having 1,500&#x200a;<i>l.</i> in the first instance,
he would be <span class="xxpn" id="p071">{71}</span>
enabled to advance, from his own private funds, the residue
of the 3,000&#x200a;<i>l.</i>, or even 5,000&#x200a;<i>l.</i>, which he then imagined the
Engine might possibly cost; so that he would not again have
occasion to apply to Government until it was completed.
Some ob­ser­va­tions were made by the Chancellor of the Exchequer
about the mode of accounting for the money received,
as well as about its expenditure; but it seemed to be admitted
that it was not possible to prescribe any very definite
system, and that much must be left to Mr. Babbage’s own
judgment.</p>

<p>Very unfortunately, no Minute of that conversation was
made at the time, nor was any sufficiently distinct understanding
between the parties arrived at. Mr. Babbage’s conviction
was, that whatever might be the labour and difficulty
of the undertaking, the Engine itself would, of course, become
the property of the Government, which had paid for its
construction.</p>

<p>Soon after this interview with the Chancellor of the
Exchequer, a letter was sent from the Treasury to the Royal
Society, informing that body that the Lords of the Treasury</p>

<div class="dblockquote">
<p>“Had directed the issue of 1,500&#x200a;<i>l.</i> to Mr. Babbage, to enable him to bring
his invention to perfection, in the manner recommended.”</p></div>

<p>These latter words, “<i>in the manner recommended</i>,” can only
refer to the previous recommendation of the Royal Society;
but it does not appear, from the Report of the Royal Society,
that <i>any plan</i>, <i>terms</i>, or <i>conditions</i> had been pointed out by
that body.</p>

<p>Towards the end of July, 1823, Mr. Babbage took measures for
the construction of the present <i>Difference Engine</i>,* and it
was regularly proceeded with for four years. <span class="xxpn"
id="p072">{72}</span></p>

<div class="dftnt">
<p class="pfirst">* <span class="smcap">N<b>OTE.</b></span>—It will be
convenient to distinguish between—</p>
<ul>
<li>1. The small <i>Model</i> of the original or Difference Engine.</li>

<li class="padtopc">2. The <i>Difference</i> Engine itself, belonging to the Government, a part
only of which has been put together.</li>

<li class="padtopc">3. The designs for another <i>Engine</i>, which in this Statement is called
the Analytical Engine.</li>
</ul></div><!--dftnt-->

<p>In October, 1827, the expense incurred had amounted to
3,475&#x200a;<i>l.</i>; and Mr. Babbage having suffered severe domestic
affliction, and being in a very ill state of health, was recommended
by his medical advisers to travel on the Continent.
He left, however, sufficient drawings to enable the work to
be continued, and gave an order to his own banker to advance
1,000&#x200a;<i>l.</i> during his absence: he also received, from time to
time, drawings and inquiries relating to the mechanism, and
returned in­struc­tions to the engineer who was constructing it.</p>

<p>As it now appeared probable that the expense would much
exceed what Mr. Babbage had originally anticipated, he
thought it desirable to inform the Government of that fact,
and to procure a further grant. As a preliminary step, he
wrote from Italy to his brother-in-law, Mr. Wolryche Whitmore,
to request that he would see Lord Goderich upon the
subject of the interview in July, 1823; but it is probable
that he did not sufficiently inform Mr. Whitmore of all the
circumstances of the case.</p>

<p>Mr. Whitmore, having had some conversation with Lord
Goderich on the subject, addressed a letter, dated on the 29th
of February, 1828, to Mr. Babbage, who was then at Rome,
stating that</p>

<div class="dblockquote">
<p>“That interview was unsat­is­fac­tory; that Lord Goderich did not like to
admit that there was any understanding, at the time the 1,500&#x200a;<i>l.</i> was
advanced, that more would be given by Government.”</p></div>

<p>On Mr. Babbage’s return to England, towards
the end of <span class="xxpn" id="p073">{73}</span>
1828, he waited in person upon Lord Goderich, who admitted
that the understanding of 1823 was not very definite. He
then addressed a statement to the Duke of Wellington, as the
head of the Government, explaining the previous steps in the
affair; stating the reasons for his inferences from what took
place at the interview with the Chancellor of the Exchequer
in July, 1823; and referring his Grace for further information
to Lord Goderich, to whom also he sent a copy of that
statement.</p>

<p>The Duke of Wellington, in consequence of this application,
requested the Royal Society to <span class="nowrap">inquire—</span></p>

<div class="dblockquote">
<p>“Whether the progress of the Machine confirms them in their former
opinion, that it will ultimately prove adequate to the important object it
was intended to attain.”</p></div>

<p>The Royal Society reported, in February, 1829, <span class="nowrap">that—</span></p>

<div class="dblockquote">
<p>“They had not the slightest hesitation in pronouncing their decided
opinion in the affirmative.”</p></div>

<p>The Royal Society also expressed their hope <span class="nowrap">that—</span></p>

<div class="dblockquote">
<p>“Whilst Mr. Babbage’s mind is intensely occupied in an undertaking
likely to do so much honour to his country, he may be relieved, as much as
possible, from all other sources of anxiety.”</p></div>

<p>On the 28th of April, 1829, a Treasury Minute directed a
further payment to Mr. Babbage of</p>

<div class="dblockquote">
<p>“1,500&#x200a;<i>l.</i> to enable him to complete the Machine by which such important
benefit to Science might be expected.”</p></div>

<p>At that time the sum expended on the Engine amounted
to 6,697&#x200a;<i>l.</i> 12&#x200a;<i>s.</i>, of which 3,000&#x200a;<i>l.</i> had been received from the
Treasury; so that Mr. Babbage had provided 3,697&#x200a;<i>l.</i> 12&#x200a;<i>s.</i>
from his own private funds.</p>

<p>Under these circumstances, by the advice of Mr. Wolryche
Whitmore, a meeting of Mr. Babbage’s personal friends was
held on the 12th of May, 1829. It
consisted <span class="nowrap">of—</span>
<span class="xxpn" id="p074">{74}</span></p>

<ul class="ulindenta">
<li><span class="smcap">T<b>HE</b></span>
<span class="smcap">D<b>UKE</b></span>
<span class="smmaj">OF</span>
<span class="smcap">S<b>OMERSET</b>,</span></li>
<li><span class="smcap">L<b>ORD</b></span>
<span class="smcap">A<b>SHLEY</b>,</span></li>
<li><span class="smcap">S<b>IR</b></span>
<span class="smcap">J<b>OHN</b></span>
<span class="smcap">F<b>RANKLIN</b>,</span></li>
<li><span class="smcap">M<b>R.</b></span>
<span class="smcap">W<b>OLRYCHE</b></span>
<span class="smcap">W<b>HITMORE</b>,</span></li>
<li><span class="smcap">D<b>R.</b></span>
<span class="smcap">F<b>ITTON</b>,</span></li>
<li><span class="smcap">M<b>R.</b></span>
<span class="smcap">F<b>RANCIS</b></span>
<span class="smcap">B<b>AILY</b>,</span></li>
<li><span class="smcap">M<b>R.</b></span> (now
<span class="smcap">S<b>IR</b></span>
<span class="smcap">J<b>OHN</b>)</span>
<span class="smcap">H<b>ERSCHEL</b>.</span></li>
</ul>

<p>Being satisfied, upon inquiry, of the following facts, they
came to the annexed <span class="nowrap">resolutions:—</span></p>

<div class="dblockquote">
<p>“1st. That Mr. Babbage was originally induced to take up the work, on
its present extensive scale, by an understanding on his part that it was the
wish of Government that he should do so, and by an advance of 1,500&#x200a;<i>l.</i>, at
the outset; with a full impression on his mind, that such further advances
would be made as the work might require.</p>

<p>“2nd. That Mr. Babbage’s expenditure had amounted to nearly 7,000&#x200a;<i>l.</i>,
while the whole sum advanced by Government was 3,000&#x200a;<i>l.</i></p>

<p>“3rd. That Mr. Babbage had devoted the most assiduous and anxious
attention to the progress of the Engine, to the injury of his health, and the
neglect and refusal of other profitable occupations.</p>

<p>“4th. That a very large expense remained to be incurred; and that his
private fortune was not such as would justify his completing the Engine,
without further and effectual assistance from Government.</p>

<p>“5th. That a personal application upon the subject should be made to
the Duke of Wellington.</p>

<p>“6th. That if such application should be unsuccessful in procuring effectual
and adequate assistance, they must regard Mr. Babbage (considering
the great pecuniary and personal sacrifices he will then have made; the
entire expenditure of all he had received from the public on the subject
of its destination; and the moral certainty of completing it, to which it
was, by his exertions, reduced) as no longer called on to proceed with an
undertaking which might destroy his health, and injure, if not ruin, his
fortune.</p>

<p>“7th. That Mr. Wolryche Whitmore and Mr. Herschel should request
an interview with the Duke of Wellington, to state to his Grace these
opinions on the subject.”</p></div>

<p>Mr. Whitmore and Mr. Herschel accordingly had an interview
with the Duke of Wellington; and some time after they
were informed by the Chancellor of the Exchequer, to whom
they had applied for his Grace’s answer, that
the Duke of <span class="xxpn" id="p075">{75}</span>
Wellington intended to see the portion of the Engine which
had been then made.</p>

<p>In November, 1829, the Duke of Wellington, accompanied
by the Chancellor of the Exchequer (Mr. Goulburn) and
Lord Ashley, saw the <i>Model</i> of the Engine, the drawings, and
the parts in progress. On the 23rd of that month Mr. Babbage
received a note from Mr. Goulburn, dated on the 20th, informing
him that the Duke of Wellington and himself had
recommended the Treasury to make a further payment towards
the completion of the Machine; and that their Lordships
had in consequence directed a payment of 3,000&#x200a;<i>l.</i> to be
made to him. This letter also contained a suggestion about
separating the Calculating from the Printing part of the
Machine, which was repeated in the letter from the Treasury
of the 3rd of December, 1829, communicating officially the
information contained in Mr. Goulburn’s private note, and
stating that directions had been <span class="nowrap">given—</span></p>

<div class="dblockquote">
<p>“To pay to you the further sum of 3,000&#x200a;<i>l.</i>, to enable you to complete
the Machine which you have invented for the calculation of various tables;
but I have to intimate to you that, in making this additional payment, my
Lords think it extremely desirable that the Machine should be so constructed,
that, if any failure should take place in the attempt to print by
it, the calculating part of the Machine may nevertheless be perfect and
available for that object.”</p></div>

<p>Mr. Babbage inferred from this further grant, that Government
had adopted his view of the arrangement entered into
with the Chancellor of the Exchequer in July, 1823; but, to
prevent the recurrence of difficulty from any remaining indistinctness,
he wrote to Mr. Goulburn, stating that, before
he received the 3,000&#x200a;<i>l.</i>, he wished to propose some general
arrangements for expediting the completion of the Engine,
further notes of which he would shortly submit to him. On
the 25th of November, 1829, he addressed a
letter to Lord <span class="xxpn" id="p076">{76}</span>
Ashley, to be communicated to the Chancellor of the Exchequer,
stating the grounds on which he thought the following
arrangements <span class="nowrap">desirable:—</span></p>

<ul>
<li>1st. That the Engine should be considered as the property
of Government.</li>

<li>2nd. That pro­fes­sion­al engineers should be appointed by
Government to examine the charges made for the work
already executed, as well as for its future progress; and that
such charges should be defrayed by Government.</li>

<li>3rd. That under this arrangement he himself should continue
to direct the construction of the Engine, as he had
hitherto done.</li></ul>

<p>Mr. Babbage also stated that he had been obliged to suspend
the work for nearly nine months; and that such delay
risked the final completion of the Engine.</p>

<p>In reply to these suggestions, Mr. Goulburn wrote to Lord
Ashley, <span class="nowrap">stating—</span></p>

<div class="dblockquote">
<p>“That we (the Government) could not adopt the course which
Mr. Babbage had pointed out, consistently with the principle on which
we have rendered him assistance in the construction of his Machine, and
without considerable inconvenience. The view of the Government was, to
assist an able and ingenious man of science, whose zeal had induced him to
exceed the limits of prudence, in the construction of a work which would,
if successful, redound to his honour, and be of great public advantage. We
feel ourselves, therefore, under the necessity of adhering to our original
intention, as expressed in the Minute of the Treasury, which granted
Mr. Babbage the last 3,000&#x200a;<i>l.</i>, and in the letter in which I informed him
of that grant.”</p></div>

<p>Mr. Goulburn’s letter was enclosed by Lord Ashley to
Mr. Babbage, with a note, in which his Lordship observed,
with reference to Mr. Goulburn’s opinion, that it was</p>

<div class="dblockquote">
<p>“A wrong view of the position in which Mr. Babbage was placed, after
his conference with Lord Goderich—which must be explained to him
(Mr. Goulburn).” <span class="xxpn" id="p077">{77}</span></p></div>

<p>“<i>The original intention</i>” of the Government is here stated
to have been communicated to Mr. Babbage, both in the
letter from the Treasury of the 3rd of December, 1829,
granting the 3,000&#x200a;<i>l.</i>, and also in Mr. Goulburn’s private letter
of the 20th of November, 1829. These letters have been just
given; and it certainly does not appear from either of them,
that the “original intention” was then in any degree more
apparent than it was at the commencement of the undertaking
in July, 1823.</p>

<p>On the 16th of December, 1829, Mr. Babbage wrote to
Lord Ashley, observing, that Mr. Goulburn seemed to think
that he [Mr. Babbage] had commenced the machine on his own
account; and that, pursuing it zealously, he had expended
more than was prudent, and had then applied to Government
for aid. He remarked, that a reference to papers and
dates would confirm his own positive declaration, that this
was never for one moment, in <i>his</i> apprehension, the ground
on which the matter rested; and that the following facts
would prove that it was absolutely impossible it could have
been <span class="nowrap">so:—</span></p>

<ul><li>1stly. Mr. Babbage referred to the passage<a class="afnanc"
href="#fn17" id="fnanc17">17</a> (already quoted) in his letter
to Sir Humphry Davy, in which he had expressed his opinion as
<i>decidedly adverse</i> to the plan of making a larger Machine, on his own
account.</li>

<li>2ndly. Mr. Babbage stated that the small Model of the Machine seen
by the Duke of Wellington and Mr. Goulburn, was completed <i>before</i> his
interview with Lord Goderich in July, 1823; for it was alluded to in
the Report of the Royal Society, of the 1st of May, 1823.</li>

<li>3rdly. That the interview with Lord Goderich having taken
place in July, 1823; the present Machine (<i>i.e.</i> the <i>Difference</i>
<span class="xxpn" id="p078">{78}</span> Engine) was commenced
in <i>consequence</i> of that interview; and <i>after</i> Mr. Babbage had
received the first grant of 1,500&#x200a;<i>l.</i> on the 7th of August,
1823.</li></ul>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc17" id="fn17">17</a>
See page <a href="#p069" title="go to pag&#x65; 69">69</a>.</p></div>

<p>Having thus shown that the light in which Mr. Goulburn
viewed these transactions was founded on a misconception,
Mr. Babbage requested Lord Ashley to inquire whether the
facts to which he had called Mr. Goulburn’s attention might
not induce him to reconsider the subject. And in case Mr.
Goulburn should decline revising his opinion, then he
wished Lord Ashley to ascertain the opinion of Government,
upon the contingent questions which he enclosed; <span class="nowrap">viz.—</span></p>

<div class="dblockquote">
<p>1. Supposing Mr. Babbage received the 3,000&#x200a;<i>l.</i> now directed to be issued,
what are the claims which Government will have on the Engine, or on
himself?</p>

<p>2. Would Mr. Babbage owe the 6,000&#x200a;<i>l.</i>, or any part of that sum to the
Government?</p>

<p>If this question be answered in the negative,</p>

<p>3. Is the portion of the Engine now made, as completely Mr. Babbage’s
property as if it had been entirely paid for with his own money?</p>

<p>4. Is it expected by Government that Mr. Babbage should continue to
construct the Engine at his own private expense; and, if so, to what extent
in money?</p>

<p>5. Supposing Mr. Babbage should decline resuming the construction of
the Engine, to whom do the drawings and parts already made belong?</p></div>

<p>The following statement was also <span class="nowrap">enclosed:—</span></p>

<div class="dtablebox fsz6">
<table summary="">
<tr>
 <th class="tdleft" scope="row">Expenses
 up to 9th May, 1829, when the work ceased</th>
 <td class="tdleft"></td>
 <td><p class="tdpright"><a class="afnanc" href="#fn18"
 id="fnanc18">&#x2a;</a>£6,628</p></td></tr>
<tr>
 <th class="tdleft" scope="row">Two grants of
 1,500&#x200a;<i>l.</i> each, amounting
 to</th>
 <td><p class="tdpright">£3,000</p></td></tr>
<tr>
 <th class="tdleft" scope="row">By Treasury Minute,
 Nov. 1829, but not yet received</th>
 <td><p class="tdpright">3,000</p></td></tr>
<tr>
 <th class="tdleft" scope="row" title="subtotal"></th>
 <td>────</td>
 <td><p class="tdpright">6,000</p></td></tr>
<tr>
 <th class="tdleft" scope="row" title="difference"></th>
 <td></td>
 <td class="borbblk bor10"><p class="tdpright">£628</p></td></tr>
</table></div>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc18" id="fn18">&#x2a;</a>
The difference between this sum and 6,697&#x200a;<i>l.</i> 12&#x200a;<i>s.</i>
mentioned in page <a href="#p073" title="go to pag&#x65; 73">73</a>, seems to have arisen from the fact of the
former sum having included the estimated amount of a bill which, when
received, was found to be less than had been anticipated.</p></div>

<p>In January, 1830, Mr. Babbage wrote to
Lord Goderich, <span class="xxpn" id="p079">{79}</span>
stating that the Chancellor of the Exchequer (Mr. Goulburn)
would probably apply to his Lordship respecting the interview
in July, 1823. He therefore recalled some of the circumstances
attending it to Lord Goderich, and concluded
<span class="nowrap">thus:—</span></p>

<div class="dblockquote">
<p>“The matter was, as you have justly observed on another occasion, left,
in a certain measure, indefinite; and I have never contended that any
promise was made to me. My subsequent conduct was founded upon the
impression left on my mind by that interview. I always considered that,
whatever difficulties I might encounter, it could never happen that I should
ultimately suffer any pecuniary loss.</p>

<p>“I understand that Mr. Goulburn wishes to ascertain from your Lordship
whether, from the nature of that interview, it was reasonable that I should
have such expectation.”</p></div>

<p>In the mean time Mr. Babbage had encountered difficulties
of another kind. The Engineer who had been constructing
the Engine under Mr. Babbage’s direction had
delivered his bills in such a state that it was impossible to
judge how far the charges were just and reasonable; and
although Mr. Babbage had paid several thousand pounds, yet
there remained a considerable balance, which he was quite
prepared and willing to pay, as soon as the accounts should
be examined, and the charges approved of by pro­fes­sion­al
engineers.</p>

<p>The delay in deciding whether the Engine was the property
of Government, added greatly to this embarrassment.
Mr. Babbage, therefore, wrote to Lord Ashley on the 8th of
February, to mention these difficulties; and to point out the
serious inconvenience which would arise, in the future progress
of the Engine, from any dispute between the Engineer and
himself relative to payments.</p>

<p>On the 24th of February, 1830, Mr. Babbage called on
Lord Ashley, to request he would represent to the Duke of
Wellington the facts of the case, and point out
to his Grace <span class="xxpn" id="p080">{80}</span>
the importance of a decision. In the afternoon of the same
day, he again saw Lord Ashley, who communicated to him the
decision of the Government; to the following <span class="nowrap">effect:—</span></p>

<ul>
<li>1&#x200a;<i>st.</i> <i>Although the Government would not pledge themselves to</i>
<span class="smmaj">COMPLETE</span> <i>the Machine, they were willing to declare it their
property</i>.</li>

<li>2&#x200a;<i>nd.</i> <i>That pro­fes­sion­al Engineers should be appointed to examine
the bills.</i></li>

<li>3&#x200a;<i>rd.</i> <i>That the Government were willing to advance</i> 3,000&#x200a;<i>l.</i>
<i>more than the sum</i> (6,000&#x200a;<i>l.</i>) <i>already granted</i>.</li>

<li>4&#x200a;<i>th.</i> <i>That, when the Machine was completed, the Government
would be willing to attend to any claim of Mr. Babbage to
remuneration, either by bringing it before the Treasury, or the
House of Commons.</i></li></ul>

<p>Thus, after considerable discussion, the doubts arising
from the indefiniteness of the understanding with the Chancellor
of the Exchequer, in July, 1823, were at length
removed. Mr. Babbage’s impression of the original arrangement
entered into between Lord Goderich and himself was
thus formally adopted in the first three propositions: and the
Government voluntarily added the expression of their disposition
to attend to any claim of his for remuneration when the
Engine should be completed.</p>

<p>When the arrangements consequent upon this decision
were made, the work of the Engine was resumed, and continued
to advance.</p>

<p>After some time, the increasing amount of costly drawings,
and of parts of the Engine already executed, remaining
exposed to destruction from fire and from other casualties
became a source of some anxiety.</p>

<p>These facts having been represented to Lord Althorp
(then Chancellor of the Exchequer), an
experienced surveyor <span class="xxpn" id="p081">{81}</span>
was directed to find a site adapted for a building for the reception
of the Engine in the neighbourhood of Mr. Babbage’s
residence.</p>

<p>On the 19th of January the Surveyor’s reports were forwarded
to Lord Althorp (the Chancellor of the Exchequer),
who referred the case to a committee of practical Engineers
for their opinion. This committee reported strongly in favour
of the removal, on the grounds of security, and of economy
in completing the Engine; and also recommended the site
which had been previously selected by the Surveyor. The
Royal Society, also, to whom Lord Althorp had applied,
examined the question, and likewise reported strongly to the
same effect.</p>

<p>A lease of some property, adjacent to Mr. Babbage’s residence,
was therefore sub­se­quent­ly granted by him to the
Government; and a fire-proof building, capable of containing
the Engine, with its drawings, and workshops necessary for
its completion, were erected.</p>

<p>With respect to the expenses of constructing the Engine,
the following plan was agreed upon and carried out:—The
great bulk of the work was executed by the Engineer under
the direction of Mr. Babbage. When the bills were sent in,
they were immediately forwarded by him to two eminent
Engineers, Messrs. Donkin and Field, who, at the request of
Government, had undertaken to examine their accuracy.
On these gentlemen certifying those bills to be correct,
Mr. Babbage trans­mit­ted them to the Treasury; and after the
usual forms, a warrant was issued directing the payment of
the respective sums to Mr. Babbage. This course, however,
required considerable time; and the Engineer having represented
that he was unable to pay his workmen without more
immediate advances, Mr. Babbage, to
prevent delay in <span class="xxpn" id="p082">{82}</span>
completing the Engine, did himself, from time to time, advance
from his own funds several sums of money; so that he was,
in fact, usually in advance from 500&#x200a;<i>l.</i> to 1,000&#x200a;<i>l.</i> Those sums
were, of course, repaid when the Treasury warrants were
issued.</p>

<p>Early in the year 1833, an event of great importance in
the history of the Engine occurred. Mr. Babbage had
directed a portion of it, consisting of sixteen figures, to be put
together. It was capable of calculating Tables having two or
three orders of differences; and, to some extent, of forming
other Tables. The action of this portion completely justified
the expectations raised, and gave a most sat­is­fac­tory assurance
of its final success.</p>

<p>The fire-proof building and workshops having been completed,
arrangements were made for the removal of the
Engine. Mr. Babbage finding it no longer convenient to
make payments in advance, informed the Engineer that he
should in future not pay him until the money was received
from the Treasury. Upon receiving this intimation, the
Engineer immediately discontinued the construction of the
Engine, and dismissed the workmen employed on it; which fact
Mr. Babbage immediately communicated to the Treasury.</p>

<p>In this state of affairs it appeared, both to the Treasury
and to Mr. Babbage, that it would be better to complete the
removal of the drawings, and all the parts of the Engine to
the fire-proof building; and then make such arrangements between
the Treasury and the Engineer, respecting the future
payments, as might prevent further discussion on that subject.</p>

<p>After much delay and difficulty the whole of the drawings,
and parts of the Engine, were at length removed to the fire-proof
building in East-street, Manchester-square. Mr. Babbage
wrote, on the 16th of July, 1834,
to the Treasury, <span class="xxpn" id="p083">{83}</span>
informing their Lordships of the fact;—adding that no
advance had been made in its construction for above a year
and a quarter; and requesting further in­struc­tions on the
subject.</p>

<p>Mr. Babbage received a letter from the Treasury, expressing
their Lordships’ sat­is­fac­tion at learning that the drawings,
and parts of the Calculating Engine were removed to the
fire-proof building, and stating that as soon as Mr. Clement’s
Accounts should be received and examined, they would</p>

<div class="dblockquote">
<p>“Take into consideration what further proceedings may be requisite with
a view to its completion.”</p></div>

<p>A few weeks afterwards Mr. Babbage received a letter
from the Treasury, conveying their Lordships’ authority to
proceed with the construction of the Engine.</p>

<p>During the time which had elapsed since the Engineer
had ceased to proceed with the construction of the Engine,
Mr. Babbage had been deprived of the use of his own drawings.
Having, in the meanwhile, naturally speculated upon
the general principles on which machinery for calculation
might be constructed, <i>a principle of an entirely new kind</i>
occurred to him, the power of which over the most complicated
arithmetical operations seemed nearly unbounded.
On re-examining his drawings when returned to him by the
Engineer, the new principle appeared to be limited only by
the extent of the mechanism it might require. The invention
of simpler mechanical means for executing the elementary
operations of the Engine now derived a far greater importance
than it had hitherto possessed; and should such simp­li­fi­ca­tions
be discovered, it seemed difficult to anticipate, or
even to over-estimate, the vast results which might be
attained. In the Engine for calculating by differences, such
simp­li­fi­ca­tions affected only about a
hundred and twenty <span class="xxpn" id="p084">{84}</span>
similar parts, whilst in the new or <i>Analytical</i> Engine, they
would affect a great many thousand. The <i>Difference</i> Engine
might be constructed with more or less advantage by employing
various mechanical modes for the operation of
addition: the <i>Analytical</i> Engine could not <i>exist</i> without
inventing for it a method of mechanical addition possessed of
the utmost simplicity. In fact, it was not until upwards of
twenty different mechanical modes for performing the operation
of addition had been designed and drawn, that the
necessary degree of simplicity required for the Analytical
Engine was ultimately attained. Hence, therefore, the
powerful motive for simp­li­fi­ca­tion.</p>

<p>These new views acquired additional importance, from
their bearings upon the Engine already partly executed for
the Government. For, if such simp­li­fi­ca­tions should be discovered,
it might happen that the <i>Analytical</i> Engine would
execute more rapidly the calculations for which the <i>Difference</i>
Engine was intended; or, that the <i>Difference</i> Engine would
itself be superseded by a far simpler mode of construction.
Though these views might, perhaps, at that period have
appeared visionary, both have sub­se­quent­ly been completely
realized.</p>

<p>To withhold those new views from the Government, and
under such circumstances to have allowed the construction of
the Engine to be resumed, would have been improper; yet
the state of uncertainty in which those views were then
necessarily involved rendered any <i>written</i> communication
respecting their probable bearing on the Difference Engine a
matter of very great difficulty. It appeared to Mr. Babbage
that the most straightforward course was to ask for an interview
on the subject with the Head of the Government, and to
communicate to him the exact state
of the case. <span class="xxpn" id="p085">{85}</span></p>

<p>Had that interview taken place, the First Lord of the
Treasury might have ascertained from his inquiries, in a
manner quite impracticable by any written communications,
the degree of importance which Mr. Babbage attached to his
new inventions, and his own opinion of their probable effect,
in superseding the whole or any part of the original, or
<i>Difference</i>, Engine. The First Lord of the Treasury would
then have been in a position to decide, either on the immediate
continuation and completion of the original design, or
on its temporary suspension, until the character of the new
views should be more fully developed by further drawings and
examination.</p>

<p>There was another, although a far less material point, on
which also it was desirable to obtain the opinion of the
Government: the serious impediments to the progress of
the Engine, arising from the Engineer’s conduct, as well as
the consequent great expense, had induced Mr. Babbage to
consider, whether it might not be possible to employ some
other person as his agent for constructing it. His mind had
gradually become convinced of the practicability of that
measure; but he was also aware that however advantageous
it might prove to the Government, from its greater economy,
yet that it would add greatly to his own personal labour, responsibility,
and anxiety.</p>

<p>On the 26th of September, 1834, Mr. Babbage therefore
requested an interview with Lord Melbourne, for the purpose
of placing before him these views. Lord Melbourne acceded
to the proposed interview, but it was then postponed; and
soon after, the Administration of which his Lordship was
the Head went out of Office, without the interview having
taken place.</p>

<p>For the same purpose, Mr. Babbage applied
in December, <span class="xxpn" id="p086">{86}</span>
1834, for an interview with the Duke of Wellington, who, in
reply, expressed his wish to receive a written communication
on the subject. He accordingly addressed a statement to his
Grace, pointing out the only plans which, in his opinion, could
be pursued for terminating the questions relative to the
<i>Difference</i> Engine; namely,</p>

<ul><li>1st. The Government might desire Mr. Babbage to continue
the construction of the Engine, in the hands of the person
who has hitherto been employed in making it.</li>

<li>2ndly. The Government might wish to know whether any
other person could be substituted for the Engineer at present
employed to continue the construction;—a course which was
possible.</li>

<li>3rdly. The Government might (although he did not presume
that they would) substitute some person to superintend
the completion of the Engine instead of Mr. Babbage himself.</li>

<li>4thly. The Government might be disposed to give up the
undertaking entirely.</li></ul>

<p>He also stated to the Duke of Wellington, the circumstances
which had led him to the invention of a <i>new</i> Engine,
of far more extensive powers of calculation; which he then
observed did not supersede the former one, but added greatly
to its utility.</p>

<p>At this period, the impediments relating to the <i>Difference</i>
Engine had been partially and temporarily removed. The
chief difficulty would have been either the formation of new
arrangements with the Engineer, or the appointment of some
other person to supply his place. This latter alternative,
which was of great importance for economy as well as for its
speedy completion, Mr. Babbage had carefully examined, and
was then prepared to point out means for
its accomplishment. <span class="xxpn" id="p087">{87}</span></p>

<p>The duration of the Duke of Wellington’s Administration
was short; and no decision on the subject of the <i>Difference</i>
Engine was obtained.</p>

<p>On the 15th of May the <i>Difference</i> Engine was alluded to
in the House of Commons; when the Chancellor of the Exchequer
did Mr. Babbage the justice to state distinctly, that
the whole of the money voted had been expended in paying
the workmen and for the materials employed in constructing
it, and that not one shilling of it had ever gone into his own
pocket.</p>

<p>About this time several communications took place between
the Chancellor of the Exchequer and Mr. Babbage, respecting
a reference to the Royal Society for an opinion on the subject
of the Engine.</p>

<hr class="hrblk" />

<p>A new and serious impediment to the possibility of executing
one of the plans which had been suggested to the Duke of
Wellington for completing the <i>Difference</i> Engine arose from
these delays. The draftsman whom Mr. Babbage had, at his
own expense, employed, both on the <i>Difference</i> and on the
<i>Analytical</i> Engine, received an offer of a very liberal salary,
if he would enter into an engagement abroad, which would
occupy many years. His assistance was indispensable, and
his services were retained only by Mr. Babbage considerably
increasing his salary.</p>

<p>On the 14th of January, 1836, Mr. Babbage received a communication
from the Chancellor of the Exchequer (Mr. Spring Rice<a class="afnanc"
href="#fn19" id="fnanc19">19</a>&#x202f;), expressing his desire
to come to some definite result on the subject of the Calculating
Engine, in which he remarked, that the conclusion to be drawn from
Mr. Babbage’s statement to the Duke of Wellington was, that he <span
class="xxpn" id="p088">{88}</span> (Mr. Babbage) having invented a
new machine, of far greater powers than the former one, wished to be
informed if the Government would undertake to defray the expense of
this <i>new</i> Engine.</p>

<p>The Chancellor of the Exchequer then pointed out reasons
why he should feel himself bound to look to the completion of
the first machine, before he could propose to Parliament to
enter on the consideration of the second: and he proposed to
refer to the Royal Society for their opinion, authorizing them,
if they thought fit, to employ any practical mechanist or
engineer to assist them in their inquiries. The Chancellor of
the Exchequer concluded with expressing his readiness to
communicate with Mr. Babbage respecting the best mode of
attaining that result.</p>

<p>From these statements it is evident that Mr. Babbage had
failed in making his own views distinctly understood by the
Chancellor of the Exchequer. His first anxiety, when applying
to Lord Melbourne, had been respecting the question,
whether the <i>Discoveries</i> with which he was then advancing
might not ultimately supersede the work already executed.
His second object had been to point out a possible arrangement,
by which great expense might be saved in the mechanical
construction of the <i>Difference</i> Engine.</p>

<p>So far was Mr. Babbage from having proposed to the
Government to defray the expenses of the <i>new</i> or <i>Analytical</i>
Engine, that though he expressly pointed out in the statement
to the Duke of Wellington<a class="afnanc" href="#fn20" id="fnanc20">20</a>
four courses which it was possible
for the Government to take,—yet in no one of them was the
construction of the <i>new</i> Engine alluded to.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc19" id="fn19">19</a>
The present Lord Monteagle.</p>

<p class="pfirst padtopc"><a class="afnlabel" href="#fnanc20" id="fn20">20</a>
See page <a href="#p086" title="go to pag&#x65; 86">86</a>.</p></div>

<hr class="hrblk" />

<p>Those views of improved machinery
for making calculations <span class="xxpn" id="p089">{89}</span>
which had appeared in but faint perspective in 1834, as likely
to lead to important consequences, had, by this time, assumed
a form and distinctness which fully justified the anticipations
then made. By patient inquiry, aided by extensive drawings
and notations, the projected <i>Analytical</i> Engine had acquired
such powers, that it became necessary, for its further advancement,
to simplify the elements of which it was composed. In
the progress of this inquiry, Mr. Babbage had gradually arrived
at simpler mechanical modes of performing those arithmetical
operations on which the action of the <i>Difference</i> Engine depended;
and he felt it necessary to communicate these new
circumstances, as well as their consequences, to the Chancellor
of the Exchequer.</p>

<p>On the 20th of January, 1836, Mr. Babbage wrote, in
answer to the communication from the Chancellor of the
Exchequer, that he did not, on re-examining the statement
addressed to the Duke of Wellington, perceive that it contained
<i>any application to take up the new or Analytical Engine</i>;
and he accompanied this reply by a statement relative
to the progress of the <i>Analytical</i> Engine, and its bearing upon
the <i>Difference</i> Engine belonging to the Government. The
former, it was said,</p>

<div class="dblockquote">
<p>“Is not only capable of accomplishing all those other complicated calculations
which I had intended, but it also performs all calculations which
were peculiar to the Difference Engine, both in less time, and to a greater
extent: in fact, it completely supersedes the Difference Engine.”</p></div>

<p>The Reply then referred to the statement laid before
the Duke of Wellington in July, 1834, in which it was
said,</p>

<div class="dblockquote">
<p>“That all the elements of the Analytical were essentially different from
those of the Difference Engine;”</p></div>

<p class="pcontinue">and that the mechanical simplicity to which its elements had
now been reduced was such, that it would
probably cost more <span class="xxpn" id="p090">{90}</span>
to finish the <i>old Difference</i> Engine on its original plan than
to construct a <i>new</i> Difference Engine with the simplified elements
devised for the <i>Analytical</i> Engine.</p>

<p>It then proceeded to state <span class="nowrap">that—</span></p>

<div class="dblockquote">
<p>“The fact of a <i>new</i> superseding an <i>old</i> machine, in a very few years, is
one of constant occurrence in our manufactories; and instances might be
pointed out in which the advance of invention has been so rapid, and the
demand for machinery so great, that half-finished machines have been
thrown aside as useless before their completion.</p>

<p>“It is now nearly fourteen years since I undertook for the Government
to superintend the making of the Difference Engine. During nearly four
years its construction has been absolutely stopped, and, instead of being
employed in overcoming the physical impediments, I have been harassed by
what may be called the moral difficulties of the question. It is painful to
reflect that, in the time so employed, the first Difference Engine might,
under more favourable circumstances, have been completed.</p>

<p>“In making this Report, I wish distinctly to state, that I do not entertain
the slightest doubt of the success of the Difference Engine; <i>nor do I
intend it as any application to finish the one or to construct the other</i>; but I
make it from a conviction that the information it contains ought to be communicated
to those who must decide the question relative to the Difference
Engine.”</p></div>

<p>The reference to the Royal Society, proposed by the Chancellor
of the Exchequer, in his letter of the 14th of January,
1836,<a class="afnanc" href="#fn21" id="fnanc21">21</a>
did not take place; and during more than a year and
a half no further measures appear to have been adopted by
the Government respecting the Engine.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc21" id="fn21">21</a>
See page <a href="#p088" title="go to pag&#x65; 88">88</a>.</p></div>

<hr class="hrblk" />

<p>It was obviously of the greatest importance to Mr. Babbage
that a final decision should be made by the Government.
When he undertook to superintend the construction of the
<i>Difference</i> Engine for the Government, it was, of course,
understood that he would not leave it unfinished. He had
now been engaged fourteen years upon an
object which he <span class="xxpn" id="p091">{91}</span>
had anticipated would not require more than two or three;
and there seemed no limit to the time his engagement with
the Government might thus be supposed to endure, unless
some steps were taken to terminate it. Without such a
decision Mr. Babbage felt that he should be impeded in any
plans he might form, and liable to the most serious in­ter­rup­tion,
if he should venture to enter upon the execution of
them. He therefore most earnestly pressed, both by his
personal applications and by those of his friends, for the
settlement of the question. Mr. Wolryche Whitmore, in
particular, repeatedly urged upon the Chancellor of the
Exchequer, personally, as well as by letter, the injustice of
keeping Mr. Babbage so very long in a state of suspense.</p>

<p>Time, however, passed on, and during nearly two years the
question remained in the same state. Mr. Babbage, wearied
with this delay, determined upon making a last effort to
obtain a decision. He wrote to the First Lord of the Treasury
(Lord Melbourne) on the 26th of July, 1838, recalling
to his Lordship’s attention the frequency of his applications
on this subject, and urging the necessity of a final decision
upon it. He observed, that if the question had become more
difficult, because he had invented superior mechanism, which
had superseded that which was already partly executed, this
consequence had arisen from the very delay against which he
had so repeatedly remonstrated. He then asked, for the last
time, not for any favour, but for that which it was an injustice
to withhold—a decision.</p>

<p>On the 16th of August Mr. Spring Rice (the Chancellor of
the Exchequer) addressed a note to Mr. Babbage, in reference
to his application to Lord Melbourne. After recapitulating
his former statement of the subject, which had been shown to
be founded on a misapprehension,
viz., that Mr. Babbage <span class="xxpn" id="p092">{92}</span>
had made an <i>application</i> to the Government to construct for
them the <i>Analytical</i> Engine, the Chancellor of the Exchequer
inquired whether he was solicitous that steps should be taken
for the completion of the old, or for the commencement of a
new machine,—and what he considered would be the cost of
the one proceeding, and of the other?</p>

<p>Being absent on a distant journey, Mr. Babbage could not
reply to this note until the 21st of October. He then reminded
the Chancellor of the Exchequer of his previous
communication of the 20th of January, 1836 (see p. 89), in
which it was expressly stated that he did <i>not</i> intend to make
any application to construct a <i>new</i> machine; but that the
communication to the Duke of Wellington and the one to
himself were made, simply because he thought it would be
unfair to conceal such important facts from those who were
called upon to decide on the continuance or discontinuance of
the construction of the <i>Difference Engine</i>.</p>

<p>With respect to the expense of either of the courses
pointed out by the Chancellor of the Exchequer, Mr. Babbage
observed that, not being a pro­fes­sion­al Engineer, and his past
experience having taught him not to rely upon his own judgment
on matters of that nature, he should be very reluctant
to offer any opinion upon the subject.</p>

<p>In conclusion, Mr. Babbage stated that the question he
wished to have settled <span class="nowrap">was—</span></p>

<p><i>Whether the Government required him to superintend the
completion of the Difference Engine, which had been suspended
during the last five years, according to the original plan and
principles; or whether they intended to discontinue it altogether&#x202f;?</i></p>

<p>In November, 1841, Mr. Babbage, on his return from the
Continent, finding that Sir Robert Peel
had become First <span class="xxpn" id="p093">{93}</span>
Lord of the Treasury, determined upon renewing his application
for a decision of the question. With this view the previous
pages of this Statement were drawn up, and a copy of
it was forwarded to him, accompanied by a letter from Mr.
Babbage, in which he <span class="nowrap">observed—</span></p>

<div class="dblockquote">
<p>“Of course, when I undertook to give the invention of the Calculating
Engine to the Government, and to superintend its construction, there must
have been an implied understanding that I should carry it on to its termination.
I entered upon that understanding, believing that two or at
the utmost that three years would complete it. The better part of my life
has now been spent on that machine, and no progress whatever having been
made since 1834, that understanding may possibly be considered by the
Government as still subsisting: I am therefore naturally very anxious
that this state of uncertainty should be put an end to as soon as
possible.”</p></div>

<p>Mr. Babbage, in reply, received a note from Sir George
Clerk (Secretary to the Treasury), stating that Sir Robert
Peel feared that it would not be in his power to turn his
attention to the subject for some days, but that he hoped, as
soon as the great pressure of business previous to the opening
of the session of Parliament was over, he might be able to
determine on the best course to be pursued.</p>

<p>The session of Parliament closed in August, and Mr.
Babbage had received no further communication on the
subject. Having availed himself of several private channels
for recalling the question to Sir Robert Peel’s attention
without effect, Mr. Babbage, on the 8th of October, 1842,
again wrote to him, requesting an early decision.</p>

<p>On the 4th of November, 1842, a note from Sir Robert
Peel explained to Mr. Babbage that some delay had arisen,
from his wish to communicate personally with the Chancellor
of the Exchequer, who would shortly announce to him their
joint conclusion on the subject.</p>

<p>On the same day Mr. Babbage received a
letter from Mr. <span class="xxpn" id="p094">{94}</span>
Goulburn (the Chancellor of the Exchequer), who stated that
he had communicated with Sir Robert Peel, and that they
both regretted the necessity of abandoning the completion of
a machine, on which so much scientific labour had been
bestowed. He observed, that the expense necessary for rendering
it either sat­is­fac­tory to Mr. Babbage or generally
useful appeared, on the lowest calculation, so far to exceed
what they should be justified in incurring, that they considered
themselves as having no other alternative.</p>

<p>Mr. Goulburn concluded by expressing their hope, that by
the Government withdrawing all claim to the machine as
already constructed, and placing it entirely at Mr. Babbage’s
disposal, they might in some degree assist him in his future
exertions in the cause of Science.</p>

<p>On the 6th of November, 1842, Mr. Babbage wrote to Sir
Robert Peel and the Chancellor of the Exchequer, acknowledging
the receipt of their decision, thanking them for the
offer of the machine as already constructed, but, under all
the circumstances, declining to accept it.<a class="afnanc" href="#fn22" id="fnanc22">22</a></p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc22" id="fn22">22</a>
The part of the <i>Difference</i> Engine already constructed,
together with all the Drawings relating to the whole machine, were, in
January, 1843 (by the direction of the Government), deposited in the
Museum of King’s College, London.</p></div>

<p>On the 11th of November Mr. Babbage obtained an interview
with Sir Robert Peel, and stated, that having given the
original Invention to the Government—having superintended
for them its construction—having dem­on­strated the possibility
of the undertaking by the completion of an important
portion of it—and that the non-completion of the design
arose neither from his fault nor his desire, but was the act of
the Government itself, he felt that he had some claims on
their consideration.</p>

<p>He rested those claims upon the sacrifices he had made,
<span class="xxpn" id="p095">{95}</span>
both personal and pecuniary, in the advancement of the Mechanical
Arts and of Science—on the anxiety and the injury
he had experienced by the delay of eight years in the decision
of the Government on the subject, and on the great
annoyance he had constantly been exposed to by the prevailing
belief in the public mind that he had been amply
remunerated by large grants of public money. Nothing, he
observed, but some public act of the Government could ever
fully refute that opinion, or repair the injustice with which he
had been treated.</p>

<p>The result of this interview was entirely unsat­is­fac­tory.
Mr. Babbage went to it prepared, had his statement produced
any effect, to have pointed out two courses, by either of
which it was probable that not only a Difference Engine, but
even the Analytical Engine, might in a few years have been
completed. The state of Sir Robert Peel’s information on
the subject, and the views he took of Mr. Babbage’s services
and position, prevented Mr. Babbage from making any allusion
to either of those plans.</p>

<p>Thus finally terminated an engagement, which had existed
upwards of twenty years. During no part of the last eight of
those years does there appear to have been any reason why
the same decision should not have been arrived at by the
Government as was at last actually pronounced.</p>

<p>It was during this last period that all the great principles
on which the <i>Analytical</i> Engine rests were discovered, and
that the mechanical contrivances in which they might be
embodied were invented. The establishment which Mr.
Babbage had long maintained in his own house, and at his
own expense, was now directed with increased energy to the
new inquiries required for its perfection.</p>

<p>In this Statement the heavy sacrifices,
both pecuniary and <span class="xxpn" id="p096">{96}</span>
personal, which the invention of these machines has entailed
upon their author, have been alluded to as slightly as possible.
Few can imagine, and none will ever know their full
extent. Some idea of those sacrifices must nevertheless have
occurred to every one who has read this Statement. During
upwards of twenty years Mr. Babbage has employed, in his
own house, and at his own expense, workmen of various kinds,
to assist him in making experiments necessary for attaining a
knowledge of every art which could possibly tend to the perfection
of those Engines; and with that object he has frequently
visited the manufactories of the Continent, as well as
our own.</p>

<p>Since the discontinuance of the Difference Engine belonging
to the Government, Mr. Babbage has himself maintained
an establishment for making drawings and descriptions dem­on­strat­ing
the nature and power of the <i>Analytical</i> Engine,
and for its construction at some future period, when its value
may be appreciated.</p>

<div class="dkeeptgth">
<p>To these remarks it will only be added, that at an early
stage of the construction of the <i>Difference</i> Engine he refused
more than one highly desirable and profitable situation, in
order that he might give his whole time and thoughts to the
fulfilment of the engagement which he considered himself to
have entered into with the Government.</p>

<p class="padtopb fsz6"><i>August, 1843.</i></p>
</div><!--dkeeptgth--></div><!--section-->

<div class="section" id="p097">

<h2 class="h2herein">CHAPTER VII.
<span class="hsmall">DIFFERENCE ENGINE NO. II.</span></h2>

<div class="dsynopsis">
Difference Engine No. 2&#x200a;—&#x200a;The Earl of Rosse, President
of the Royal Society, proposed to the Government a Plan by which the
Difference Engine No. 2 might have been executed&#x200a;—&#x200a;It was
addressed to the Earl of Derby, and rejected by his Chancellor of the
Exchequer.</div>

<p class="pfirst"><span class="smcap">I<b>T</b></span>
was not until 1848, when I had mastered the subject of
the Analytical Engine, that I resolved on making a complete
set of drawings of the Difference Engine No. 2. In this I
proposed to take advantage of all the improvements and
simp­li­fi­ca­tions which years of unwearied study had produced
for the Analytical Engine.</p>

<p>In 1852, the Earl of Rosse, who, from its commencement,
had looked forward with the greatest interest to the application
of mechanism to purposes of calculation, and who
was well acquainted with the drawings and notations of the
Difference Engine No. 2, inquired of me whether I was
willing to give them to the Government, provided they
would have the Engine constructed. My feeling was, after
the sad experience of the past, that I ought not to think of
sacrificing any further portion of my life upon the subject.
If, however, they chose to have the Difference Engine made,
I was ready to give them the whole of the drawings, and also
the notations by which it was dem­on­strated that such a
machine could be constructed, and that when made it would
necessarily do the work
prescribed for it. <span class="xxpn" id="p098">{98}</span></p>

<p>My much-valued friend, the late Sir Benjamin Hawes, had
also been consulted, and it was agreed that the draft of a
letter to Lord Derby, who was then prime minister, should
be prepared; in which I should make this offer. Lord
Rosse proposed to place my letter in Lord Derby’s hands,
with his own statement of a plan by which the whole question
might be determined.</p>

<p>Lord Rosse’s suggestion was, that the Government should
apply to the President of the Institution of Civil Engineers
to ascertain,</p>

<ul>
<li>1st. Whether it was possible, from the drawings and
notations, to make an estimate of the cost of constructing
the machine?</li>

<li>2ndly. In case this question was answered in the affirmative—then,
could a Mechanical Engineer be found
who would undertake to construct it, and at what
expense?</li></ul>

<p>The Institution of Civil Engineers was undoubtedly the
highest authority upon the first question. That being decided
in the affirmative, no other body had equal power to find out
those mechanical engineers who might be willing to undertake
the contract.</p>

<p>Supposing both these questions, or even the latter only,
answered in the negative, the proposition, of course, fell to
the ground. But if they were both answered in the affirmative,
then there would have arisen a further question for the
consideration of the Government: namely, Whether the
object to be obtained was worthy of the expenditure?</p>

<div class="dsdnote">〈LORD ROSSE’S ADDRESS TO THE ROYAL SOCIETY.〉</div>

<p>The final result of this eminently <i>practical</i> plan was
communicated to the Royal Society by their President, in his address
at their anniversary on the 30th November, 1854. The following
is an <span class="nowrap">extract:—</span> <span class="xxpn"
id="p099">{99}</span></p>

<p class="padtopb">“The progress of the work was suspended: there was a
change of Government. Science was weighed against gold
by a new standard, and it was resolved to proceed no
further. No enterprise could have had its beginning under
more auspicious circumstances: the Government had taken
the initiative—they had called for advice, and the adviser
was the highest scientific authority in this country;—your
Council; guided by such men as Davy, Wollaston, and
Herschel. By your Council the undertaking was inaugurated,—by
your Council it was watched over in its progress.
That the first great effort to employ the powers of calculating
mechanism, in aid of the human intellect, should
have been suffered in this great country to expire fruitless,
because there was no tangible evidence of immediate profit,
as a British subject I deeply regret, and as a Fellow my
regret is accompanied with feelings of bitter disappointment.
Where a question has once been disposed of, succeeding
Governments rarely reopen it, still I thought I
should not be doing my duty if I did not take some opportunity
of bringing the facts once more before Government.
Circumstances had changed, mechanical engineering had
made much progress; the tools required and trained workmen
were to be found in the workshops of the leading
mechanists, the founder’s art was so advanced that casting
had been substituted for cutting, in making the change
wheels, even of screw-cutting engines, and therefore it was
very probable that persons would be found willing to undertake
to complete the Difference Engine for a specific sum.</p>

<p>“That finished, the question would then have arisen, how
far it was advisable to endeavour, by the same means, to
turn to account the great labour which had been expended
under the guidance of inventive powers
the most original, <span class="xxpn" id="p100">{100}</span>
controlled by mathematics of a very high order; and which
had been wholly devoted for so many years to the great
task of carrying the powers of calculating machinery to its
utmost limits. Before I took any step I wrote to several
very eminent men of science, inquiring whether, in their
opinion, any great scientific object would be gained if Mr.
Babbage’s views, as explained in Ménabrèa’s little essay,
were completely realized. The answers I received were
strongly in the affirmative. As it was necessary the subject
should be laid before Government in a form as practical
as possible, I wrote to one of our most eminent mechanical
engineers to inquire whether I should be safe in stating
to Government that the expense of the Calculating Engine
had been more than repaid in the improvements in mechanism
directly referable to it; he replied,—unquestionably.
Fortified by these opinions, I submitted this proposition
to Government:—that they should call upon the
President of the Society of Civil Engineers to report
whether it would be practicable to make a contract for the
completion of Mr. Babbage’s Difference Engine, and if so,
for what sum. This was in 1852, during the short administration
of Lord Derby, and it led to no result. The
time was unfortunate; a great political contest was impending,
and before there was a lull in politics, so that the
voice of Science could be heard, Lord Derby’s government
was at an end.”</p>

<div class="dsdnote">〈MR. BABBAGE’S LETTER TO THE EARL OF DERBY.〉</div>

<p>The following letter was then drawn up, and placed in
Lord Derby’s hands by Lord <span class="nowrap">Rosse:—</span></p>

<p class="pfirst padtopb"><span class="dfloatright"><i>June 8,
 1852</i>.&nbsp;&nbsp;</span>
<span class="smcap">M<b>Y</b></span>
<span class="smcap">L<b>ORD</b>,</span></p>

<p>I
<span class="smmaj">TAKE</span> the liberty of drawing your Lordship’s attention
to the subject of the construction of a
Difference Engine, for <span class="xxpn" id="p101">{101}</span>
calculating and printing Astronomical and Nautical Tables,
which was brought under the notice of the Government so
far back as the year 1823, and upon which the Government
of that day desired the opinion of the Royal Society.</p>

<p>I annex a copy of the correspondence which took place at
that time, and which your Lordship will observe was laid
before Parliament.</p>

<p>The Committee of the Royal Society, to which the subject was
referred, reported generally that the invention was one “fully adequate
to the attainment of the objects proposed by the inventor, and that
they considered Mr. Babbage as highly deserving of public encouragement
in the prosecution of his arduous undertaking.”—<i>Report of Royal
Society</i>, 1&#x200a;<i>st</i> <i>May</i>, 1823. <i>Parliamentary Paper</i>, 370,
22&#x200a;<i>nd</i> <i>May</i>, 1823.</p>

<p>And in a subsequent and more detailed Report, which
I annex also, they <span class="nowrap">state:—</span></p>

<p>“The Committee have no intention of entering into any
consideration of the abstract math­e­mat­i­cal principle on which
the practicability of such a machine as Mr. Babbage’s relies,
nor of its public utility when completed. They consider
the former as not only sufficiently clear in itself, but as
already admitted and acted on by the Council in their former
proceedings. The latter they regard as obvious to every one
who considers the immense advantage of accurate numerical
Tables in all matters of calculation, especially in those which
relate to Astronomy and Navigation, and the great variety
and extent of those which it is the object and within the
compass of Mr. Babbage’s Engine to calculate and print
with perfect accuracy.”—<i>Report of Committee of Royal
Society, 12th Feb., 1829.</i></p>

<p>Upon the first of these Reports, the Government determined
to construct the machine,
under my personal <span class="xxpn" id="p102">{102}</span>
superintendence and direction. The Engine was accordingly
commenced and partially completed. Tables of figures were
calculated, limited in extent only by the number of wheels
put together.</p>

<p>Delays, from various causes arose in the progress of the
work, and great expenses were incurred. The machine was
altogether new in design and construction, and required the
utmost mechanical skill which could be obtained for its execution.
“It involved,” to quote again from the Report of the
Committee of the Royal Society, “the necessity of constructing,
and in many instances inventing, tools and machinery
of great expense and complexity (and in many instances of
ingenious contrivances likely to prove useful for other purposes
hereafter), for forming with the requisite precision
parts of the apparatus dissimilar to any used in ordinary
mechanical works; that of making many previous trials to
ascertain the validity of proposed movements; and that of
altering, improving, and simplifying those already contrived
and reduced to drawings. Your Committee are so far from
being surprised at the time it has occupied to bring it to its
present state, that they feel more disposed to wonder it has
been possible to accomplish so much.” The true explanation
both of the slow progress and of the cost of the work is
clearly stated in this passage; and I may remark in passing,
that the tools which were invented for the construction of the
machine were afterwards found of utility, and that this
anticipation of the Committee has been realized, as some
of our most eminent mechanical engineers will readily
testify.</p>

<p>Similar circumstances will, I apprehend, always attend
and prolong the period of bringing to perfection inventions
which have no parallel in the previous
history of mechanical <span class="xxpn" id="p103">{103}</span>
construction. The necessary science and skill specially acquired
in executing such works must also, as experience is
gained, suggest deviations from, and improvements in, the
original plan of those works; and the adoption or rejection
of such changes, especially under circumstances similar to
those in which I was placed, often involves questions of the
greatest difficulty and anxiety.</p>

<p>From whatever cause, however, the delays and expenses
arose, the result was that the Government was discouraged,
and declined to proceed further with the work.</p>

<p>Mr. Goulburn’s letter, intimating this decision to me, in
1842, will be found in the accompanying printed Statement.
And that the impediments to the completion of the engine,
described by the Royal Society, were those which influenced
the Government in the determination they came to, I infer
from the reason assigned by Mr. Goulburn for its discontinuance,
viz., “the expense which would be necessary in order to
render it either sat­is­fac­tory to yourself or generally useful.”
I readily admit that the work could not have been rendered
sat­is­fac­tory to myself unless I was free to introduce every
improvement which experience and thought could suggest.
But that even with this additional source of expense its
general usefulness would have been impaired, I cannot assent
to, for I believe, in the words of the Report I have already
quoted, the “immense advantage of accurate Numerical
Tables in all matters of calculation, especially in those which
relate to Astronomy and Navigation, cannot, within any
reasonable limits, be over-estimated.” As to the expense
actually incurred upon the first Difference Engine, that of
the Government was about 17,000&#x200a;<i>l</i>. On my own part, and
out of my own private resources, I have sacrificed upon this
and other works of science
upwards of 20,000&#x200a;<i>l</i>. <span class="xxpn" id="p104">{104}</span></p>

<p>From the date of Mr. Goulburn’s letter, nothing has been
done towards the further completion of the Difference
Engine by the Government or myself. So much of it as
was completed was deposited in the Museum of King’s College,
where it now remains.</p>

<p>Three consequences have, however, resulted from my subsequent
labours, to which I attach great importance.</p>

<p>First, I have been led to conceive the most important
elements of another Engine upon a new principle (the
details of which are reduced accurately to paper), the power
of which over the most complicated analytical operations
appears nearly unlimited; but no portion of which is yet
commenced. I have called this engine, in contradistinction
to the other, the Analytical Engine.</p>

<p>Secondly, I have invented and brought to maturity a
system of signs for the explanation of machinery, which I
have called Mechanical Notation, by means of which the
drawings, the times of action, and the trains for the transmission
of force, are expressed in a language at once simple
and concise. Without the aid of this language I could not
have invented the Analytical Engine; nor do I believe that
any machinery of equal complexity can ever be contrived
without the assistance of that or of some other equivalent
language. The Difference Engine No. 2, to which I shall
presently refer, is entirely described by its aid.</p>

<p>Thirdly, in labouring to perfect this Analytical Machine
of greater power and wider range of computation, I have
discovered the means of simplifying and expediting the
mechanical processes of the first or Difference Engine.</p>

<p>After what has passed, I cannot expect the Government to
undertake the construction of the Analytical Engine, and I
do not offer it for that purpose. It is not so
matured as to <span class="xxpn" id="p105">{105}</span>
enable any other person, without long previous training and
application, even to attempt its execution; and on my own
part, to superintend its construction would demand an
amount of labour, anxiety, and time which could not, after
the treatment I have received, be expected from me. I
therefore make no such offer.</p>

<p>But that I may fulfil to the utmost of my power the
original expectation that I should be able to complete, for
the Government, an Engine capable of calculating astronomical
and nautical Tables with perfect accuracy, such as
that which is described in the Reports of the Royal Society,
I am willing to place at the disposal of Government (if they
will undertake to execute a new Difference Engine) all those
improvements which I have invented and have applied to
the Analytical Engine. These comprise a complete series
of drawings and explanatory notations, finished in 1849, of
the Difference Engine No. 2,—an instrument of greater
power as well as of greater simplicity than that formerly
commenced, and now in the possession of the Government.</p>

<p>I have sacrificed time, health, and fortune, in the desire to
complete these Calculating Engines. I have also declined
several offers of great personal advantage to myself. But,
not­with­stand­ing the sacrifice of these advantages for the
purpose of maturing an engine of almost in­tel­lec­tual power,
and after expending from my own private fortune a larger
sum than the Government of England has spent on that
machine, the execution of which it only commenced, I have
received neither an acknowledgment of my labours, nor even
the offer of those honours or rewards which are allowed to
fall within the reach of men who devote themselves to purely
scientific investigations. I might, perhaps, advance some
claims to consideration, founded
on my works and <span class="xxpn" id="p106">{106}</span>
cont­ri­bu­tions in aid of various departments of industrial and physical
science,—but it is for others to estimate those services.</p>

<p>I now, however, simply ask your Lordship to do me the
honour to consider this statement and the offer I make. I
prefer no claim to the distinctions or the advantages which
it is in the power of the Crown or the Government to bestow.
I desire only to discharge whatever <i>imagined</i> obligation may
be supposed to rest upon me, in connexion with the original
undertaking of the Difference Engine; though I cannot but
feel that whilst the public has already derived advantage
from my labours, I have myself experienced only loss and
neglect.</p>

<p>If the work upon which I have bestowed so much time
and thought were a mere triumph over mechanical difficulties,
or simply curious, or if the execution of such engines
were of doubtful practicability or utility, some justification
might be found for the course which has been taken; but I
venture to assert that no mathematician who has a reputation
to lose will ever <i>publicly</i> express an opinion that such a
machine would be useless if made, and that no man distinguished
as a Civil Engineer will venture to declare the
construction of such machinery impracticable. The names
appended to the Report of the Committee of the Royal
Society fully justify my expressing this opinion, which I
apprehend will not be disputed.</p>

<p>And at a period when the progress of physical science is
obstructed by that exhausting in­tel­lec­tual and manual labour,
indispensable for its advancement, which it is the object of the
Analytical Engine to relieve, I think the application of machinery
in aid of the most complicated and abstruse calculations
can no longer be deemed unworthy of the attention
of the country. In fact, there is no reason
why mental as <span class="xxpn" id="p107">{107}</span>
well as bodily labour should not be economized by the aid of
machinery.</p>

<p>With these views I have addressed your Lordship, as the
head of the Government; and whatever may be my sense of
the injustice that has hitherto been done me, I feel, in laying
this rep­re­sen­ta­tion before your Lordship, and in making the
offer I now make, that I have discharged to the utmost
limit every implied obligation I originally contracted with the
country.</p>

<div>I have the honour to be,</div>
<div>&amp;c., &amp;c., &amp;c.,</div>
<div class="psignature"><span class="smcap">C<b>HARLES</b></span>
 <span class="smcap">B<b>ABBAGE</b>.</span></div>

<p class="pfirst fsz6"><i>Dorset Street, Manchester Square.</i></p>
<p class="fsz6"><i>June</i> 8, 1852.</p>

<p class="padtopa">As this question was one of finance and of calculation, the
sagacious Premier adroitly turned it over to his Chancellor
of the Exchequer—that official being, from his office, <i>supposed</i>
to be well versed in both subjects.</p>

<p>The opinion pronounced by the novelist and financier was,
“That Mr. Babbage’s projects appear to be so indefinitely
expensive, the ultimate success so problematical, and the
expenditure certainly so large and so utterly incapable of
being calculated, that the Government would not be justified
in taking upon itself any further liability.”—<i>Extract from
the Reply of Earl Derby to the application of the Earl of Rosse,
K.P., President of the Royal Society.</i></p>

<div class="dsdnote">〈REFERRED TO THE CHANCELLOR OF THE EXCHEQUER.〉</div>

<p>The answer of Lord Derby to Lord Rosse was in <span class="nowrap">substance—</span></p>

<p>That he had consulted the Chancellor of the Exchequer,
who pronounced Mr.
Babbage’s project <span class="nowrap">as—</span>
<span class="xxpn" id="p108">{108}</span></p>

<ul>
<li>1. “Indefinitely expensive.”</li>

<li>2. “The ultimate success problematical.”</li>

<li>3. “The expenditure utterly incapable of being calculated.”</li></ul>

<p>1. With regard to the “indefinite expense.” Lord Rosse
had proposed to refer this question to the President of the
Institution of Civil Engineers, who would have given his
opinion after a careful examination of the drawings and
notations. These had not been seen by the Chancellor of
the Exchequer; and, if seen by him, would not have been
comprehended.</p>

<p>The objection that its success was “problematical” may
refer either to its mechanical construction or to its math­e­mat­i­cal
principles.</p>

<p>Who, possessing one grain of common sense, could look
upon the unrivalled workmanship of the then existing portion
of the Difference Engine No. 1, and doubt whether a simplified
form of the same engine could be executed?</p>

<p>As to any doubt of its math­e­mat­i­cal principles, this was
excusable in the Chancellor of the Exchequer, who was
himself too practically acquainted with the fallibility of
his own figures, over which the severe duties of his office
had stultified his brilliant imagination. Far other figures
are dear to him—those of speech, in which it cannot be
denied he is indeed pre-eminent.</p>

<p>Any junior clerk in his office might, however, have told
him that the power of computing Tables by differences merely
required a knowledge of simple addition.</p>

<p>As to the impossibility of ascertaining the expenditure,
this merges into the first objection; but a poetical brain must
be pardoned when it repeats or amplifies. I will recall to the
ex-Chancellor of the Exchequer what
Lord Rosse really <span class="xxpn" id="p109">{109}</span>
proposed, namely, that the Government should take the opinion
of the President of the Institution of Civil Engineers upon
the question, whether a contract could be made for constructing
the Difference Engine, and if so, for what sum.</p>

<p>But the very plan proposed by Lord Rosse and refused by
Lord Derby, for the construction of the <i>English</i> Difference
Engine, was adopted some few years after by another administration
for the <i>Swedish</i> Difference Engine. Messrs.
Donkin, the eminent Engineers, <i>made an estimate</i>, and a
<i>contract was</i> in consequence executed to construct for Government
a fac-simile of the <i>Swedish</i> Difference Engine, which
is now in use in the department of the Registrar-General,
at Somerset House. There were far greater mechanical difficulties
in the production of that machine than in the one the
drawings of which I had offered to the Government.</p>

<p>From my own experience of the cost of executing such
works, I have no doubt, although it was highly creditable to
the skill of the able firm who constructed it, but that it must
have been commercially unprofitable. Under such circumstances,
surely it was harsh on the part of the Government to
refuse Messrs. Donkin permission to exhibit it as a specimen
of English workmanship at the Exhibition of 1862.</p>

<div class="dsdnote">〈HIS OPINION WORTHLESS.〉</div>

<p>But the machine upon which everybody could calculate,
had little chance of fair play from the man on whom nobody
could calculate.</p>

<p>If the Chancellor of the Exchequer had read my letter to
Lord Derby, he would have found the opinion of the Committee
of the Royal Society expressed in these <span class="nowrap">words:—</span></p>

<p>“They consider the former [the abstract math­e­mat­i­cal
principle] as not only sufficiently clear in itself, but as
already admitted and acted on by the Council in their
former proceedings. <span class="xxpn" id="p110">{110}</span></p>

<p>“The latter [its public utility] they consider as obvious to
every one who considers the immense advantage of accurate
numerical tables in all matters of calculation, especially in
those which relate to astronomy and navigation.”—<i>Report
of the Royal Society, 12th Feb., 1829.</i></p>

<p>Thus it <span class="nowrap">appears:—</span></p>

<ul>
<li>1st. That the Chancellor of the Exchequer presumed to
set up his <i>own idea</i> of the utility of the Difference
Engine in direct opposition to that of the Royal
Society.</li>

<li>2nd. That he <i>refused</i> to take the opinion of the highest
mechanical authority in the country on its probable
cost, and even <i>to be informed</i> whether a contract
for its construction at a definite sum might
not be attainable: he then boldly pronounced
the expense to be “utterly incapable of being
calculated.”</li></ul>

<div class="dsdnote">〈DIFFERENCE ENGINE No. 2.
 FEELS FOR THE CHANCELLOR OF THE EXCHEQUER.〉</div>

<p>This much-abused Difference Engine is, however, like its
prouder relative the Analytical, a being of sensibility, of
impulse, and of power.</p>

<p>It can not only calculate the millions the ex-Chancellor of the
Exchequer squandered, but it can deal with the smallest quantities;
nay, it feels even for zeros.<a class="afnanc" href="#fn23"
id="fnanc23">23</a> It is as conscious as Lord Derby himself is of
the presence of a <i>negative quantity</i>, and it is not beyond the ken
of either of them to foresee the existence of <i>impossible ones</i>.<a
class="afnanc" href="#fn24" id="fnanc24">24</a></p>

<div class="dftnt"> <p class="pfirst"><a class="afnlabel"
href="#fnanc23" id="fn23">23</a> It discovers the roots of equations by
feeling whether all the figures in a certain column are <i>zeros</i>.</p>

<p class="pfirst padtopc"><a class="afnlabel" href="#fnanc24"
id="fn24">24</a> It may be necessary to explain to the unmath­e­mat­i­cal
reader and to the ex-Chancellor of the Exchequer that <i>impossible
quantities</i> in algebra are something like <i>mare’s-nests</i> in ordinary
life.</p></div>

<p>Yet should any unexpected course of
events ever raise the <span class="xxpn" id="p111">{111}</span>
ex-Chancellor of the Exchequer to his former dignity, I am
sure he will be its <i>friend</i> as soon as he is convinced that it
can be made <i>useful</i> to him.</p>

<p>It may possibly enable him to un-muddle even his own
financial accounts, and <span class="nowrap">to&#x202f;———</span></p>

<p>But as I have no wish to crucify him, I will leave his
name in obscurity.</p>

<p>The Herostratus of Science, if he escape oblivion, will be
linked with the destroyer of
the Ephesian Temple.</p>
</div><!--section-->

<div class="section" id="p112">

<h2 class="h2herein">CHAPTER VIII.
<span class="hsmall">OF THE ANALYTICAL ENGINE.</span></h2>

<hr class="hr20" />
<div class="dpoemctr fsz7"><div class="dstanzactr">
<div class="dpp00">Man wrongs, and Time avenges.</div></div>
<div class="dpoemcite"><span class="smcap">B<b>YRON.</b></span>—<i>The
 Prophecy of Dante.</i></div>
</div><hr class="hr20" />

<div class="dsynopsis">
Built Workshops for constructing the Analytical
Engine&#x200a;—&#x200a;Difficulties about carrying the
Tens&#x200a;—&#x200a;Unexpectedly solved&#x200a;—&#x200a;Application
of the Jacquard Principle&#x200a;—&#x200a;Treatment
of Tables&#x200a;—&#x200a;Probable Time required for
Arithmetical Operations&#x200a;—&#x200a;Conditions it must
fulfil&#x200a;—&#x200a;Unlimited in Number of Figures, or in extent of
Analytical Operations&#x200a;—&#x200a;The Author invited to Turin in
1840&#x200a;—&#x200a;Meetings for Discussion&#x200a;—&#x200a;Plana,
Menabrea, MacCullagh, Mosotti&#x200a;—&#x200a;Difficulty proposed by
the latter&#x200a;—&#x200a;Ob­ser­va­tions on the Errata of Astronomical
Tables&#x200a;—&#x200a;Suggestions for a Reform of Analytical
Signs.</div>

<p class="pfirst"><span class="smcap">T<b>HE</b></span>
circular arrangement of the axes of the Difference
Engine round large central wheels led to the most extended
prospects. The whole of arithmetic now appeared within
the grasp of mechanism. A vague glimpse even of an
Analytical Engine at length opened out, and I pursued with
enthusiasm the shadowy vision. The drawings and the experiments
were of the most costly kind. Draftsmen of the
highest order were necessary to economize the labour of my
own head; whilst skilled workmen were required to execute
the experimental machinery to which I was obliged constantly
to have recourse.</p>

<p>In order to carry out my pursuits successfully, I had purchased
a house with above a quarter of an acre of
ground in a <span class="xxpn" id="p113">{113}</span>
very quiet locality. My coach-house was now converted into a
forge and a foundry, whilst my stables were transformed into
a workshop. I built other extensive workshops myself, and
had a fire-proof building for my drawings and draftsmen.
Having myself worked with a variety of tools, and having
studied the art of constructing each of them, I at length laid
it down as a principle—that, except in rare cases, I would
never do anything myself if I could afford to hire another
person who could do it for me.</p>

<div class="dsdnote">〈THE MECHANICAL NOTATION.〉</div>

<p>The complicated relations which then arose amongst the
various parts of the machinery would have baffled the most
tenacious memory. I overcame that difficulty by improving
and extending a language of signs, the Mechanical Notation,
which in 1826 I had explained in a paper printed in the
“Phil. Trans.” By such means I succeeded in mastering
trains of investigation so vast in extent that no length of
years ever allotted to one individual could otherwise have
enabled me to control. By the aid of the Mechanical Notation,
the Analytical Engine became a reality: for it became
susceptible of demonstration.</p>

<p>Such works could not be carried on without great
expenditure. The fluctuations in the demand and supply
of skilled labour were considerable. The railroad mania
withdrew from other pursuits the most in­tel­lec­tual and
skilful draftsmen. One who had for some years been my
chief assistant was tempted by an offer so advantageous that
in justice to his own family he could scarcely have declined
it. Under these circumstances I took into consideration the
plan of advancing his salary to one guinea per day. Whilst
this was in abeyance, I consulted my venerable surviving
parent. When I had fully explained the circumstances, my
excellent mother replied: “My dear son,
you have advanced <span class="xxpn" id="p114">{114}</span>
far in the accomplishment of a great object, which is worthy
of your ambition. You are capable of completing it. My
advice is—pursue it, even if it should oblige you to live on
bread and cheese.”</p>

<p>This advice entirely accorded with my own feelings. I
therefore retained my chief assistant at his advanced salary.</p>

<div class="dsdnote">〈CARRYING THE TENS BY ANTICIPATION.〉</div>

<p>The most important part of the Analytical Engine was
undoubtedly the mechanical method of carrying the tens.
On this I laboured incessantly, each succeeding improvement
advancing me a step or two. The difficulty did not consist
so much in the more or less complexity of the contrivance
as in the reduction of the <i>time</i> required to effect the carriage.
Twenty or thirty different plans and modifications had been
drawn. At last I came to the conclusion that I had exhausted
the principle of successive carriage. I concluded
also that nothing but teaching the Engine to foresee and then
to act upon that foresight could ever lead me to the object I
desired, namely, to make the whole of any unlimited number
of carriages in one unit of time. One morning, after I had
spent many hours in the drawing-office in endeavouring to
improve the system of successive carriages, I mentioned these
views to my chief assistant, and added that I should retire to
my library, and endeavour to work out the new principle. He
gently expressed a doubt whether the plan was <i>possible</i>, to
which I replied that, not being able to prove its impossibility,
I should follow out a slight glimmering of light
which I thought I perceived.</p>

<p>After about three hours’ examination, I returned to the
drawing-office with much more definite ideas upon the subject.
I had discovered a principle that proved the possibility,
and I had contrived mechanism which, I thought, would
accomplish my object. <span class="xxpn" id="p115">{115}</span></p>

<p>I now commenced the explanation of my views, which I
soon found were but little understood by my assistant; nor
was this surprising, since in the course of my own attempt at
explanation, I found several defects in my plan, and was also
led by his questions to perceive others. All these I removed
one after another, and ultimately terminated at a late hour
my morning’s work with the conviction that <i>anticipating</i>
carriage was not only within my power, but that I had devised
one mechanism at least by which it might be accomplished.</p>

<p>Many years after, my assistant, on his return from a long
residence abroad, called upon me, and we talked over the
progress of the Analytical Engine. I referred back to the
day on which I had made that most important step, and
asked him if he recollected it. His reply was that he
perfectly remembered the circumstance; for that on retiring
to my library, he seriously thought that my intellect was
beginning to become deranged. The reader may perhaps
be curious to know how I spent the rest of that remarkable
day.</p>

<p>After working, as I constantly did, for ten or eleven hours
a day, I had arrived at this sat­is­fac­tory conclusion, and was
revising the rough sketches of the new contrivance, when
my servant entered the drawing-office, and announced that
it was seven o’clock—that I dined in Park Lane—and that it
was time to dress. I usually arrived at the house of my
friend about a quarter of an hour before the appointed time,
in order that we might have a short conversation on subjects
on which we were both much interested. Having mentioned
my recent success, in which my host thoroughly sympathized,
I remarked that it had produced an exhilaration of the spirits
which not even his excellent champagne could rival. Having
enjoyed the society of Hallam, of Rogers, and
of some few <span class="xxpn" id="p116">{116}</span>
others of that delightful circle, I retired, and joined one or
perhaps two much more extensive reunions. Having thus
forgotten science, and enjoyed society for four or five hours,
I returned home. About one o’clock I was asleep in my
bed, and thus continued for the next five hours.</p>

<hr class="hrblk" />

<p>This new and rapid system of carrying the tens when two
numbers are added together, reduced the actual time of the
addition of any number of digits, however large, to nine units
of time for the addition, and one unit for the carriage. Thus
in ten’s units of time, any two numbers, however large,
might be added together. A few more units of time, perhaps
five or six, were required for making the requisite previous
arrangements.</p>

<p>Having thus advanced as nearly as seemed possible to the
minimum of time requisite for arithmetical operations, I felt
renewed power and increased energy to pursue the far higher
object I had in view.</p>

<p>To describe the successive improvements of the Analytical
Engine would require many volumes. I only propose here
to indicate a few of its more important functions, and to give
to those whose minds are duly prepared for it some information
which will remove those vague notions of wonder, and
even of its impossibility, with which it is surrounded in the
minds of some of the most enlightened.</p>

<div class="dsdnote">〈JACQUARD LOOM.〉</div>

<p>To those who are acquainted with the principles of the
Jacquard loom, and who are also familiar with analytical
formulæ, a general idea of the means by which the Engine
executes its operations may be obtained without much difficulty.
In the Exhibition of 1862 there were many splendid
examples of such looms.</p>

<p>It is known as a fact that the Jacquard loom
is capable of <span class="xxpn" id="p117">{117}</span>
weaving any design which the imagination of man may
conceive. It is also the constant practice for skilled artists to
be employed by man­u­fac­turers in designing patterns. These
patterns are then sent to a peculiar artist, who, by means
of a certain machine, punches holes in a set of pasteboard
cards in such a manner that when those cards are placed in
a Jacquard loom, it will then weave upon its produce the
exact pattern designed by the artist.</p>

<div class="dsdnote">〈WEAVING FORMULÆ.〉</div>

<p>Now the man­u­fac­turer may use, for the warp and weft of
his work, threads which are all of the same colour; let us
suppose them to be unbleached or white threads. In this
case the cloth will be woven all of one colour; but there
will be a damask pattern upon it such as the artist designed.</p>

<p>But the man­u­fac­turer might use the same cards, and put
into the warp threads of any other colour. Every thread
might even be of a different colour, or of a different shade of
colour; but in all these cases the <i>form</i> of the pattern will
be precisely the same—the colours only will differ.</p>

<p>The analogy of the Analytical Engine with this well-known
process is nearly perfect.</p>

<p>The Analytical Engine consists of two <span
class="nowrap">parts:—</span></p>

<ul>
<li>1st. The store in which all the variables to be operated
upon, as well as all those quantities which have arisen from
the result of other operations, are placed.</li>

<li>2nd. The mill into which the quantities about to be operated
upon are always brought.</li></ul>

<p>Every formula which the Analytical Engine can be required
to compute consists of certain algebraical operations to be performed
upon given letters, and of certain other modifications
depending on the numerical value assigned to those
letters.</p>

<p>There are therefore two sets of cards, the first
to direct the <span class="xxpn" id="p118">{118}</span>
nature of the operations to be performed—these are called
operation cards: the other to direct the particular variables
on which those cards are required to operate—these latter
are called variable cards. Now the symbol of each variable
or constant, is placed at the top of a column capable of containing
any required number of digits.</p>

<p>Under this arrangement, when any formula is required to
be computed, a set of operation cards must be strung together,
which contain the series of operations in the order in which
they occur. Another set of cards must then be strung
together, to call in the variables into the mill, the order in
which they are required to be acted upon. Each operation
card will require three other cards, two to represent the variables
and constants and their numerical values upon which
the previous operation card is to act, and one to indicate the
variable on which the arithmetical result of this operation is
to be placed.</p>

<p>But each variable has below it, on the same axis, a certain
number of figure-wheels marked on their edges with the ten
digits: upon these any number the machine is capable of
holding can be placed. Whenever variables are ordered into
the mill, these figures will be brought in, and the operation
indicated by the preceding card will be performed upon them.
The result of this operation will then be replaced in the store.</p>

<div class="dsdnote">〈LAW OF DEVELOPMENT.〉</div>

<p>The Analytical Engine is therefore a machine of the most
general nature. Whatever formula it is required to develop,
the law of its development must be communicated to it by
two sets of cards. When these have been placed, the engine
is special for that particular formula. The numerical value
of its constants must then be put on the columns of wheels
below them, and on setting the Engine in motion it will calculate
and print the numerical results
of that formula. <span class="xxpn" id="p119">{119}</span></p>

<p>Every set of cards made for any formula will at any future
time recalculate that formula with whatever constants may
be required.</p>

<p>Thus the Analytical Engine will possess a library of its
own. Every set of cards once made will at any future time
reproduce the calculations for which it was first arranged.
The numerical value of its constants may then be inserted.</p>

<p>It is perhaps difficult to apprehend these descriptions without
a familiarity both with analytical forms and mechanical
structures. I will now, therefore, confine myself to the
math­e­mat­i­cal view of the Analytical Engine, and illustrate by
example some of its supposed difficulties.</p>

<p>An excellent friend of mine, the late Professor MacCullagh,
of Dublin, was discussing with me, at breakfast, the various
powers of the Analytical Engine. After a long conversation
on the subject, he inquired what the machine could do if, in
the midst of algebraic operations, it was required to perform
logarithmic or trigonometric operations.</p>

<div class="dsdnote">〈ITS USE OF TABLES.〉</div>

<p>My answer was, that whenever the Analytical Engine
should exist, all the developments of formula would be
directed by this condition—that the machine should be able
to compute their numerical value in the shortest possible
time. I then added that if this answer were not sat­is­fac­tory,
I had provided means by which, with equal accuracy, it might
compute by logarithmic or other Tables.</p>

<div class="dsdnote">〈DISCOVERS A MISTAKE.〉</div>

<p>I explained that the Tables to be used must, of course, be
computed and punched on cards by the machine, in which
case they would undoubtedly be correct. I then added that
when the machine wanted a tabular number, say the logarithm
of a given number, that it would ring a bell and then stop itself.
On this, the attendant would look at a certain part of the
machine, and find that it wanted the logarithm
of a given <span class="xxpn" id="p120">{120}</span>
number, say of 2303. The attendant would then go to the
drawer containing the pasteboard cards representing its table
of logarithms. From amongst these he would take the
required logarithmic card, and place it in the machine.
Upon this the engine would first ascertain whether the
assistant had or had not given him the correct logarithm of
the number; if so, it would use it and continue its work.
But if the engine found the attendant had given him a wrong
logarithm, it would then ring a louder bell, and stop itself.
On the attendant again examining the engine, he would
observe the words, “Wrong tabular number,” and then
discover that he really had given the wrong logarithm, and of
course he would have to replace it by the right one.</p>

<p>Upon this, Professor MacCullagh naturally asked why, if
the machine could tell whether the logarithm was the right
one, it should have asked the attendant at all? I told
him that the means employed were so ridiculously simple
that I would not at that moment explain them; but that if
he would come again in the course of a few days, I should be
ready to explain it. Three or four days after, Bessel and
Jacobi, who had just arrived in England, were sitting with
me, inquiring about the Analytical Engine, when fortunately
my friend MacCullagh was announced. The meeting was
equally agreeable to us all, and we continued our conversation.
After some time Bessel put to me the very same
question which MacCullagh had previously asked. On this
Jacobi remarked that he, too, was about to make the same
inquiry when Bessel had asked the question. I then
explained to them the following very simple means by which
that verification was accomplished.</p>

<div class="dsdnote">〈KNOWS WHAT IT WANTS.〉</div>

<p>Besides the sets of cards which direct the nature of the
operations to be performed, and the
variables or constants <span class="xxpn" id="p121">{121}</span>
which are to be operated upon, there is another class of cards
called number cards. These are much less general in their
uses than the others, although they are necessarily of much
larger size.</p>

<p>Any number which the Analytical Engine is capable of
using or of producing can, if required, be expressed by a card
with certain holes in it; <span class="nowrap">thus—</span></p>

<div class="dtablebox">
<table class="borall" summary="">
<tr>
 <th colspan="4" scope="colgroup">N<b>UMBER</b>.</th>
 <th>&nbsp;&nbsp;</th>
 <th colspan="7" scope="colgroup">T<b>ABLE</b>.</th></tr>
<tr>
 <th class="bor13" scope="col">2</th>
 <th class="bor13" scope="col">3</th>
 <th class="bor13" scope="col">0</th>
 <th class="bor13" scope="col">3</th>
 <th class="bor13" scope="col">&nbsp;&nbsp;</th>
 <th class="bor13" scope="col">3</th>
 <th class="bor13" scope="col">6</th>
 <th class="bor13" scope="col">2</th>
 <th class="bor13" scope="col">2</th>
 <th class="bor13" scope="col">9</th>
 <th class="bor13" scope="col">3</th>
 <th class="bor13" scope="col">9</th></tr>
<tr>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">&nbsp;&nbsp;</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td></tr>
<tr>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">&nbsp;&nbsp;</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td></tr>
<tr>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">&nbsp;&nbsp;</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">•</td></tr>
<tr>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">&nbsp;&nbsp;</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td></tr>
<tr>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">&nbsp;&nbsp;</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td></tr>
<tr>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">&nbsp;&nbsp;</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td></tr>
<tr>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">&nbsp;&nbsp;</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td></tr>
<tr>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">&nbsp;&nbsp;</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td></tr>
<tr>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">&nbsp;&nbsp;</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td>
 <td class="tdcntr">◊</td>
 <td class="tdcntr">•</td></tr>
</table></div>

<p>The above card contains eleven vertical rows for holes,
each row having nine or any less number of holes. In this
example the tabular number is 3&nbsp;6&nbsp;2&nbsp;2&nbsp;9&nbsp;3&nbsp;9, whilst its number
in the order of the table is 2&nbsp;3&nbsp;0&nbsp;3. In fact, the former
number is the logarithm of the latter.</p>

<p>The Analytical Engine will contain,</p>

<ul>
<li>1st. Apparatus for printing on paper, one, or, if required,
two copies of its results.</li>

<li>2nd. Means for producing a stereotype mould of the tables
or results it computes.</li>

<li>3rd. Mechanism for punching on blank pasteboard cards or
metal plates the numerical results of any of its computations.</li></ul>

<div class="dsdnote">〈STOPS AND RINGS A BELL.〉</div>

<p>Of course the Engine will compute all
the Tables which <span class="xxpn" id="p122">{122}</span>
it may itself be required to use. These cards will therefore
be entirely free from error. Now when the Engine requires
a tabular number, it will stop, ring a bell, and ask for such
number. In the case we have assumed, it asks for the logarithm
of 2&nbsp;3&nbsp;0&nbsp;3.</p>

<p>When the attendant has placed a tabular card in the
Engine, the first step taken by it will be to verify the <i>number</i>
of the card given it by subtracting its number from 2&nbsp;3&nbsp;0&nbsp;3,
the number whose logarithm it asked for. If the remainder
is zero, then the engine is certain that the logarithm must be
the right one, since it was computed and punched by itself.</p>

<p>Thus the Analytical Engine first computes and punches on
cards its own tabular numbers. These are brought to it by
its attendant when demanded. But the engine itself takes
care that the <i>right</i> card is brought to it by verifying the
<i>number</i> of that card by the number of the card which it
demanded. The Engine will always reject a wrong card by
continually ringing a loud bell and stopping itself until supplied
with the precise in­tel­lec­tual food it demands.</p>

<p>It will be an interesting question, which time only can solve,
to know whether such tables of cards will ever be required
for the Engine. Tables are used for saving the time of continually
computing individual numbers. But the computations
to be made by the Engine are so rapid that it seems
most probable that it will make shorter work by computing
directly from proper formulæ than by having recourse even to
its own Tables.</p>

<p>The Analytical Engine I propose will have the power of
expressing every number it uses to fifty places of figures. It
will multiply any two such numbers together, and then, if
required, will divide the product of one hundred figures by
number of fifty
places of figures. <span class="xxpn" id="p123">{123}</span></p>

<div class="dsdnote">〈ARITHMETICAL DIFFICULTIES.〉</div>

<p>Supposing the velocity of the moving parts of the Engine
to be not greater than forty feet per minute, I have no doubt
that</p>

<ul>
<li>Sixty additions or subtractions may be completed and
printed in one minute.</li>

<li>One multiplication of two numbers, each of fifty figures,
in one minute.</li>

<li>One division of a number having 100 places of figures
by another of 50 in one minute.</li></ul>

<p>In the various sets of drawings of the modifications of the
mechanical structure of the Analytical Engines, already numbering
upwards of thirty, two great principles were embodied
to an unlimited extent.</p>

<ul>
<li>1st. The entire control over <i>arithmetical</i> operations, however
large, and whatever might be the number of their digits.</li>

<li>2nd. The entire control over the <i>combinations</i> of algebraic
symbols, however lengthened those processes may be required.
The possibility of fulfilling these two conditions
might reasonably be doubted by the most accomplished mathematician
as well as by the most ingenious mechanician.</li></ul>

<p>The difficulties which naturally occur to those capable of
examining the question, as far as they relate to arithmetic,
are <span class="nowrap">these,—</span></p>

<ul>
<li>(<i>a</i>). The number of digits in <i>each constant</i> inserted in the
Engine must be without limit.</li>

<li>(<i>b</i>). The number of constants to be inserted in the Engine
must also be without limit.</li>

<li>(<i>c</i>). The number of operations necessary for arithmetic is
only four, but these four may be repeated an <i>unlimited</i>
number of times.</li>

<li>(<i>d</i>). These operations may occur in any order, or
follow an <i>unlimited</i> number of laws. <span class="xxpn"
id="p124">{124}</span></li></ul>

<div class="dsdnote">〈ALGEBRAICAL DIFFICULTIES.〉</div>

<p>The following conditions relate to the algebraic portion of
the Analytical <span class="nowrap">Engine:—</span></p>

<ul>
<li>(<i>e</i>). The number of <i>litteral</i> constants
must be <i>unlimited</i>.</li>

<li>(<i>f</i>). The number of <i>variables</i> must be <i>without limit</i>.</li>

<li>(<i>g</i>). The combinations of the algebraic signs must <i>be
unlimited</i>.</li>

<li>(<i>h</i>). The number of <i>functions</i> to be employed must be <i>without
limit</i>.</li></ul>

<p>This enumeration includes eight conditions, each of which
is absolutely <i>unlimited</i> as to the number of its combinations.</p>

<p>Now it is obvious that no <i>finite</i> machine can include infinity.
It is also certain that no question <i>necessarily</i> involving infinity
can ever be converted into any other in which the idea
of infinity under some shape or other does not enter.</p>

<p>It is impossible to construct machinery occupying unlimited
space; but it is possible to construct finite machinery, and to
use it through unlimited time. It is this substitution of the
<i>infinity of time</i> for the <i>infinity of space</i> which I have made
use of, to limit the size of the engine and yet to retain its
unlimited power.</p>

<p>(<i>a</i>). I shall now proceed briefly to point out the means by
which I have effected this change.</p>

<div class="dsdnote">〈LARGER NUMBERS TREATED.〉</div>

<p>Since every calculating machine must be constructed for
the calculation of a definite number of figures, the first datum
must be to fix upon that number. In order to be somewhat
in advance of the greatest number that may ever be required,
I chose fifty places of figures as the standard for the Analytical
Engine. The intention being that in such a machine
two numbers, each of fifty places of figures, might be multiplied
together and the resultant product of one hundred
places might then be divided by another
number of fifty <span class="xxpn" id="p125">{125}</span>
places. It seems to me probable that a long period must
elapse before the demands of science will exceed this limit.
To this it may be added that the addition and subtraction of
numbers in an engine constructed for <i>n</i> places of figures
would be equally rapid whether <i>n</i> were equal to five or five
thousand digits. With respect to multiplication and division,
the time required is <span class="nowrap">greater:—</span></p>

<p>Thus if <i>a</i>&#x2009;.&#x202f;10<sup>50</sup>&#x2009;+&#x202f;<i>b</i>
and
<i>a′</i>&#x2009;.&#x202f;10<sup>50</sup>&#x2009;+&#x202f;<i>b′</i> are two numbers
each of less than a hundred places of figures, then each can
be expressed upon two columns of fifty figures, and <i>a</i>, <i>b</i>, <i>a′</i>, <i>b′</i>
are each less than fifty places of figures: they can therefore
be added and subtracted upon any column holding fifty places
of figures.</p>

<p>The product of two such numbers <span class="nowrap">is—</span></p>

<div>
<i>a</i>&#x200a;<i>a′</i>&#x200a;10<sup>100</sup>&#x2009;+&#x202f;(<i>a</i>&#x200a;<i>b′</i>&#x2009;+&#x202f;<i>a′</i>&#x200a;<i>b</i>)&#x200a;10<sup>50</sup>&#x2009;+&#x202f;<i>b</i>&#x200a;<i>b′</i>.
</div>

<p>This expression contains four pair of factors, <i>a</i>&#x200a;<i>a′</i>,
<i>a</i>&#x200a;<i>b′</i>, <i>a′</i>&#x200a;<i>b</i>,
<i>b</i>&#x200a;<i>b′</i>, each factor of
which has less than fifty places of figures. Each multiplication can
therefore be executed in the Engine. The time, however, of multiplying
two numbers, each consisting of any number of digits between fifty and
one hundred, will be nearly four times as long as that of two such
numbers of less than fifty places of figures.</p>

<p>The same reasoning will show that if the numbers of digits
of each factor are between one hundred and one hundred and
fifty, then the time required for the operation will be nearly
nine times that of a pair of factors having only fifty digits.</p>

<p>Thus it appears that whatever may be the number of digits
the Analytical Engine is capable of holding, if it is required
to make all the computations with <i>k</i> times that number of
digits, then it can be executed by the same Engine, but in an
amount of time equal to <i>k</i><sup>2</sup> times the
former. Hence the <span class="xxpn" id="p126">{126}</span>
condition (<i>a</i>), or the unlimited number of digits contained in
each constant employed, is fulfilled.</p>

<p>It must, however, be admitted that this advantage is gained
at the expense of diminishing the number of the constants the
Engine can hold. An engine of fifty digits, when used as one of a
hundred digits, can only contain half the number of variables. An
engine containing <i>m</i> columns, each holding <i>n</i> digits, if used
for computations requiring
<span class="nowrap"><i>k</i>&#x200a;<i>n</i></span> digits, can only hold
<span class="nowrap"><i>m</i>&#x200a;/&#x200a;<i>k</i></span> constants or
variables.</p>

<div class="dsdnote">〈OF PUNCHING CARDS.〉</div>

<p>(<i>b</i>). The next step is therefore to prove (<i>b</i>), viz.: to show
that a finite engine can be used as if it contained an unlimited
number of constants. The method of punching cards for tabular numbers
has already been alluded to. Each Analytical Engine will contain one
or more apparatus for printing any numbers put into it, and also an
apparatus for punching on pasteboard cards the holes corresponding to
those numbers. At another part of the machine a series of number cards,
resembling those of Jacquard, but delivered to and computed by the
machine itself, can be placed. These can be called for by the Engine
itself in any order in which they may be placed, or according to <i>any
law</i> the Engine may be directed to use. Hence the condition (<i>b</i>) is
fulfilled, namely: an <i>unlimited number of constants</i> can be inserted
in the machine in an <i>unlimited</i> time.</p>

<p>I propose in the Engine I am constructing to have places
for only a thousand constants, because I think it will be more
than sufficient. But if it were required to have ten, or even
a hundred times that number, it would be quite possible to
make it, such is the simplicity of its structure of that portion
of the Engine.</p>

<div class="dsdnote">〈A THOUSAND VARIABLES.〉</div>

<p>(<i>c</i>). The next stage in the arithmetic is the
number of times <span class="xxpn" id="p127">{127}</span>
the four processes of addition, subtraction, multiplication, and
division can be repeated. It is obvious that four different
cards thus punched</p>

<div class="dctr01"><img src="images/i127.png"
width="600" height="80" alt="" /></div>

<p class="pcontinue">would give the orders for the four rules of
arithmetic.</p>

<p>Now there is no limit to the number of such cards which
may be strung together according to the nature of the operations
required. Consequently the condition (<i>c</i>) is fulfilled.</p>

<p>(<i>d</i>). The fourth arithmetical condition (<i>d</i>), that the order
of succession in which these operations can be varied, is itself
<i>unlimited</i>, follows as a matter of course.</p>

<p>The four remaining conditions which must be fulfilled, in
order to render the Analytical Engine as general as the
science of which it is the powerful executive, relate to algebraic
quantities with which it operates.</p>

<p>The thousand columns, each capable of holding any number of less
than fifty-one places of figures, may each represent a constant or a
variable quantity. These quantities I have called by the comprehensive
title of variables, and have denoted them by V<sub><i>n</i></sub>, with
an index below. In the machine I have designed, <i>n</i> may vary from
0 to 999. But after any one or more columns have been used for
variables, if those variables are not required afterwards, they may be
printed upon paper, and the columns themselves again used for other
variables. In such cases the variables must have a new index; thus,
<sup><i>m</i></sup>V<sup><i>n</i></sup>.
I propose to make <i>n</i> vary from 0 to
99. If more variables are required, these may be supplied by Variable
Cards, which may follow each other in unlimited succession. Each card
will cause its symbol to be printed with its proper indices. <span
class="xxpn" id="p128">{128}</span></p>

<p>For the sake of uniformity, I have used V with as many
indices as may be required throughout the Engine. This,
however, does not prevent the printed result of a development
from being represented by any letters which may be
thought to be more convenient. In that part in which the
results are printed, type of any form may be used, according
to the taste of the proposer of the question.</p>

<p>It thus appears that the two conditions, (<i>e</i>) and (<i>f</i>), which
require that the number of constants and of variables should
be unlimited, are both fulfilled.</p>

<p>The condition (<i>g</i>) requiring that the number of combinations
of the four algebraic signs shall be unlimited, is easily
fulfilled by placing them on cards in any order of succession
the problem may require.</p>

<p>The last condition (<i>h</i>), namely, that the number of functions
to be employed must be without limit, might seem at
first sight to be difficult to fulfil. But when it is considered
that any function of any number of operations performed
upon any variables is but a combination of the four simple
signs of operation with various quantities, it becomes apparent
that any function whatever may be represented by
two groups of cards, the first being signs of operation, placed
in the order in which they succeed each other, and the second
group of cards representing the variables and constants placed
in the order of succession in which they are acted upon by the
former.</p>

<div class="dsdnote">〈A FINITE MACHINE MAY MAKE UNLIMITED CALCULATION.〉</div>

<p>Thus it appears that the whole of the conditions which
enable a <i>finite</i> machine to make calculations of <i>unlimited</i>
extent are fulfilled in the Analytical Engine. The means I
have adopted are uniform. I have converted the infinity of
space, which was required by the conditions of the problem,
into the infinity of time. The means I have
employed are in <span class="xxpn" id="p129">{129}</span>
daily use in the art of weaving patterns. It is accomplished by
systems of cards punched with various holes strung together
to any extent which may be demanded. Two large boxes,
the one empty and the other filled with perforated cards, are
placed before and behind a polygonal prism, which revolves
at intervals upon its axis, and advances through a short space,
after which it immediately returns.</p>

<p>A card passes over the prism just before each stroke of the
shuttle; the cards that have passed hang down until they
reach the empty box placed to receive them, into which they
arrange themselves one over the other. When the box is full,
another empty box is placed to receive the coming cards, and
a new full box on the opposite side replaces the one just
emptied. As the suspended cards on the entering side are
exactly equal to those on the side at which the others are
delivered, they are perfectly balanced, so that whether the
formulæ to be computed be excessively complicated or very
simple, the force to be exerted always remains nearly the
same.</p>

<div class="dsdnote">〈DISCUSSIONS AT TURIN.〉</div>

<p>In 1840 I received from my friend M. Plana a letter pressing me
strongly to visit Turin at the then approaching meeting of Italian
phi­los­o­phers. In that letter M. Plana stated that he had inquired
anxiously of many of my countrymen about the power and mechanism of the
Analytical Engine. He remarked that from all the information he could
collect the case seemed to stand <span class="nowrap">thus:—</span></p>

<p>“Hitherto the <i>legislative</i> department of our analysis has
been all powerful—the <i>executive</i> all feeble.</p>

<p>“Your engine seems to give us the same control over the
executive which we have hitherto only possessed over the
legislative department.”</p>

<p>Considering the exceedingly
limited information which <span class="xxpn" id="p130">{130}</span>
could have reached my friend respecting the Analytical
Engine, I was equally surprised and delighted at his exact
prevision of its powers. Even at the present moment I could
not express more clearly, and in fewer terms, its real object.
I collected together such of my models, drawings, and notations
as I conceived to be best adapted to give an insight
into the principles and mode of operating of the Analytical
Engine. On mentioning my intention to my excellent
friend the late Professor MacCullagh, he resolved to give up
a trip to the Tyrol, and join me at Turin.</p>

<p>We met at Turin at the appointed time, and as soon as the
first bustle of the meeting had a little abated, I had the great
pleasure of receiving at my own apartments, for several mornings,
Messrs. Plana, Menabrea, Mossotti, MacCullagh, Plantamour,
and others of the most eminent geometers and engineers
of Italy.</p>

<p>Around the room were hung the formula, the drawings,
notations, and other illustrations which I had brought with
me. I began on the first day to give a short outline of the
idea. My friends asked from time to time further explanations
of parts I had not made sufficiently clear. M. Plana
had at first proposed to make notes, in order to write an outline
of the principles of the engine. But his own laborious
pursuits induced him to give up this plan, and to transfer
the task to a younger friend of his, M. Menabrea, who had
already established his reputation as a profound analyst.</p>

<p>These discussions were of great value to me in several
ways. I was thus obliged to put into language the various
views I had taken, and I observed the effect of my explanations
on different minds. My own ideas became clearer, and
I profited by many of the remarks made by my highly-gifted
friends. <span class="xxpn" id="p131">{131}</span></p>

<div class="dsdnote">〈MOSOTTI’S DIFFICULTY.〉</div>

<p>One day Mosotti, who had been unavoidably absent from
the previous meeting, when a question of great importance
had been discussed, again joined the party. Well aware of
the acuteness and rapidity of my friend’s intellect, I asked
my other friends to allow me five minutes to convey to Professor
Mosotti the substance of the preceding sitting. After
putting a few questions to Mosotti himself, he placed before
me distinctly his greatest difficulty.</p>

<p>He remarked that he was now quite ready to admit the
power of mechanism over numerical, and even over algebraical
relations, to any extent. But he added that he had no
conception how the machine could perform the act of judgment
sometimes required during an analytical inquiry, when
two or more different courses presented themselves, especially
as the proper course to be adopted could not be known in
many cases until all the previous portion had been gone
through.</p>

<div class="dsdnote">〈SOLUTION OF EQUATIONS.〉</div>

<p>I then inquired whether the solution of a numerical equation
of any degree by the usual, but very tedious proceeding
of approximation would be a type of the difficulty to be
explained. He at once admitted that it would be a very
eminent one.</p>

<p>For the sake of perspicuity and brevity I shall confine my
present explanation to possible roots.</p>

<p>I then mentioned the successive <span class="nowrap">stages:—</span></p>

<ul>
<li class="li0">
<p class="padtopc" id="pp131">Number of<br />Operation<br />Cards used.</p>
<p class="phanga">1 <i>a.</i> Ascertain the number of possible roots by applying Sturm’s
theorem to the coefficients.</p></li>

<li class="li0"><p class="phanga">2 <i>b.</i>
 Find a number greater than the greatest root.</p></li>

<li class="li0"><p class="phanga">3 <i>c.</i>
 Substitute the powers of ten (commencing with that next greater than
 the greatest root, and <span class="xxpn" id="p132">{132}</span>
 diminishing the powers by unity at each step) for the value of <i>x</i> in
 the given equation.</p>

<p class="pina">Continue this until the sign of the resulting number
changes from positive to negative.</p>

<p class="pina">The index of the last power of ten (call it <i>n</i>),
which is positive, expresses the number of digits in that part
of the root which consists of whole numbers. Call this index
<i>n</i>&#x2009;+&#x202f;1.</p></li>

<li class="li0"><p class="phanga">4 <i>d.</i> Substitute successively
for <i>x</i> in the original equation 0&#x2009;×&#x202f;10<sup>n</sup>,
1&#x2009;×&#x202f;10<sup>n</sup>, 2&#x2009;×&#x202f;10<sup>n</sup>,
3&#x2009;×&#x202f;10<sup>n</sup>,&nbsp;.&nbsp;.&nbsp;.&nbsp;.
9&#x2009;×&#x202f;10<sup>n</sup>, until a change of sign occurs in the
result. The digit previously substituted will be the first figure of
the root sought.</p></li>

<li class="li0"><p class="phanga">5 <i>e.</i> Transform the original
equation into another whose roots are less by the number thus found.</p>

<p class="pina">The transformed equation will have a real root, the
digit, less than 10<sup>n</sup>.</p></li>

<li class="li0"><p class="phanga">6 <i>f.</i> Substitute
1&#x2009;×&#x202f;10<sup>n−1</sup>, 2&#x2009;×&#x202f;10<sup>n−1</sup>,
3&#x2009;×&#x202f;10<sup>n−1</sup>, &amp;c., successively for the root
of this equation, until a change of sign occurs in the result, as in
process 4.</p>

<p class="pina">This will give the second figure of the root.</p>

<p class="pina">This process of alternately finding a new figure in the
root, and then transforming the equation into another (as in process
4 and 5), must be carried on until as many figures as are required,
whether whole numbers or decimals, are arrived at.</p></li>

<li class="li0"><p class="phanga">7 <i>g.</i> The root thus found must now
be used to reduce the original equation to one dimension lower. <span
class="xxpn" id="p133">{133}</span></p></li>

<li class="li0"><p class="phanga">8 <i>h.</i> This new equation of one
dimension lower must now be treated by sections 3, 4, 5, 6, and 7,
until the new root is found.</p></li>

<li class="li0"><p class="phanga">9 <i>i.</i> The repetition of sections 7
and 8 must go on until all the roots have been found.</p></li></ul>

<p class="padtopc">Now it will be observed that Professor Mosotti was quite
ready to admit at once that each of these different processes
could be performed by the Analytical Machine through the
medium of properly-arranged sets of Jacquard cards.</p>

<p>His real difficulty consisted in teaching the engine to know
when to change from one set of cards to another, and back
again repeatedly, at intervals not known to the person who
gave the orders.</p>

<p>The dimensions of the algebraic equation being known,
the number of arithmetical processes necessary for Sturm’s
theorem is consequently known. A set of operation cards
can therefore be prepared. These must be accompanied by
a corresponding set of variable cards, which will represent
the columns in the store, on which the several coefficients of
the given equation, and the various combinations required
amongst them, are to be placed.</p>

<p>The next stage is to find a number greater than the greatest
root of the given equation. There are various courses for
arriving at such a number. Any one of these being selected,
another set of operation and variable cards can be prepared
to execute this operation.</p>

<p>Now, as this second process invariably follows the first, the
second set of cards may be attached to the first set, and the
engine will pass on from the first to the second process, and
again from the second to
the third process. <span class="xxpn" id="p134">{134}</span></p>

<p>But here a difficulty arises: successive powers of ten are to
be substituted for <i>x</i> in the equation, until a certain event
happens. A set of cards may be provided to make the substitution
of the highest power of ten, and similarly for the
others; but on the occurrence of a certain event, namely,
the change of a sign from + to −, this stage of the calculation
is to terminate.</p>

<p>Now at a very early period of the inquiry I had found it
necessary to teach the engine to know when any numbers it
might be computing passed through zero or infinity.</p>

<p>The passage through zero can be easily ascertained, thus:
Let the continually-decreasing number which is being computed
be placed upon a column of wheels in connection with
a carrying apparatus. After each process this number will be
diminished, until at last a number is subtracted from it
which is greater than the number expressed on those wheels.</p>

<div class="dtablebox">
<table summary="">
<tr>
 <th class="tdleft" scope="row">Thus let it be</th>
 <td class="tdleft">00000,00000,00000,00423</td></tr>
<tr>
 <th class="tdleft" scope="row">Subtract</th>
 <td class="tdleft">00000,00000,00000,00511</td></tr>
<tr>
 <th class="tdleft" scope="row" title="difference"></th>
 <td class="tdleft bor10">99999,99999,99999,99912</td></tr>
</table></div>

<p>Now in every case of a carriage becoming due, a certain
lever is transferred from one position to another in the cage
next above it.</p>

<p>Consequently in the highest cage of all (say the fiftieth in
the Analytical Engine), an arm will be moved or not moved
accordingly as the carriages do or do not run up beyond the
highest wheel.</p>

<p>This arm can, of course, make any change which has previously
been decided upon. In the instance we have been
considering it would order the cards to be turned on to the
next set.</p>

<p>If we wish to find when any number,
which is increasing, <span class="xxpn" id="p135">{135}</span>
exceeds in the number of its digits the number of wheels on
the columns of the machine, the same carrying arm can be
employed. Hence any directions may be given which the
circumstances require.</p>

<p>It will be remarked that this does not actually prove, even
in the Analytical Engine of fifty figures, that the number
computed has passed through infinity; but only that it has
become greater than any number of fifty places of figures.</p>

<p>There are, however, methods by which any machine made
for a given number of figures may be made to compute the same
formulæ with double or any multiple of its original number.
But the nature of this work prevents me from explaining that
method.</p>

<p>It may here be remarked that in the process, the cards
employed to make the substitutions of the powers of ten are
operation cards. They are, therefore, quite independent of
the numerical values substituted. Hence the same set of
<i>operation</i> cards which order the substitutions 1&#x2009;×&#x202f;10<sup>n</sup> will, if
backed, order the substitution of 2&#x2009;×&#x202f;10<sup>n</sup>, &amp;c. We may,
therefore, avail ourselves of mechanism for backing these
cards, and call it into action whenever the circumstances
themselves require it.</p>

<p>The explanation of M. Mosotti’s difficulty is this:—Mechanical
means have been provided for backing or advancing
the operation cards to any extent. There exist means of
expressing the conditions under which these various processes
are required to be called into play. It is not even necessary
that two courses only should be possible. Any number
of courses may be possible at the same time; and the choice
of each may depend upon any number of conditions.</p>

<div class="dsdnote">〈GENERAL MENABREA’S DESCRIPTION.〉</div>

<p>It was during these meetings that my highly valued friend,
M. Menabrea, collected the materials for
that lucid and <span class="xxpn" id="p136">{136}</span>
admirable description which he sub­se­quent­ly published in
the Bibli. Univ. de Genève, t. xli. Oct. 1842.</p>

<p>The elementary principles on which the Analytical Engine
rests were thus in the first instance brought before the public
by General Menabrea.</p>

<div class="dsdnote">〈THE COUNTESS OF LOVELACE’S NOTES.〉</div>

<p>Some time after the appearance of his memoir on the
subject in the “Bibliothèque Universelle de Genève,” the
late Countess of Lovelace<a class="afnanc" href="#fn25" id="fnanc25">25</a>
informed me that she had translated
the memoir of Menabrea. I asked why she had not
herself written an original paper on a subject with which she
was so intimately acquainted? To this Lady Lovelace replied
that the thought had not occurred to her. I then suggested
that she should add some notes to Menabrea’s memoir; an
idea which was immediately adopted.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc25" id="fn25">25</a>
Ada Augusta, Countess of Lovelace,
only child of the Poet Byron.</p></div>

<p>We discussed together the various illustrations that might
be introduced: I suggested several, but the selection was
entirely her own. So also was the algebraic working out of
the different problems, except, indeed, that relating to the
numbers of Bernouilli, which I had offered to do to save
Lady Lovelace the trouble. This she sent back to me for
an amendment, having detected a grave mistake which I had
made in the process.</p>

<p>The notes of the Countess of Lovelace extend to about
three times the length of the original memoir. Their author
has entered fully into almost all the very difficult and abstract
questions connected with the subject.</p>

<p>These two memoirs taken together furnish, to those who
are capable of understanding the reasoning, a complete demonstration—<i>That
the whole of the developments and operations
of analysis are now capable of being executed by machinery</i>.</p>

<div class="dsdnote">〈VARIOUS APPLICATIONS.〉</div>

<p>There are various methods by which
these developments <span class="xxpn" id="p137">{137}</span>
are arrived at:—1. By the aid of the Differential and Integral
Calculus. 2. By the Combinatorial Analysis of Hindenburg.
3. By the Calculus of Derivations of Arbogast.</p>

<p>Each of these systems professes to expand any function
according to any laws. Theoretically each method may be
admitted to be perfect; but practically the time and attention
required are, in the greater number of cases, more than the
human mind is able to bestow. Consequently, upon several
highly interesting questions relative to the Lunar theory,
some of the ablest and most indefatigable of existing analysts
are at variance.</p>

<p>The Analytical Engine is capable of executing the laws
prescribed by each of these methods. At one period I examined
the Combinatorial Analysis, and also took some pains
to ascertain from several of my German friends, who had had
far more experience of it than myself, whether it could be
used with greater facility than the Differential system. They
seemed to think that it was more readily applicable to all
the usual wants of analysis.</p>

<p>I have myself worked with the system of Arbogast, and if
I were to decide from my own limited use of the three
methods, I should, for the purposes of the Analytical Engine,
prefer the Calcul des Derivations.</p>

<p>As soon as an Analytical Engine exists, it will necessarily
guide the future course of the science. Whenever any result
is sought by its aid, the question will then arise—By what
course of calculation can these results be arrived at by the
machine in the <i>shortest time</i>?</p>

<p>In the drawings I have prepared I proposed to have a
thousand variables, upon each of which any number not
having more than fifty figures can be placed. This machine
would multiply 50 figures by other 50, and
print the product <span class="xxpn" id="p138">{138}</span>
of 100 figures. Or it would divide any number having 100
figures by any other of 50 figures, and print the quotient of
50 figures. Allowing but a moderate velocity for the machine,
the time occupied by either of these operations would be about
one minute.</p>

<p>The whole of the <i>numerical</i> constants throughout the works
of Laplace, Plana, Le Verrier, Hansen, and other eminent
men whose indefatigable labours have brought astronomy to
its present advanced state, might easily be recomputed.
They are but the numerical coefficients of the various terms
of functions developed according to certain series. In all
cases in which these numerical constants can be calculated
by more than one method, it might be desirable to compute
them by several processes until frequent practice shall have
confirmed our belief in the infallibility of mechanism.</p>

<div class="dsdnote">〈ERRORS OF TABLES.〉</div>

<p>The great importance of having accurate Tables is admitted
by all who understand their uses; but the multitude of errors
really occurring is comparatively little known. Dr. Lardner,
in the “Edinburgh Review,” has made some very instructive
remarks on this subject.</p>

<p>I shall mention two within my own experience: these are
selected because they occurred in works where neither care
nor expense were spared on the part of the Government
to insure perfect accuracy. It is, however, but just to the
eminent men who presided over the preparation of these
works for the press to observe, that the real fault lay not in
them but in <i>the nature of things</i>.</p>

<p>In 1828 I lent the Government an original MS. of the
table of Logarithmic Sines, Cosines, &amp;c., computed to every
second of the quadrant, in order that they might have it
compared with Taylor’s Logarithms, 4to., 1792, of which
they possessed a considerable number
of copies. Nineteen <span class="xxpn" id="p139">{139}</span>
errors were thus detected, and a list of these errata was published
in the Nautical Almanac for 1832: these may be
called</p>

<div class="dp139">Nineteen errata of the first
order&nbsp;.&nbsp;.&nbsp;1832.</div>

<p class="pcontinue">An error being detected in one of these errata, in
the following Nautical Almanac we find an</p>

<div class="dp139">Erratum of the errata in N. Alm.
1832&nbsp;.&nbsp;.&nbsp;1833.</div>

<p class="pcontinue">But in this very erratum of the second order a new
mistake was introduced larger than any of the original mistakes. In the
year next following there ought to have been found</p>

<div class="dp139">Erratum in the erratum of the errata in N. Alm.
1832&nbsp;.&nbsp;.&nbsp;1834.</div>

<p>In the “Tables de la Lune,” by M. P. A. Hansen, 4to, 1857,
published at the expense of the English Government, under
the direction of the Astronomer Royal, is to be found a list
of errata amounting to 155. In the 21st of these original
errata there have been found <i>three</i> mistakes. These are
duly noted in a newly-printed list of errata discovered during
computations made with them in the “Nautical Almanac;”
so that we now have the errata of an erratum of the original
work.</p>

<p>This list of errata from the office of the “Nautical Almanac”
is larger than the original list. The total number of errors
at present (1862) discovered in Hansen’s “Tables of the
Moon” amounts to above three hundred and fifty. In
making these remarks I have no intention of imputing the
slightest blame to the Astronomer Royal, who, like other
men, cannot avoid submitting to inevitable fate. The only
circumstance which is really extraordinary is that, when it
was dem­on­strated that all tables are capable of being computed
by machinery, and even when a
machine existed which <span class="xxpn" id="p140">{140}</span>
computed certain tables, that the Astronomer Royal did not
become the most enthusiastic supporter of an instrument
which could render such invaluable service to his own science.</p>

<p>In the Supplementary Notices of the Astronomical Society,
No. 9, vol. xxiii., p. 259, 1863, there occurs a Paper by
M. G. de Ponteculant, in which forty-nine numerical coefficients
relative to the Longitude, Latitude, and Radius vector
of the Moon are given as computed by Plana, Delaunay, and
Ponteculant. The computations of Plana and Ponteculant
agree in thirteen cases; those of Delaunay and Ponteculant
in two; and in the remaining thirty-four cases they all three
differ.</p>

<div class="dsdnote">〈REMARKS ON ANALYSIS.〉</div>

<p>I am unwilling to terminate this chapter without reference
to another difficulty now arising, which is calculated to impede
the progress of Analytical Science. The extension of
analysis is so rapid, its domain so unlimited, and so many
inquirers are entering into its fields, that a variety of new
symbols have been introduced, formed on no common principles.
Many of these are merely new ways of expressing
well-known functions. Unless some philosophical principles
are generally admitted as the basis of all notation, there
appears a great probability of introducing the confusion of
Babel into the most accurate of all languages.</p>

<p>A few months ago I turned back to a paper in the Philosophical
Transactions, 1844, to examine some analytical
investigations of great interest by an author who has thought
deeply on the subject. It related to the separation of symbols
of operation from those of quantity, a question peculiarly
interesting to me, since the Analytical Engine contains the
embodiment of that method. There was no ready, sufficient,
and simple mode of distinguishing letters which represented
quantity from those which
indicated operation. To <span class="xxpn" id="p141">{141}</span>
understand the results the author had arrived at, it became necessary
to read the whole Memoir.</p>

<p>Although deeply interested in the subject, I was obliged,
with great regret, to give up the attempt; for it not only
occupied much time, but placed too great a strain on the
memory.</p>

<p>Whenever I am thus perplexed it has often occurred to me
that the very simple plan I have adopted in my <i>Mechanical
Notation</i> for lettering drawings might be adopted in analysis.</p>

<p>On the geometrical drawings of machinery every piece of
matter which represents framework is invariably denoted by
an <i>upright</i> letter; whilst all letters indicating moveable parts
are marked by <i>inclined</i> letters.</p>

<p>The analogous rule would <span class="nowrap">be—</span></p>

<p>Let all letters indicating operations or modifications be
expressed by <i>upright</i> letters;</p>

<p>Whilst all letters representing quantity should be represented
by <i>inclined</i> letters.</p>

<p>The subject of the principles and laws of notation is so
important that it is desireable, before it is too late, that the
scientific academies of the world should each contribute the
results of their own examination and conclusions, and that
some congress should assemble to discuss them. Perhaps
it might be still better if each academy would draw up its
own views, illustrated by examples, and have a sufficient
number printed to send to
all other academies.</p></div><!--section-->

<div class="section" id="p142">
<h2 class="h2herein">CHAPTER IX.
<span class="hsmall">OF THE MECHANICAL NOTATION.</span></h2>

<div class="dsynopsis">Art of Lettering Drawings&#x200a;—&#x200a;Of
expressing the Time and Duration of Action of every
Part&#x200a;—&#x200a;A New Demonstrative Science&#x200a;—&#x200a;Royal
Medals of 1826.</div>

<p class="pfirst"><span class="smcap">S<b>OON</b></span>
after I had commenced the Difference Engine, my
attention was strongly directed to the imperfection of all
known modes of explaining and dem­on­strat­ing the construction
of machinery. It soon became apparent that my
progress would be seriously impeded unless I could devise
more rapid means of understanding and recalling the interpretation
of my own drawings.</p>

<p>By a new system of very simple signs I ultimately succeeded
in rendering the most complicated machine capable
of explanation almost without the aid of words.</p>

<p>In order thoroughly to understand the action of any
machine, we must have full information upon the following
subjects, and it is of the greatest importance that this
information should be acquired in the shortest possible
time.</p>

<p>I. The actual shape and relative position of every piece of
matter of which the machine is composed.</p>

<p>This can be accomplished by the ordinary mechanical
drawings. Such drawings usually have letters upon them
for the sake of reference in the description of the machine.
Hitherto such letters were chosen
without any principle, <span class="xxpn" id="p143">{143}</span>
and in fact gave no indication of anything except the mere
spot upon the paper on which they were written.</p>

<div class="dsdnote">〈RULES FOR LETTERING.〉</div>

<p>I then laid down rules for the selection of letters. I shall
only mention one or two of <span class="nowrap">them:—</span></p>

<ul>
<li>1. All upright letters, as a, c, d, e, A, B, represent framing.</li>

<li>2. All inclined letters, as <i>a</i>, <i>c</i>, <i>d</i>, <i>e</i>, <i>A</i>, <i>B</i>, represent moveable
parts.</li>

<li>3. All small letters represent working points. One of the
most obvious advantages of these rules is that they enable
the attention to be more easily confined to the immediate
object sought.</li></ul>

<p>By other rules it is rendered possible, when looking at a
plan of any complicated machine, to perceive the <i>relative
order</i> of super-position of any number of wheels, arms, &amp;c.,
without referring to the elevation or end view.</p>

<p>II. The actual time and duration of every motion throughout
the action of any machine can be ascertained almost instantly
by a system of signs called the Notations of Periods.</p>

<p>It possesses equal facilities for ascertaining every contemporaneous
as well as for every successive system of movements.</p>

<p>III. The actual connection of each moveable piece of the
machine with every other on which it acts. Thus, taking
from any special part of the drawing the indicating letter,
and looking for it on a certain diagram, called the trains, the
whole course of its movements may be traced, up to the
prime mover, or down to the final result.</p>

<p>I have called this system of signs the Mechanical Notation.
By its application to geometrical drawing it has given us
a new demonstrative science, namely, that of proving that
any given machine can or cannot exist; and if it can exist,
that it will accomplish
its desired object. <span class="xxpn" id="p144">{144}</span></p>

<p>It is singular that this addition to human knowledge
should have been made just about the period when it was
beginning to be felt by those most eminently skilled in
analysis that the time has arrived when many of its conclusions
rested only on probable evidence. This state of things
arose chiefly from the enormous extent to which the developments
were necessarily carried in the lunar and planetary
theories.</p>

<div class="dsdnote">〈ASTRONOMICAL MEDAL.〉</div>

<p>After employing this language for several years, it was
announced, in December 1825, that King William IV. had
founded two medals of fifty guineas each, to be given
annually by the Royal Society according to rules to be laid
down by the Council.</p>

<p>On the 26th January 1826, it was resolved,</p>

<p>“That it is the opinion of the Council that the medals
be awarded for the most important discoveries or series
of investigations, completed and made known to the Royal
Society in the year preceding the day of the award.”</p>

<p>This rule reduced the number of competitors to a very
few. Although I had had some experience as to the mode
in which medals were awarded, and therefore valued them
accordingly, I was simple enough to expect that the Council
of the Royal Society would not venture upon a fraud on
the very first occasion of exercising the royal liberality. I
had also another motive for taking a ticket in this philosophical
lottery of medals.</p>

<div class="dsdnote">〈ROYAL SOCIETY MEDAL.〉</div>

<p>In 1824, the Astronomical Society did me the honour to
award to me the first gold medal they ever bestowed. It
was rendered still more grateful by the address of that
eminent man, the late Henry Thomas Colebrooke, the President,
who in a spirit of prophecy anticipated the results of
years, at that
period, long future. <span class="xxpn" id="p145">{145}</span></p>

<p>“It may not, therefore, be deemed too sanguine an anticipation,
when I express the hope that an instrument which
in its simpler form attains to the extraction of the roots of
numbers, and approximates to the roots of equations, may,
in a more advanced state of improvement, rise to the
approximate solutions of algebraic equations of elevated
degrees. I refer to solutions of such equations proposed
by Lagrange, and more recently by other analysts, which
involve operations too tedious and intricate for use, and
which must remain without efficacy, unless some mode be
devised of abridging the labour or facilitating the means of
performance.”<a class="afnanc" href="#fn26" id="fnanc26">26</a></p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc26" id="fn26">26</a>
‘Discourse of the President on delivering the first Gold
Medal of the Astronomical Society to Charles Babbage, Esq.’ ‘Memoirs of
the Astronomical Society,’ vol. i. p. 509.</p></div>

<p>I felt, therefore, that the <i>first</i> Royal Medal might fairly
become an object of ambition, whatever might be the worth
of subsequent ones.</p>

<p>In order to qualify myself for this chance, I carefully drew
up a paper, “On a Method of expressing by Signs the
Action of Machinery,” which I otherwise should not have
published at that time.</p>

<p>This Memoir was read at the Royal Society on the 16th
March, 1826. To the system of signs which it first expounded
I afterwards gave the name of “Mechanical Notation.”
It had been used in England and in Ireland, although
not taught in its schools. It applies to the description of
a combat by sea or by land. It can assist in representing
the functions of animal life; and I have had both from the
Continent and from the United States, specimens of such
applications. Finally, to whatever degree of simplicity I
may at last have reduced the
Analytical Engine, the course <span class="xxpn" id="p146">{146}</span>
through which I arrived at it was the most entangled and
perplexed which probably ever occupied the human mind.
Through the aid of the Mechanical Notation I examined
numberless plans and systems of computing, and I am sure,
from the nature of its self-necessary verifications that it is
impossible I can have been deceived.</p>

<p>On the 16th November, 1826, that very Council of the
Royal Society which had made the law took the earliest
opportunity to violate it by awarding the two Royal Medals,
the first to Dalton, whose great discovery had been made
nearly twenty years before, and the other to Ivory, for
a paper published in their “Transactions” three years before.
The history of their proceedings will be found in the
“Decline of Science in England,”
p. 115, 1830.</p></div><!--section-->

<div class="section" id="p147">
<h2 class="h2herein">CHAPTER X.
<span class="hsmall">THE EXHIBITION OF 1862.</span></h2>

<hr class="hr20" />
<div class="depigram"><p>“En administration, toutes les sottises
sont mères.”—<i>Maximes</i>, par M. G. De Levis.</p>

<p>“An abject worship of princes and an unaccountable appetite for
knighthood are probably unavoidable results of placing second-rate men
in prominent positions.”—<i>Saturday Review</i>, January 16, 1864.</p>

<p>“Whose fault is this? But tallow, toys, and sweetmeats evidently
stand high in the estimation of Her Majesty’s Com­mis­sion­ers.”—<i>The
Times</i>, August 13, 1862.</p></div>
<hr class="hr20" />

<div class="dsynopsis"> Mr. Gravatt suggests to King’s College the
exhibition of the Dif­fer­ence Engine No. 1, and offers to superintend
its Trans­mis­sion and Return&#x200a;—&#x200a;Place allotted to it
most unfit&#x200a;—&#x200a;Not Exhibited in 1851&#x200a;—&#x200a;Its
Loan refused to New York&#x200a;—&#x200a;Refused to the Dublin
Exhibition in 1847&#x200a;—&#x200a;Not sent to the great
French Exhibition in 1855&#x200a;—&#x200a;Its Exhibition in
1862 entirely due to Mr. Gravatt&#x200a;—&#x200a;Space for its
Drawings refused&#x200a;—&#x200a;The Payment of Six Shillings
a Day for a compe­tent person to explain it refused by the
Com­mis­sioners&#x200a;—&#x200a;Copy of Swedish Dif­fer­ence Engine made
by English Workmen not exhibited&#x200a;—&#x200a;Loan of various
other Cal­cu­la­ting Machines offered&#x200a;—&#x200a;Anecdote of Count
Strzelecki’s&#x200a;—&#x200a;The Royal Com­mis­sion­ers’ elaborate taste
for Children’s Toys&#x200a;—&#x200a;A plan for making such Exhibitions
prof­i­table&#x200a;—&#x200a;Extrav­a­gance of the Com­mis­sioners to their
favourite&#x200a;—&#x200a;Contrast between his Treat­ment and that of
Indust­rious Workmen&#x200a;—&#x200a;The Inventor of the Dif­fer­ence
Engine publicly insulted by his Country­men in the Exhibition of
1862.</div>

<h3 class="h3herein"><i>Circumstances connected with the Exhibition of the Difference
Engine No. 1 in the International Exhibition of 1862.</i></h3>

<p class="pfirst"><span class="smcap">W<b>HEN</b></span>
the construction of the Difference Engine No. 1 was
abandoned by the Government in 1842, I was consulted respecting
the place in which it should be deposited. Well
aware of the unrivalled perfection of
its workmanship, and <span class="xxpn" id="p148">{148}</span>
conscious that it formed the first great step towards reducing
the whole science of number to the absolute control of
mechanism, I wished it to be placed wherever the greatest
number of persons could see it daily.</p>

<div class="dsdnote">〈ENGINE No. 1 IN KING’S COLLEGE.〉</div>

<p>With this view, I advised that it should be placed in one
of the much-frequented rooms of the British Museum. Another
locality was, however, assigned to it, and it was confided
by the Government to the care of King’s College,
Somerset House. It remained in safe custody within its
glass case in the Museum of that body for twenty years.
It is remarkable that during that long period no person
should have studied its structure, and, by explaining its
nature and use, have acquired an amount of celebrity which
the singularity of that knowledge would undoubtedly have
produced.</p>

<p>The College authorities did justice to their charge. They
put it in the place of honour, in the centre of their Museum,
and would, no doubt have given facilities to any of their
members or to other persons who might have wished to
study it.</p>

<div class="dsdnote">〈THE GOVERNMENT IGNORE IT.〉</div>

<p>But the system quietly pursued by the Government, of
ignoring the existence of the Difference Engine and its
inventor doubtlessly exercised its deadening influence<a class="afnanc" href="#fn27" id="fnanc27">27</a>
on
those who were inclined, by taste or acquirements, to take
such a course. <span class="xxpn" id="p149">{149}</span></p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc27" id="fn27">27</a>
An illustration fell under my notice a few days after
this paragraph was printed. A <i>new</i> work on Geometrical Drawing,
commissioned by the Committee of Council on Education, was published
by Professor Bradley. I have not been able to find in it a single word
concerning “Mechanical Notation,” not even the very simplest portion
of that science, namely, the Art of Lettering Drawings. It would seem
impossible that any <i>Professor</i> of so limited a subject could be
ignorant of the existence of such an important addition to its powers.</p></div>

<p>I shall enumerate a few instances.</p>

<p>1. In 1850, the Government appointed a Commission to
organize the Exhibition of 1851.</p>

<p>The name of the author of the <i>Economy of Man­u­fac­tures</i>
was not thought worthy by the Government to be placed on
that Commission.</p>

<p>2. In 1851, the Com­mis­sion­ers of the International Exhibition
did not think proper to exhibit the Difference
Engine, although it was the property of the nation. They
were as insensible to the greatest mechanical as to, what has
been regarded by some, the greatest in­tel­lec­tual triumph of
their country.</p>

<p>3. When it was decided by the people of the United
States to have an Exhibition at New York, they sent a
Com­mis­sion­er to Europe to make arrangement for its success.
He was authorized to apply for the loan of the Difference
Engine for a few months, and was empowered to give any
pecuniary guarantee which might be required for its safe
return.</p>

<p>That Com­mis­sion­er, on his arrival, applied to me on
the subject. I explained to him the state of the case, and
advised him to apply to the Government, whose property it
was. I added that, if his application was successful, I would at
my own expense put the machine in good working order, and
give him every information requisite for its safe conveyance
and use. His application was, however, unsuccessful.</p>

<p>4. In 1847, Mr. Dargan nobly undertook at a vast expense
to make an Exhibition in Dublin to aid in the relief of his
starving countrymen. It was thought that the exhibition of
the Difference Engine would be a great attraction. I was
informed at the time that an application was made to the
Government for its loan, and that it
was also unsuccessful. <span class="xxpn" id="p150">{150}</span></p>

<p>5. In 1855 the great French Exhibition occurred. Previously
to its opening, our Government sent Com­mis­sion­ers
to arrange and superintend the English department.</p>

<p>These Com­mis­sion­ers reported that the English cont­ri­bu­tion
was remarkably deficient in what in France are termed
“instruments de précision,” a term which includes a variety
of instruments for scientific purposes. They recommended
that “a Committee should be appointed who could represent
to the producers of Philosophical Instruments how necessary
it was that they should, upon an occasion of this kind, maintain
their credit in the eyes of Europe.” The Government
also applied to the Royal Society for advice; but neither did
the Royal Society advise, nor the Government propose, to
exhibit the Difference Engine.</p>

<p>6. The French Exhibition of 1855 was remarkable beyond
all former ones for the number and ingenuity of the machines
which performed arithmetical operations.</p>

<p>Pre-eminently above all others stood the Swedish Machine
for calculating and printing math­e­mat­i­cal Tables. It is
honourable to France that its highest reward was deservedly
given to the inventor of that machine; whilst it is somewhat
remarkable that the English Com­mis­sion­ers appointed to
report upon the French Exhibition omitted all notice of these
Calculating Machines.</p>

<div class="dsdnote">〈MR. GRAVATT SUCCEEDS IN EXHIBITING IT IN 1862.〉</div>

<p>The appearance of the finished portion of the unfinished
Difference Engine No. 1 at the Exhibition of 1862 is entirely
due to Mr. Gravatt. That gentleman had a few years before
paid great attention to the Swedish Calculating Engine of
M. Scheutz, and was the main cause of its success in this
country.</p>

<p>Being satisfied that it was possible to calculate and print
all Tables by machinery, Mr. Gravatt
became convinced that <span class="xxpn" id="p151">{151}</span>
the time must arrive when no Tables would ever be calculated
or printed except by machines. He felt that it was of great
importance to accelerate the arrival of that period, more
especially as numerical Tables, which are at present the most
expensive kind of printing, would then become the cheapest.</p>

<p>In furtherance of this idea, Mr. Gravatt wrote to Dr. Jelf,
the Principal of King’s College, Somerset House, to suggest
that the Difference Engine of Mr. Babbage, which had for so
many years occupied a prominent place in the museum,
should be exhibited in the International Exhibition of 1862.
He at the same time offered his assistance in the removal and
reinstatement of that instrument.</p>

<p>The authorities of the College readily acceded to this
plan. On further inquiry, it appeared that the Difference
Engine belonged to the Government, and was only deposited
with the College. It was then found necessary to make an
application to the Treasury for permission to exhibit it, which
was accordingly done by the proper authorities.</p>

<p>The Government granted the permission, and referred it to
the Board of Works to superintend its placement in the
building.</p>

<p>The Board of Works sent to me a copy of the correspondence
relative to this matter, asking my opinion whether
any danger might be apprehended for the safety of the
machine during its transport, and also inquiring whether I
had any other suggestion to make upon the subject.</p>

<p>Knowing the great strength of the work, I immediately
answered that I did not anticipate the slightest injury
from its transport, and that, under the superintendence of
Mr. Gravatt, I considered it might be removed with perfect
safety. The only suggestion I ventured to offer was, that as
the Government possessed in the
department of the <span class="xxpn" id="p152">{152}</span>
Registrar-General a copy, made by English workmen, of the
Swedish Difference Engine, that it should be exhibited by
the side of mine: and that both the Engines should be kept
constantly working with a very slow motion.</p>

<div class="dsdnote">〈SWEDISH ENGINE NOT EXHIBITED.〉</div>

<p>By a subsequent communication I was informed that the
Swedish Machine could not be exhibited, because it was then
in constant use, computing certain Tables relating to the
values of lives. I regretted this very much. I had intended
to alter the handle of my own Engine in order to make it
moveable circularly by the same catgut which I had hoped
might have driven both. The Tables which the Swedish
Machine was employed in printing were <i>not</i> of any pressing
necessity, and their execution could, upon such an occasion,
have been postponed for a few months without loss or inconvenience.</p>

<p>Besides, if the Swedish Engine had, as I proposed, been
placed at work, its superintendent might have continued his
table-making with but little delay, and the public would have
been highly gratified by the sight.</p>

<p>He could also have given information to the public by
occasional explanations of its principles; thus might Her
Majesty’s Com­mis­sion­ers have gratified thousands of her
subjects who came, with intense curiosity, prepared to be
pleased and instructed, and whom they sent away amazed
and disappointed.</p>

<p>From the experience I had during the first week of the
Exhibition, I am convinced that if a fit place had been provided
for the two Calculating Machines, so that the public
might have seen them both in constant but slow motion, and if
the superintendent had oc­ca­sion­al­ly given a short explanation
of the principles on which they acted, they would have been
one of the greatest attractions
within the building. <span class="xxpn" id="p153">{153}</span></p>

<p>On Mr. Gravatt applying to the Com­mis­sion­ers for space,
it was stated that the Engine must be placed amongst philosophical
instruments, Class XIII.</p>

<div class="dsdnote">〈ENGLISH ENGINE POKED INTO A HOLE.〉</div>

<p>The only place offered for its reception was a small hole,
4 feet 4 inches in front by 5 feet deep. On one side of this
was the <i>only</i> passage to the office of the superintendent
of the class. The opposite side was occupied by a glass
case in which I placed specimens of the separate parts of
the unfinished engine. These, although executed by English
workmen above thirty years ago, were yet, in the opinion
of the most eminent engineers, unsurpassed by any work
the building of 1862 contained. The back of this recess
was closed in and dark, and only allowed a space on the wall
of about five feet by four, on which to place the <i>whole</i> of the
drawings and illustrations of the Difference Engine. Close
above the top of the machine was a flat roof, which deprived
the drawings and the work itself of much light.</p>

<p>The public at first flocked to it: but it was so placed that
only three persons could conveniently see it at the same time.
When Mr. Gravatt kindly explained and set it in motion, he
was continually interrupted by the necessity of moving away in
order to allow access to the numerous persons whose business
called them to the superintendent’s office. At a very early
period various rep­re­sen­ta­tions were made to the Com­mis­sion­ers
by the Jury, the superintendent, and very strongly by
the press, of the necessity of having some qualified person to
explain the machine to the public. I was continually informed
by the attendants that hundreds of persons had, during
my absence asked, when they could get an opportunity of
seeing the machine in motion.</p>

<p>Admiring the earnestness of purpose and the sagacity with
which Mr. Gravatt had steadily followed out
the convictions of <span class="xxpn" id="p154">{154}</span>
his own mind relative to the abolition of all tables except
those made and stereotyped by machinery, I offered all the
assistance in my power to accelerate the accomplishment of
his task.</p>

<p>I lent him for exhibition numerous specimens of the
unfinished portions of the Difference Engine No. 1. These I
had purchased on the determination of the Government to
abandon its construction in 1842.</p>

<p>I proposed also to lend him the Mechanical Notations of
the Difference Engine, which had been made at my own
expense, and were finished by myself and my eldest son,
Mr. B. Herschel Babbage.</p>

<p>I had had several applications from foreigners<a class="afnanc" href="#fn28" id="fnanc28">28</a>
for some
account of my system of Mechanical Notation, and great
desire was frequently expressed to see the illustrations of the
method itself, and of its various applications.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc28" id="fn28">28</a>
One object of the mission of Professor Bolzani was, to
take back with him to Russia such an account of the Mechanical Notation
as might facilitate its teaching in the Russian Universities. I regret
that it was entirely out of my power to assist him.</p></div>

<p>These, however, were so extensive that it was impossible,
without very great inconvenience, to exhibit them even in
my own house.</p>

<div class="dsdnote">〈THE LOAN OF OTHER CALCULATING MACHINES OFFERED.〉</div>

<p>I therefore wrote to Mr. Gravatt to offer him the loan of
the following property for the <span class="nowrap">Exhibition:—</span></p>

<ul>
<li class="li0"><p class="phanga">
1. A small Calculating Machine of the simplest order for
adding together any number of separate sums of
money, provided the total was under 100,000&#x200a;<i>l.</i>, by
Sir Samuel Morland. 1666.</p></li>

<li class="li0"><p class="phanga">
2. A very complete and well-executed Machine for
answering all questions in plane trigonometry, by
Sir Samuel Morland. 1663. <span class="xxpn" id="p155">{155}</span></p></li>

<li class="li0"><p class="phanga">
3. An original set of Napier’s bones.</p></li>

<li class="li0"><p class="phanga">
4. A small Arithmetical Machine, by Viscount Mahon,
afterwards Earl Stanhope. Without date.</p></li>

<li class="li0"><p class="phanga">
5. A larger Machine, to add, subtract, multiply, and
divide, by Viscount Mahon. 1775.</p></li>

<li class="li0"><p class="phanga">
6. Another similar Machine, of a somewhat different
construction, for the same operations, by Viscount
Mahon. 1777.</p></li>

<li class="li0"><p class="phanga">
7. A small Difference Engine, made in London, in consequence
of its author having read Dr. Lardner’s
article in the “Edinburgh Review” of July, 1834,
No. CXX.</p></li></ul></div><!--section-->

<div class="section">
<h3 class="h3herein"><i>List of Mechanical Notations proposed to be Lent for the
Exhibition.</i></h3>

<ul>
<li class="li0"><p class="phanga">
1. All the drawings explaining the principles of the
Mechanical Notation.</p></li>

<li class="li0"><p class="phanga">
2. The complete Mechanical Notations of the Swedish
Calculating Engine of M. Scheutz.</p>

<p class="pina">
These latter drawings had been made and used by my youngest son,
Major Henry P. Babbage, now resident in India, in explaining the
principles of the Mechanical Notation at the meeting of the British
Association at Glasgow, and afterwards in London, at a meeting of
the Institution of Civil Engineers.<a class="afnanc" href="#fn29"
id="fnanc29">29</a></p></li>

<li class="li0"><p class="phanga">
3. The Mechanical Notations of the Difference Engine
No. 1. <span class="xxpn" id="p156">{156}</span></p>

<p class="pina">
These had been made at my own expense, and
were finished by myself and my eldest son,
Mr. B. Herschel Babbage, now resident in
South Australia.</p></li>

<li class="li0"><p class="phanga">
4. A complete set of the drawings of the Difference
Engine No. 2, for calculating and printing tables,
with seven orders of differences, and thirty places of
figures. Finished in 1849.</p></li>

<li class="li0"><p class="phanga">
5. A complete set of the Notations necessary for the
explanation and demonstration of Difference Engine
No. 2, finished in 1849.</p></li></ul>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc29" id="fn29">29</a>
See Proceedings of British Association at Glasgow, 1855,
p. 203; also Minutes of Proceedings of the Institution of Civil
Engineers, vol. xv., 1856.</p></div>

<p>These drawings and notations would have required for their
exhibition about seven or eight hundred square feet of wall.
My letter to Mr. Gravatt was forwarded to the Com­mis­sion­ers
with his own application for space to exhibit them. The
Com­mis­sion­ers declined this offer; yet during the first six
weeks of the Exhibition there was at a short distance from
the Difference Engine an empty space of wall large enough for
the greater part of these instructive diagrams. This portion
of wall was afterwards filled up by a vast oil-cloth. Other
large portions of wall, to the amount of thousands of square
feet, were given up to other oil-cloths, and to numberless
carpets. It is evident the Royal Com­mis­sion­ers were much
better qualified to judge of furniture for the feet than of furniture
for the head.</p>

<p>I was myself frequently asked why I did not employ a
person to explain the Difference Engine. In reply to some
of my friends, I inquired whether, when they purchased a
carriage, they expected the builder to pay the wages of their
coachman.</p>

<div class="dsdnote">〈FOREIGN VISITORS PUZZLED.〉</div>

<p>But my greatest difficulty was with foreigners; no explanation
I could devise, and I tried many,
appeared at all <span class="xxpn" id="p157">{157}</span>
to satisfy their minds. The thing seemed to them entirely
in­com­pre­hen­sible.</p>

<p>That the nation possessing the greatest military and commercial
marine in the world—the nation which had spent so
much in endeavouring to render perfect the means of finding
the longitude—which had recently caused to be computed
and published at considerable expense an entirely new set of
lunar Tables should not have availed itself <i>at any cost</i> of
mechanical means of computing and stereotyping such Tables,
seemed entirely beyond their comprehension.</p>

<p>At last they asked me whether the Com­mis­sion­ers were
<i>bêtes</i>. I assured them that the only <i>one</i> with whom I was
personally acquainted certainly was not.</p>

<p>When hard pressed by difficult questions, I thought it my
duty as an Englishman to save my country’s character, even
at the expense of my own. So on one occasion I suggested
to my unsatisfied friends that Com­mis­sion­ers were usually
selected from the highest class of society, and that possibly
four out of five had never heard of my name.</p>

<p>But here again my generous efforts to save the character
of my country and its Com­mis­sion­ers entirely failed. Several
of my foreign friends had known me in their own homes,
and had seen the estimation in which I was held by their
own countrymen and by their own sovereign. These were
still more astonished.</p>

<div class="dsdnote">〈CHINESE INQUIRE ABOUT IT.〉</div>

<p>On another occasion an anecdote was quoted against me
to prove that my name was well known even in China. It
may, perhaps, amuse the reader. A short time after the
arrival of Count Strzelecki in England, I had the pleasure of
meeting him at the table of a common friend. Many inquiries
were made relative to his residence in China. Much
interest was expressed by several of the party
to learn on <span class="xxpn" id="p158">{158}</span>
what subject the Chinese were most anxious to have information.
Count Strzelecki told them that the subject of most
frequent inquiry was Babbage’s Calculating Machine. On
being further asked as to the nature of the inquiries, he
said they were most anxious to know whether it would go
into the pocket. Our host now introduced me to Count
Strzelecki, opposite to whom I was then sitting. After expressing
my pleasure at the introduction, I told the Count
that he might safely assure his friends in the Celestial
Empire that it was in every sense of the word an <i>out-of-pocket</i>
machine.</p>

<p>At last the Com­mis­sion­ers were moved, not to supply the
deficiency themselves, but to address the Government, to
whom the Difference Engine belonged, to send somebody to
explain it. I received a communication from the Board of
Works, inquiring whether I could make any suggestions for
getting over this difficulty. I immediately made inquiries,
and found a person who formerly had been my amanuensis,
and had, under my direction, worked out many most
intricate problems. He possessed very considerable knowledge
of mathematics, and was willing, for the moderate remuneration
of six shillings a day, to be present daily during
nine hours to explain the Difference Engine.</p>

<p>I immediately sent this information to the Board of Works,
with the name and address of the person I recommended.
This, I have little doubt, was directly communicated to the
Com­mis­sion­ers; but they did not avail themselves of his
services.</p>

<div class="dsdnote">〈COMMISSIONERS INEXPLICABLE.〉</div>

<p>It is difficult, upon any principle, to explain the conduct of
the Royal Com­mis­sion­ers of the Exhibition of 1862. They
were appointed by the Government, yet when the Government
itself became an exhibitor, and sent
for exhibition a <span class="xxpn" id="p159">{159}</span>
Difference Engine, the property of the nation, these Com­mis­sion­ers
placed it in a <i>small hole</i> in a <i>dark corner</i>, where it could,
with some difficulty, be seen by six people at the same time.</p>

<p>No remonstrance was of the slightest avail; it was “Hobson’s
choice,” that or none. It was represented that all other
space was occupied.</p>

<p>A trophy of children’s toys, whose merits, it is true, the
Com­mis­sion­ers were somewhat more competent to appreciate,
filled one of the most prominent positions in the building.
On the other hand, a trophy of the workmanship of
English engineers, executed by <i>machine tools</i> thirty years
before, and admitted by the best judges to be unsurpassed
by any rival, was placed in a position not very inappropriate
for the authorities themselves who condemned it to that
locality.</p>

<p>But no hired aristocratic<a class="afnanc" href="#fn30" id="fnanc30">30</a>
agent was employed to excite
the slumbering perceptions of the Com­mis­sion­ers, who might
have secured a favourable position for the Difference Engine,
by practising on their good nature, or by imposing upon
their imbecility.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc30" id="fn30">30</a>
See “The Times,” 19 Jan., 1863, and elsewhere.</p></div>

<p>It has been urged, in extenuation of the con­duct of these
Com­mis­sion­ers, that their duty as guardians of the funds
intrusted to them, and of the interests of the Guarantors,
compelled them to practise a rigid economy.</p>

<p>Rigid economy is to be respected only when it is under the
control of judgment, not of favouritism. If the machinery
for making arithmetical calculations which was placed at
the disposal of the Com­mis­sion­ers had been properly arranged,
it might have been made at once a source of high
gratification to the public and even of <i>profit</i>
to the Exhibition. <span class="xxpn" id="p160">{160}</span></p>

<div class="dsdnote">〈A COURT FOR CALCULATING MACHINES.〉</div>

<p>Such a group of Calculating Machines might have been
placed by themselves in a small court capable of holding a
limited number of persons. Round the walls of this court
might have been hung the drawings I had offered to lend,
containing the whole of those necessary for the Difference
Engine No. 2, as well as a large number of illustrations for
the explanation of the Mechanical Notation. The Swedish
Difference Engine and my own might have been slowly
making calculations during the whole day.</p>

<p>This court should have been open to the public generally,
except at two or three periods of half an hour each, during
which it should have been accessible only to those who had
previously secured tickets at a shilling apiece.</p>

<p>During each half hour the person whom I had recommended
to the Com­mis­sion­ers might have given a short
popular explanation of the subject.</p>

<p>This attraction might have been still further increased,
and additional profit made, if a single sheet of paper had
been printed containing a woodcut of the Swedish Machine,
an impression from a page of the Tables computed and stereotyped
by it at Somerset House, and also an impression from
a stereotype plate of the Difference Engine exhibited by the
Government.</p>

<p>A plate of the Swedish Machine is in existence in London.
I am confident that, for such a purpose, I could have procured
the loan of it for the Com­mis­sion­ers, and I would willingly
have supplied them with the stereotype plate from
which the frontispage of the present volume was printed, together
with from ten to twenty lines of necessary explanation.</p>

<p>These illustrations of machinery used for computing and
printing Tables might have been put up into packets of
dozens and half dozens, and also have been
sold in single <span class="xxpn" id="p161">{161}</span>
sheets at the rate of one penny each copy. There can be no
doubt the sale of them would have been very considerable.
As it was, I found the woodcut representing the Difference
Engine No. 1 in great request, and during the exhibition
I had numberless applications for it; having given away my
whole stock of about 800 copies.</p>

<div class="dsdnote">〈AN ASSISTANT EXPLAINING.〉</div>

<p>The calculating court might have held comfortably from
sixty to eighty seats. Each lecture would have produced
say 3&#x200a;<i>l.</i> This being repeated three times each day, together
with the sale of the woodcuts, would have produced about
10&#x200a;<i>l.</i> per day, out of which the Com­mis­sion­ers would have
had six shillings per day to pay the assistant who gave the
required explanations.</p>

<p>If the dignity of the Com­mis­sion­ers would not permit them
to make money by such means, they might have announced
that the proceeds of the tickets would be given to the distressed
population of the Manchester district, and there would
then have been crowds of visitors.</p>

<p>But the rigid economy of the Com­mis­sion­ers, who refused
to expend six shillings a day for an attendant, although it
would most probably have produced a return of several hundred
pounds, was entirely laid aside when their patronage
was to be extended to a brother official.</p>

<p>Captain Fowke, an officer of engineers, whose high order
of architectural talent became afterwards so well known to
the public, and whose whole time and services were retained
and paid for by the country, was employed to make a design
for the Exhibition Building.</p>

<div class="dsdnote">〈THE COMMISSIONERS DO A JOB.〉</div>

<p>The Com­mis­sion­ers approved of this design, which comprised
two lofty domes, uniting in themselves the threefold
inconvenience of being ugly, useless, and expensive. They
then proceeded to pay him five thousand pounds
for the job. <span class="xxpn" id="p162">{162}</span>
This system of awarding large sums of money to certain
favoured public officers who are already paid for their services
by liberal salaries seems to be a growing evil. At the
period of the Irish famine the under-secretary of the Treasury
condescended to accept 2,500&#x200a;<i>l.</i> out of the fund raised to save
a famished nation. Some inquiries, even recently, were
oc­ca­sion­al­ly made whether any similar deduction will be
allowed from the liberal cont­ri­bu­tions to the sufferers by the
cotton famine.</p>

<p>The question was raised and the practice reprobated in
the House of Commons by men of opposite party politics.
Mr. Gladstone <span class="nowrap">remarked:—</span></p>

<p>“If there was one rule connected with the public service
which more than any other ought to be scrupulously observed,
it was this, that the salary of a public officer, more
especially if he were of high rank, ought to cover all the
services he might be called upon to render. Any departure
from this rule must be dangerous.” Hansard, vol. 101,
p. 138, 1848. Supply, 14 Aug. 1848. See also “The
Exposition of 1851,” 8vo., p. 217.</p>

<div class="dsdnote">〈THE ADMIRALTY REFUSE.〉</div>

<p>The following paragraph appeared in “The Times”<a class="afnanc" href="#fn31" id="fnanc31">31</a>
a
short time since, under the head Naval <span class="nowrap">Intelligence:—</span></p>

<p>“A reply has been received to the memorial trans­mit­ted
to the Admiralty some few days since from the inspectors
employed on the iron frigate ‘Achilles,’ building at Chatham
dockyard, requesting that they may be placed on the same
footing as regards increased pay as the junior officers and
mechanics working on the iron frigate for the additional
number of hours they are employed in the dockyard. The
Lords of the Admiralty intimate that they cannot accede to
the wishes of the memorialists, who are reminded that, as
<span class="xxpn" id="p163">{163}</span>
salaried officers of the establishment, the whole of their time
is at the disposal of the Admiralty. This decision has caused
considerable dissat­is­fac­tion.”</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc31" id="fn31">31</a>
About the 20th of May, 1863.</p></div>

<p>It appears that the Admiralty wisely adopted the principle
enunciated by Mr. Gladstone.</p>

<p>It may, however, not unreasonably have caused dis­sat­is­fac­tion
to those who had no interest to back them on finding
that such large sums are pocketed by those who are blessed
with influential friends in high quarters.</p>

<p>If the Com­mis­sion­ers had really wished to have obtained a
suitable building at a fair price their course was simple and
obvious. They need only have stated the nature and amount
of accommodation required, and then have selected half a
dozen of the most eminent firms amongst our great contractors,
who would each have given them an estimate of the
plans they respectively suggested.</p>

<p>The Com­mis­sion­ers might have made it one of the conditions
that they should not be absolutely bound to give the
contract to the author of the plan accepted. But in case of
not employing him a sum previously stipulated should have
been assigned for the use of the design.</p>

<p>By such means they would have had a choice of various
plans, and if those plans had, previously to the decision of
the Com­mis­sion­ers, been publicly exhibited for a few weeks,
they might have been enlightened by public criticism. Such
a course would have prevented the gigantic job they afterwards
perpetrated. It could therefore find no support from
the Com­mis­sion­ers.</p>

<p>The present Com­mis­sion­ers, however, are fit successors to
those who in 1851 ignored the existence of the author of the
“Economy of Man­u­fac­tures” and his inventions. They seem
to have been deluded into the belief
that they possessed <span class="xxpn" id="p164">{164}</span>
the strength, as well as the desire, quietly to strangle the
Difference Engine.</p>

<p>It would be idle to break such butterflies upon its matchless
wheels, or to give permanence to such names by reflecting
them from its diamond-graven plates.<a class="afnanc" href="#fn32" id="fnanc32">32</a>
Though the steam-hammer
can crack the coating without injuring the kernel of
the filbert it drops upon—the admirable precision of its
gigantic power could never be dem­on­strated by exhausting
its energy upon an empty nut-shell.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc32" id="fn32">32</a>
For the purpose of testing the steadiness and truth of
the tools employed in forming the gun-metal plates, I had some dozen
of them turned with a diamond point. The perfect equality of its cut
caused the reflected light to be resolved into those beautiful images
pointed out by Frauenhofer, and also so much admired in the celebrated
gold buttons produced by the late Mr. Barton, the Comptroller of the
Mint.</p></div>

<p>Peace, then, to their memory, aptly enshrined in unknown
characters within the penetralia of the temple of oblivion.</p>

<div class="dsdnote">〈CONSOLATION FOR THE COMMISSIONERS.〉</div>

<p>These celebrities may there at last console themselves in
the enjoyment of one enviable privilege denied to them
during their earthly career—exemption from the daily consciousness
of being “<i>found out</i>.”</p>

<p>It is, however, not quite impossible, although deciphering
is a brilliant art, that one or other of them may have heard
of the dread power of the decipherer. Having myself had
some slight acquaintance with that fascinating pursuit, it
gives me real pleasure to relieve them from this very natural
fear by assuring them that not even the most juvenile
decipherer could be so stupid as to apply himself to the interpretation
of—characters known to be meaningless.</p>

<p>Yet there is one name amongst, but not of them—a fellow-worshipper
with myself at far other fanes, whose hands, like
mine, have wielded the hammer, and whose pen, like mine,
has endeavoured to communicate faithfully to his fellow-men
<span class="xxpn" id="p165">{165}</span>
the measure of those truths he has himself laboriously
extracted from the material world. With such endowments,
it is impossible that <i>he</i> could have had any cognizance of this
part of the proceedings of his colleagues.<a class="afnanc" href="#fn33" id="fnanc33">33</a></p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc33" id="fn33">33</a>
I have since learnt, with real sat­is­fac­tion, that
my friend, Mr. Fairbairn, was <i>not</i> a member of that incompetent
Commission.</p></div>

<div class="dsdnote">〈MR. GRAVATT EXPLAINS THE ENGINE.〉</div>

<p>At the commencement of the Exhibition, Mr. Gravatt was
constantly present, and was so kind as to explain to many
anxious inquirers the nature and uses of the Difference
Engine. This, however, interfered so much with his pro­fes­sion­al
engagements as a Civil Engineer, that it would have
been unreasonable to have expected its continuance. In fact,
as not above half a dozen spectators could see the machine at
once, it was a great sacrifice of valuable time for a very small
result.</p>

<p>During the early part of my own examination of the Exhibition
I had many opportunities of conversing with experienced
workmen, well qualified to appreciate the workmanship of the
Difference Engine; these I frequently accompanied to its
narrow cell, and pointed out to them its use, as well as the
means by which its various parts had received their destined
form.</p>

<p>Oc­ca­sion­al­ly also I explained it to some few of my personal
friends. When Mr. Gravatt or myself were thus engaged,
a considerable crowd was often collected, who were anxious
to hear about, although they could not see, the Engine
itself.</p>

<p>Upon one of these occasions I was insulted by impertinent questions
conveyed in a loud voice from a person at a distance in the crowd.
My taste for music, and especially for organs, was questioned. I was
charitable enough to suppose that this was an exceptional case; but
in less than a week another instance <span class="xxpn" id="p166">{166}</span>
occurred. After this
experience, of course, I seldom went near the Difference Engine. Mr.
Gravatt who had generously sacrificed a considerable portion of his
valuable time for the information and in­struc­tion of the public was now
imperatively called away by pro­fes­sion­al engagements, and the public
had no information whatever upon a subject on which it was really very
anxious to be instructed.</p>

<div class="dsdnote">〈MR. WILMOT BUXTON EXPLAINS THE DIFFERENCE ENGINE.〉</div>

<p>Fortunately, however, the Exhibition took place during the
long vacation; and a friend of mine, Mr. Wilmot Buxton, of
the Chancery Bar, very frequently accompanied me in my
visits. Possessing a profound knowledge of the math­e­mat­i­cal
principles embodied in the mechanism, I had frequently
pointed out to him its nature and relations. These I soon
found he so well apprehended that I felt justified in intrusting
him with one of my keys of the machine, in order that he
might have access to it without the necessity of my presence.</p>

<p>Whenever he opened it for his own sat­is­fac­tion or for the
in­struc­tion of his friends, he was speedily surrounded by a
far larger portion of the public than could possibly see it, but
who were still attracted by his lucid oral explanation.</p>

<p>It was fortunate for many of the visitors to the Exhibition
that this occurred, for the demands on his time, when present,
were incessant, and hundreds thus acquired from his explanations
a popular view of the subject.</p>

<p>After the close of the Exhibition, Mr. Gravatt and myself
attended to prepare the Difference Engine for its return to
the Museum of King’s College. To our great astonishment,
we found that it had already been removed to the Museum at
South Kensington. Not only the Difference Engine itself,
but also the illustrations and all the unfinished portions of
exquisite workmanship which I had lent to the Exhibition for
its explanation, were gone. <span class="xxpn" id="p167">{167}</span></p>

<p>On Mr. Gravatt applying to the Board of Works, it was
stated that the Difference Engine itself had been placed in
the Kensington Museum because the authorities of King’s
College had declined receiving it, and immediate in­struc­tions
were of course given for the restoration of
my own property.</p></div><!--section-->

<div class="section" id="p168">
<h2 class="h2herein">CHAPTER XI.
<span class="hsmall">THE LATE PRINCE CONSORT.</span></h2>

<hr class="hr20" />
<div class="fsz7">“Suum cuique.”</div>
<hr class="hr20" />

<div class="dsynopsis">
Count Mensdorf mentions to the Duke of Wellington his
wish to see the Difference Engine&#x200a;—&#x200a;An
appointment made&#x200a;—&#x200a;Prince Albert expresses his
intention of accompanying his uncle&#x200a;—&#x200a;Time of
appointment altered&#x200a;—&#x200a;Their visit, accompanied
by the Duke of Wellington&#x200a;—&#x200a;Portrait of
Jacquard&#x200a;—&#x200a;Anecdote of Wilkie&#x200a;—&#x200a;Afghanistan
arms&#x200a;—&#x200a;Extract from the Author’s work on the Exhibition
of 1862.</div>

<p class="pfirst">I <span class="smmaj">have</span> had one
op­por­tun­i­ty of fairly estimating some por­tion of the char­ac­ter of the
late justly-lamented Prince Con­sort; to this I will now ven­ture to
al­lude.</p>

<p>In 1842 Count Mensdorf visited London. A few days
after I had a note from the late Duke of Wellington, in
which he informed me that on the previous evening he had
met at the palace the Queen’s uncle, Count Mensdorf, who
had expressed to the Duke his wish to see my Calculating
Engine. The Duke then inquired whether I could conveniently
make some arrangement for that purpose. I immediately
wrote to the Duke, that if he would appoint an hour
on any morning of the ensuing week, I should have great
pleasure in showing and explaining the Difference Engine to
Count Mensdorf. It was afterwards arranged that on the following
Tuesday, at two o’clock, Count Mensdorf and the
Duke should pay me a visit in Dorset
Street. On Monday <span class="xxpn" id="p169">{169}</span>
morning I received another note from the Duke, informing
me that Prince Albert had expressed his intention to accompany
Count Mensdorf in the proposed visit, and that it would
be more convenient if the hour were changed to one instead
of two o’clock.</p>

<p>I must freely admit that I did not greatly rejoice at this
addition to the party. I resolved, however, strictly to perform
the duties thus thrown upon me as a host, as well as all those
to which Prince Albert was entitled by his elevated position.</p>

<div class="dsdnote">〈THE WOVEN PORTRAIT.〉</div>

<p>Before I took the Prince into the fire-proof building in
which the Difference Engine was then deposited, I asked
his Royal Highness to allow me to show him a portrait of
Jacquard, which was at that time hanging up in my drawing-room,
as it would greatly assist in explaining the nature of
Calculating Machines.</p>

<p>When we had arrived in front of the portrait, I pointed it
out as the object to which I solicited the Prince’s attention.
“Oh! that engraving?” remarked the Duke of Wellington.
“No!” said Prince Albert to the Duke; “it is not an engraving.”
I felt for a moment very great surprise; but this
was changed into a much more agreeable feeling, when the
Prince instantly added, “I have seen it before.” I felt at
once that the Prince was a “good man and true,” and I
resolved that I would not confine myself to the rigid rules of
etiquette, but that I would help him with all my heart
in whatever line his inquiries might be directed.</p>

<p>The portrait of Jacquard was, in fact, a sheet of woven silk,
framed and glazed, but looking so perfectly like an engraving,
that it had been mistaken for such by two members
of the Royal Academy.</p>

<div class="dsdnote">〈WILKIE’S CONJECTURE.〉</div>

<p>A short time after I became possessed of this beautiful
work of art, I met Wilkie, and invited him to
come and see <span class="xxpn" id="p170">{170}</span>
my recent acquisition. He called on me one morning. I
placed him at a short distance in front of the portrait, which
he admired greatly. I then asked him what he thought it
was. He answered, “An engraving!” On which I asked,
“Of what kind?” To this he replied, “Line-engraving, to
be sure!” I drew him a little nearer. He then mentioned
another style of engraving. At last, having placed Wilkie
close to the portrait, he said, after a considerable pause, “Can
it be lithography?”</p>

<p>A splendid collection of arms from Afghanistan, recently
sent to me from India by Sir Edward Ryan, was lying on the
tables in one of the rooms we passed through. These had
attracted the notice of the Prince, and on returning, the
whole party examined them with the greatest interest</p>

<p>I now conducted my visitors to the fire-proof building in
which the Difference Engine was placed. Prince Albert was,
I understood, sufficiently acquainted with the higher departments
of math­e­mat­i­cal science to appreciate the influence of
such an instrument on its future progress. But the circumstance
that charmed me was—his bearing towards his uncle,
Count Mensdorf. It was perfectly natural: it could be felt,
admired, and honoured—but not described.</p>

<p>When the sad fact of the nation’s loss became known to
me, I immediately reverted with some anxiety to a work I
had published ten years before on the Exhibition of 1851. I
feared lest, in speaking of that event, I might have committed
some injustice, whilst I was indignant at that under
which I was myself suffering. I willingly reprint it here
because it contained no empty words of flattery; but analysed
the reasons which commanded our respect.</p>

<div class="dblockquote">
<p>“The merit of the original conception of
the present <span class="xxpn" id="p171">{171}</span>
Exposition [1851] is insignificant in comparison with that of the
efforts by which it was carried out, and with the importance
of its practical results.</p>

<p>“To have seen from afar its effects on the improvement,
the wealth, and the happiness of the people—to have seized
the fit moment, when, by the right use of the influence of an
exalted station, it was <i>possible</i> to overcome the deeply-rooted
prejudices of the upper classes—to remove the still more
formidable, because latent, impediments of party—generously
to have undertaken great responsibility, and with indefatigable
labour to have endeavoured to make the best out
of the only materials at hand,—these are endowments of no
ordinary kind.</p>

<p>“To move in any rank of society an exception to its general
rules, is a very difficult, and if accompanied by the consciousness
of the situation, a very painful position to a reflecting
mind.</p>

<div class="dsdnote">〈PENALTIES OF EXALTED STATION.〉</div>

<p>“Whatever may be the cause—whether exalted rank, unbounded
wealth, surpassing beauty or unrivalled wit, the
renown of daring deeds, the magic of a world-wide fame—to
all within those narrow limits the dangers and the penalties
are great. Each exists an isolated spirit; each unconsciously
imprisoned within its crystal globe perceives the colours of
all external objects modified by those tints imparted to them
by its own surrounding sphere. No change of view can teach
it to rectify this partial judgment; throughout its earthward
course the same undying rainbow attends to the last its
parent drop.</p>

<div class="dsdnote">〈ITS SYMPATHIES.〉</div>

<p>“Rarely indeed can some deep-searching mind, after long
comparison, perceive the real colours of those translucent
shells which encompass kindred spirits; and thus at length
enable him to achromatise the medium
which surrounds his <span class="xxpn" id="p172">{172}</span>
own. To one who has thus rectified the “colour-blindness”
of his in­tel­lec­tual vision, how deep the sympathy he feels for
those still involved in that hopeless obscurity from which he
has himself escaped. None can so justly appreciate that
sense of loneliness, that solitude of mind, which surrounds unquestioned
eminence on its lofty throne;—none, therefore,
can make so large an allowance for its errors;—none so
skilfully assist in guiding
its hazardous career.”</p></div></div><!--section-->

<div class="section" id="p173">
<h2 class="h2herein">CHAPTER XII.
<span class="hsmall">RECOLLECTIONS OF THE DUKE OF WELLINGTON.</span></h2>

<div class="dsynopsis">
Official visit to see the Difference Engine in
1829&#x200a;—&#x200a;Extract from a letter from the late General
Sir William Napier&#x200a;—&#x200a;Loss of the troopship
“Birkenhead”&#x200a;—&#x200a;The Author accompanies the Duke to the
Exhibition of 1851&#x200a;—&#x200a;Fixed in the crowd, the Duke plays
with a child of two years old&#x200a;—&#x200a;The late Countess of
Wilton asks a question about the Difference Engine&#x200a;—&#x200a;The
Author’s explanation&#x200a;—&#x200a;The Duke’s
remark&#x200a;—&#x200a;Sketch of one portion of the Duke’s in­tel­lec­tual
character&#x200a;—&#x200a;University Addresses&#x200a;—&#x200a;The
Duke helps a dumpy fellow to see the Queen&#x200a;—&#x200a;The Author
saves a Master of Arts from hanging&#x200a;—&#x200a;The Duke and the
Ninth Bridgewater Treatise&#x200a;—&#x200a;The Duke an economist of
time&#x200a;—&#x200a;Character of the French Marshals.</div>

<p class="pfirst"><span class="smcap">M<b>Y</b></span>
acquaintance with the late Duke of Wellington commenced
in an official visit from himself and Mr. Goulburn,
the Chancellor of the Exchequer, to inspect the drawings
and works of the Difference Engine No. 1. This was in November,
1829. Afterwards I met the Duke in private society
at the houses of one or two of his intimate friends, and sub­se­quent­ly
I was honoured not unfrequently by receiving him
at my own. During the Exhibition of 1851 I very often
accompanied him in his examination of the contents of that
building. I made no notes of any of the conversations, some
of them highly interesting, which occurred on such occasions,
because I felt that the habit of recording privately the conversations
with our acquaintances was a breach of faith towards
the individual, and tended to destroy all confidence in
society. <span class="xxpn" id="p174">{174}</span></p>

<p>I now perceive, when it is too late, that a rigid adherence
to that rule has deprived me of the power of relating circumstances
of the greatest interest to survivors, and of the highest
credit to himself. I should not even have adverted to the
subject in the present work, had I not observed in the fourth
volume of the life of the late General Sir Charles Napier of
Scinde a passage which, if not explained, might lead to the
erroneous inference that I had myself proposed to speak to
the Duke of Wellington on a certain military subject,
whereas I only did so at the repeated desire of Sir Charles
himself.</p>

<div class="dsdnote">〈THE LOSS OF THE BIRKENHEAD.〉</div>

<p>The following is a portion of a letter from General Sir
Charles Napier to his brother, General Sir William Napier,
extracted from “The Life of Sir Charles Napier,” vol. iv.,
p. <span class="nowrap">347:—</span></p>

<div class="dblockquote">
<div><span class="smcap">T<b>O</b></span>
<span class="smcap">G<b>ENERAL</b></span> W.
<span class="smcap">N<b>APIER;</b></span> 1852.</div>

<p class="psignature">“<i>May 2nd.</i></p>

<p>“I met Babbage at Miss Burdett Coutts. He talked
about the ‘Birkenhead,’ and was very eager, saying,
‘Cannot you speak to the Duke of Wellington?’ ‘No;
it would seem a criticising of his conduct.’ ‘Well, I, as
a civilian, may.’ ‘Yes; and you will do good, for the
Duke alluded to the subject at the Royal Academy dinner
an hour ago.’ Babbage did so at once, asking him to move
in the matter; and the Duke said he would. I also spoke
to Hardinge, who told me he had had a mind to allude
to it in his speech at the dinner, but feared it might
seem a reflection on the Duke.”</p>

<hr class="hr20" />

<p>“I have been told that the Duke is only awaiting an official
despatch from Harry Smith, or
Cathcart, about the <span class="xxpn" id="p175">{175}</span>
‘Birkenhead,’ to act. This is probable, as being like his cautious
way, but, to my thinking, not well in this case.”</p></div>

<p>The matter referred to arose thus. Several years ago a
troop-ship, named the “Birkenhead,” was wrecked on the
African coast, near the Cape of Good Hope. A very small
portion only of the troops were saved. According to the testimony
of the survivors, the discipline and order which prevailed
on board up to the final catastrophe was admirable,
and almost beyond example. If any human means could
have saved those invaluable lives, such discipline would have
largely contributed to the result.</p>

<p>Sharing the general regret at this severe loss, and sympathising
deeply with the feelings of the surviving relatives, it
occurred to me that very simple and inexpensive means were
available, which if employed, would at the least afford a melancholy
consolation to the afflicted relatives, might be retained
with becoming pride in their families, and would
also add to the respectability of the social position of the
soldier.</p>

<p>Observing that military offences punished by a court-martial
were made public by being read at the head of every regiment,
I suggested that in certain cases publicity should be given by
the same means to noble acts of forbearance or of self-devotion.</p>

<p>In the case of the “Birkenhead,” in which ship small detachments
of several regiments were lost, I suggested that an
order should be issued, <span class="nowrap">stating—</span></p>

<p>The circumstances under which the loss occurred, and the
nation’s approbation of the conduct of the departed.</p>

<p>That their names should be read at the head of their respective
regiments.</p>

<p>That an official letter, signed by the colonel
or other proper <span class="xxpn" id="p176">{176}</span>
officer of each regiment, describing the nature of the service
under which the loss occurred, and conveying to the nearest
surviving relative the expression of the high approbation the
Government entertained of such heroic conduct.</p>

<p>Such official testimonials would soothe the feelings of many
a relative, would become objects of just pride amongst the
relations of the departed, and be handed down as heir-looms
in many a village circle.</p>

<div class="dsdnote">〈SIR CHARLES NAPIER APPROVES.〉</div>

<p>I mentioned these views to several of my acquaintances,
and the idea seemed to meet with general approbation.
I found my military friends fully alive to the advantage of
such a course for the benefit of the service, and also as a consolation
to surviving relatives. Amongst others, I proposed
it to the late General Sir Charles Napier. He highly approved
of the plan, about which we had several conversations.
In one of these I suggested that he should mention it to the
Duke of Wellington; to which Sir Charles replied, “No, I
could not do that: you should tell him yourself.” I smiled
at the notion, not thinking that my friend was in earnest.</p>

<p>A short time after I met Sir Charles Napier at a large
evening party. We were sitting together on a sofa talking:
he resumed the plan I had proposed, spoke of it with much
approbation, and concluded by saying, “You ought to tell the
Duke of it.”</p>

<p>I replied that I had thought he was only joking when he
had on a former occasion made the same ob­ser­va­tion.</p>

<p>“No, indeed,” said Sir Charles; “I am serious. The Duke
will attend to what you say more than to any of us.”</p>

<p>“If you really think so,” I replied, “I will follow your counsel.
I hope,” I added, “the Duke may excuse me as a civilian for speaking
about it, but after such an expression of your opinion I feel bound to
take that course.” <span class="xxpn" id="p177">{177}</span></p>

<div class="dsdnote">〈MENTIONED TO THE DUKE.〉</div>

<p>The conversation then turned upon other subjects, when
shortly after the Duke of Wellington was announced.</p>

<p>“There,” observed Sir Charles, “is the Duke, now go
and talk to him about it.” I promised to do so at a proper
opportunity.</p>

<p>After the Duke had made his bow to the lady of the house,
and recognised and conversed with many of his friends, I
threw myself in his way. On the Duke shaking hands with
me, I remarked that I was par­tic­u­lar­ly glad to meet him,
because an idea had occurred to me in which I thought he
would take an interest. He stepped with me a little out of
the crowd, and I then stated shortly my views. The Duke paid
great attention to the subject; made several remarks upon it;
and when we separated, I felt satisfied that he took a strong
interest in it. I thought, however, that he had applied the
idea rather more to the officers, whilst my main object was
the interests of the privates.</p>

<p>Much later in the evening I was taking some refreshment
in another room, when the Duke entering, saw and rejoined
me. He reverted to the subject; I observed that though
officers and privates should have the same official acknowledgment,
yet that the Commander-in-Chief and the Government
possessed other more substantial means of benefiting the
surviving relatives of the officers than of the privates. We
had some further conversation about it, and I then felt quite
satisfied that he both understood and approved of it.</p>

<p>I rather think the Duke of Wellington moved in the House
of Lords for certain papers, on which he intended to found
some measure of the kind; but his death, shortly after, put
an end to the question.</p>

<p>During the year 1851 I very frequently accompanied the
Duke of Wellington to the Exhibition, or met
him there by <span class="xxpn" id="p178">{178}</span>
appointment at the crystal fountain. Sometimes one or two
of his particular friends, usually ladies, were invited to join
the party.</p>

<p>On the first occasion I spoke to one of the attending police,
simply for the purpose of facilitating our passage if we should
get into a great crowd, which, of course, did oc­ca­sion­al­ly
happen. In these cases the policeman a little preceded us,
and it was very interesting to observe the sudden changes in
the countenances of those whom the constable gently touched
in order to accelerate our passage. On the first slight pressure
of the policeman’s hand upon the arm of John Bull, he looked
round with indignation: but when the policeman quietly
asked him to be so good as to allow the Duke of Wellington
to pass, the muscles of John Bull’s countenance relaxed into
a grateful smile: he immediately made way, and in several
cases thanked the officer for giving him an opportunity of
seeing the Duke. During the most crowded of those days we
at one period became entirely blocked up and stationary for
upwards of ten minutes. Our intelligent companion was
himself wedged in, at a short distance from us. Just in front
of us stood a woman with a child in her arms of about two
years old, who was leaning over its mother’s shoulder.</p>

<div class="dsdnote">〈THE DUKE PLAYS WITH A CHILD.〉</div>

<p>The Duke began to play with the infant, pretending to touch its
ear with his finger, and then to touch its nose. The mother was
gratified,—the child was charmed. At last the crowd almost suddenly
broke up, and we went on. After we had advanced about a dozen paces
I said to the Duke of Wellington, “I must step back to speak to
the mother of your young friend.” I then asked her if she knew the
gentleman who had been playing with her child for the last ten
minutes: she said “No, Sir.” I told her it was the Duke of Wellington.
Her surprise and delight were equally great. <span class="xxpn"
id="p179">{179}</span> I desired her to tell her boy when he grew
up that, when an infant, the Duke of Wellington had played with him.
I then returned and told the Duke the object of my mission. His
approbation was indicated by a happy smile.</p>

<hr class="hrblk" />

<p>One morning the Duke of Wellington called in Dorset
Street with the late Countess of Wilton, to whom he wished
me to show the Difference Engine. Its home was at that
period in my drawing-room. We sat round it whilst I explained
its mode of action, and made it calculate some small
Table of numbers.</p>

<div class="dsdnote">〈LADY WILTON’S REMARK ON DIFFERENCE ENGINE.〉</div>

<p>When I had concluded my explanation, Lady Wilton, addressing
me, said, “Now, Mr. Babbage, can you tell me what
was your greatest difficulty in contriving this machine?” I
had never previously asked myself that question; but I knew
the nature of it well.</p>

<p>It arose not from the difficulty of contriving mechanism to
execute each individual movement, for I had contrived very
many different modes of executing each: but it really arose
from the almost innumerable <i>combinations</i> amongst all these
contrivances—a number so vast, that no human mind could
examine them all.</p>

<p>It instantly occurred to me that a similar difficulty must
present itself to a general commanding a vast army, when
about to engage in a conflict with another army of equal or of
greater amount. I therefore thought it must have been felt
by the Duke of Wellington, and I determined to make a
kind of psychological experiment upon him.</p>

<p>Carefully abstaining from any military term, I commenced
my explanation to Lady Wilton. I soon perceived by his
countenance that the Duke was already in imagination again
in Spain. I then went on boldly with the
explanation of my <span class="xxpn" id="p180">{180}</span>
own mechanical difficulty; and when I had concluded, the
Duke turned to Lady Wilton and said, “I know that difficulty
well.”</p>

<div class="dsdnote">〈THE AUTHOR’S SKETCH OF THE DUKE’S INTELLECTUAL CHARACTER.〉</div>

<p>The success of this experiment induced me in a subsequent
publication<a class="afnanc" href="#fn34" id="fnanc34">34</a>
to give an analysis of one portion of the Duke
of Wellington’s in­tel­lec­tual character, although I made no
mention of his name. Many of his admirers, however, perceived
at once the truth of those views, and recognised the
justice of their application. I therefore place them before my
readers in the following extract from the work referred <span class="nowrap">to:—</span></p>

<p>“It is now felt and admitted, that it is the civil capacity of
the great commander which prepares the way for his military
triumphs; that his knowledge of human nature enables him
to select the fittest agents, and to place them in the situations
best adapted to their powers; that his intimate acquaintance
with all the accessories which contribute to the health and
comfort of his troops, enables him to sustain their moral and
physical energy. It has been seen that he must have studied
and properly estimated the character of his foes as well as of
his allies, and have made himself acquainted with the personal
character of the chiefs of both; and still further, that
he must have scrutinized the secret motives which regulated
their respective governments.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc34" id="fn34">34</a>
“The Exposition of 1852;” 2nd edition, p. 222.</p></div>

<p>“When directly engaged in the operations of contending
armies occupying a wide extent of country, he must be able,
with rapid glance, to ascertain the force it is possible to con­cen­trate
upon each of many points in any given time, and the
greater or less chance of fairing in the attempt. He must
also be able to foresee, with something more than conjecture,
what amount of the enemy’s force can be brought to the same
spot in the same and in different times.
With these elements <span class="xxpn" id="p181">{181}</span>
he must undertake one of the most difficult of mental tasks,
that of classifying and grouping the innumerable combinations
to which either party may have recourse for purposes of
attack or defence. Out of the multitude of such combinations,
which might baffle by their simple enumeration the
strongest memory, throwing aside the less important, he must
be able to discover, to fix his attention, and to act upon the
most favourable. Finally, when the course thus selected
having been pursued, and perhaps partially carried out, is
found to be entirely deranged by one of those many chances
inseparable from such operations, then, in the midst of action,
he must be able suddenly to organise a different system of
operations, new to all other minds, yet possibly, although
unconsciously, anticipated by his own.</p>

<p>“The genius that can meet and overcome such difficulties
<i>must</i> be in­tel­lec­tual, and would, under different circumstances,
have been distinguished in many a different career.</p>

<p>“Nor even would it be very surprising that such a commander,
estimating justly the extent of his own powers, and
conscious of having planned the best combinations of which
his mind is capable, should, having issued his orders, calmly
lie down on the eve of the approaching conflict, and find in
sleep that bodily restoration so indispensable to the full exercise
of his faculties in the mighty struggle about to ensue.”</p>

<hr class="hrblk" />

<p>Soon after the Queen came to the throne, the two Uni­ver­si­ties
pre­sent­ed ad­dresses to her Majesty. I ac­com­panied that
of Cambridge. The depu­ta­tion was very numerous, and much
unseemly pushing took place. I recollect a very short dumpy
fellow pushing much more energetically than any other, for
whom I made way, as I retired from the strife in which I
was unwillingly involved. He not only
pushed, but was <span class="xxpn" id="p182">{182}</span>
continually jumping up like a parched pea in a heated frying-pan:
his object being to get a glimpse of her Majesty, and the
effect accomplished being to alight on the toes or graze the
heels of his colleagues.</p>

<p>I retired into a window close to the end of the position
occupied by the gentlemen-at-arms. The Duke of Wellington,
who had a short time before, as Chancellor of the
University of Oxford, presented the address of that body, still
remained in the state apartments. He joined me in the
recess of the window, and we entered into conversation.</p>

<div class="dsdnote">〈THE DUKE ASSISTS A PUSHING M.A.〉</div>

<p>After a time the little dumpy fellow, who had been regularly
turned out of the crowd for his pushing, came up to us,
and, mistaking the Duke of Wellington for a beef-eater or
some palace attendant, complained, almost in tears, that he
wanted to see the Queen, and that they had pushed him out,
and that he had not been able to see the Queen.</p>

<p>The Duke very good-naturedly said he would take him to
a place where he could see her Majesty without being pushed
about. Accordingly, the Duke led him behind the gentlemen-at-arms
to a situation in which the little man’s wish was
gratified, and then returned with him to the window, and
resumed the conversation.</p>

<p>On another occasion the University of Cambridge presented
an address to the Queen at Buckingham Palace. The crowd
was very great. On descending one of the flights of stairs,
a short Master of Arts was unluckily caught by the string of
his gown hooking itself upon one of the large door-handles.
He was carried off his legs by the advancing rush. To bring
back the pendant Master of Arts a single inch was impossible
from the pressure onwards. So whilst two or three of his
colleagues with difficulty supported him, I took out my pen-knife
and cut the imprisoning ribbon. <span class="xxpn" id="p183">{183}</span></p>

<div class="dsdnote">〈ALL PARCELS REJECTED.〉</div>

<p>When I published the “Ninth Bridgewater Treatise,” I
sent my servant to Apsley House with a presentation copy
for the Duke of Wellington. The next morning at breakfast
my servant informed me that the porter absolutely refused
to take it in, although he stated from whom it came.</p>

<p>I remarked to my brother-in-law, who was staying with me,
that it was a very odd circumstance, and inquired what was
to be done. He replied, “When a man refuses to receive a
parcel, nothing more can be done.” I then observed, that if
any other person than the Duke had done so, I should have
taken no further step; but, I added, that I knew his character
so well, that I was confident there was really a good and
sufficient reason, although I could not conjecture its nature.</p>

<p>After breakfast I wrote a short note to the Duke, mentioning
the circumstance, taking for granted that it arose entirely
from some misconception of his orders. I then requested
him not to take the trouble of writing to me to explain it;
but added that I would send the volume to Apsley House on
the following morning, when, I had no doubt, the mistaken
interpretation of his orders would have been rectified.</p>

<p>About three o’clock the same day a servant of the Duke’s
brought me a note, inquiring if there were any answer to
take back. The Duke stated in his note that letters, books,
parcels, maps, and even merchandise, were continually sent
to him for the purpose of being forwarded to all parts of the
world. This, he observed, threw upon his house-steward so
great a responsibility, that he had been compelled to give
directions that no parcel should be received at Apsley House
without a written order with his signature, like that which he
now enclosed. As the Duke’s servant was waiting, I gave
him the book, which he took back, and I retained the slip of
paper for any
other similar occasion. <span class="xxpn" id="p184">{184}</span></p>

<div class="dsdnote">〈THE DUKE DRESSED IN HIS CARRIAGE.〉</div>

<p>The Duke was habitually an economist of time. One day I
was going homeward in a cab to dress for a dinner engagement,
when I thought I observed him riding down St. James’s Street
towards the House of Lords. On reaching the house of the
friend with whom I was to dine, I found that the Duke of
Wellington was expected at dinner. He arrived punctually.
In the course of the evening I took an opportunity of asking
him whether I was mistaken in supposing I had seen him a
short time before dinner riding down St. James’s Street. I
then expressed my surprise at the rapidity of his movements
in getting back to Apsley House in time to dress and be
punctual to his engagement. He said, “No, I did not do
that; I had ordered my carriage to meet me at the House of
Lords, and I changed my dress whilst it was bringing me
here.”</p>

<p>The most interesting conversations generally occurred when
only a few of his intimate friends met together.</p>

<p>On one of these occasions, at a very small dinner-party,
the characters of the French marshals became the subject of
conversation. The Duke, being appealed to, pointed out
freely their various qualities, and assigned to each his peculiar
excellence.</p>

<div class="dsdnote">〈CURIOUS QUESTION—THE DUKE’S REPLY.〉</div>

<p>One question, the most highly interesting of all, naturally
presented itself to our minds. I was speculating how I could,
without impropriety, suggest it, when, to my great relief, one
of the party, addressing the Duke, <span class="nowrap">said—</span></p>

<p>“Well, sir, how was it that, with such various great qualities,
you licked them all, one after another?”</p>

<p>The Duke was evidently taken by surprise. He paused
for a moment or two, and then <span class="nowrap">said—</span></p>

<p>“Well, I don’t know exactly how it was; but I think that
if any unexpected circumstance occurred in the
midst of a <span class="xxpn" id="p185">{185}</span>
battle, which deranged its whole plan, I could perhaps
organize another plan more quickly than most of them.”</p>

<p>This strongly confirms the view of the Duke of Wellington’s
character given in the preceding pages. After examining
all the more important combinations which might be made
for the conflict, and having selected those which appeared
the best, it is quite natural, if any accident deranged the
original plan, that he should perceive, more quickly than
another commander, one amongst the many plans previously
rejected which was immediately applicable to the new and
unexpected circumstances.</p></div><!--section-->

<div class="section" id="p186">
<h2 class="h2herein">CHAPTER XIII.
<span class="hsmall">RECOLLECTIONS OF WOLLASTON, DAVY, AND ROGERS.</span></h2>

<div class="dsynopsis">
Secretaryship of Royal Society&#x200a;—&#x200a;Mr. Murray of
Albemarle Street&#x200a;—&#x200a;Remark on “The Decline of
Science”&#x200a;—&#x200a;Dr. Somerville&#x200a;—&#x200a;Explanation
of a Job of Sir Humphry Davy&#x200a;—&#x200a;History
of the Thaumatrope&#x200a;—&#x200a;Introduction
to Mr. Rogers&#x200a;—&#x200a;The Poet nearly run
over&#x200a;—&#x200a;Anecdote of the “Economy of
Man­u­fac­tures”&#x200a;—&#x200a;Teaches the Author how to live
for ever&#x200a;—&#x200a;Rapidity of composition amongst
Poets&#x200a;—&#x200a;Different effects of Imagination in the Poet
and the Phi­los­o­pher&#x200a;—&#x200a;Consultation about the Author’s
unwritten Novel.</div>

<p class="pfirst"><span class="smcap">I<b>N</b></span> 1826, one of
the secretaryships of the Royal Society became vacant. Dr. Wollaston
and several others of the leading members of the Society and of the
Council wished that I should be appointed. This would have been the
more agreeable to me, because my early friend Herschel was at that time
the senior Secretary.</p>

<p>This arrangement was agreed to by Sir H. Davy, and I left
town with the full assurance that I was to have the appointment.
In the mean time Sir H. Davy summoned a Council
at an unusual hour—eight o’clock in the evening—for a
special purpose, namely, some arrangement about the Treasurer’s
accounts.</p>

<p>After the business relating to the Treasurer was got through,
Sir H. Davy observed that there was a secretaryship vacant,
and he proposed to fill it up.</p>

<div class="dsdnote">〈SIR HUMPHRY DAVY’S DISCOURSES.〉</div>

<p>Dr. Wollaston then asked Sir Humphry Davy if he
claimed the nomination as a right of the
President, to which <span class="xxpn" id="p187">{187}</span>
Sir H. Davy replied that he did, and then nominated
Mr. Children. The President, as president, has no such right;
and even if he had possessed it, he had promised Mr. Herschel
that I should be his colleague. There were upright
and eminent men on that council; yet no one of them had
the moral courage to oppose the President’s dictation, or afterwards
to set it aside on the ground of its irregularity.</p>

<p>A few years after, whilst I was on a visit at Wimbledon
Park, Dr. and Mrs. Somerville came down to spend the day.
Dr. Somerville mentioned a very pleasant dinner he had had
with the late Mr. John Murray of Albemarle Street, and also
a conversation relating to my book “On the Decline of
Science in England.” Mr. Murray felt hurt at a remark I
had made on himself (page <a href="#p107" title="go to pag&#x65; 107">107</a>) whilst criticizing a then
unexplained job of Sir Humphry Davy’s. Dr. Somerville
assured Mr. Murray that he knew me intimately, and that if
I were convinced that I had done him an injustice, nobody
would be more ready to repair it. A few days after, Mr.
Murray put into Dr. Somerville’s hands papers explaining the
whole of the transaction. These papers were now transferred
to me. On examining them I found ample proof of what
I had always suspected. The ob­ser­va­tion I had made which
pained Mr. Murray fell to the ground as soon as the real
facts were known, and I offered to retract it in any suitable
manner. One plan I proposed was to print a supplemental
page, and have it bound up with all the remaining copies of
the “Decline of Science.”</p>

<p>Mr. Murray was satisfied with my explanation, but did not
wish me to take the course I proposed, at least, not at that
time. Various objections may have presented themselves to
his mind, but the affair was adjourned with the understanding
that at some future time I should explain the
real state of <span class="xxpn" id="p188">{188}</span>
the facts which had led to this misinterpretation of Mr.
Murray’s conduct.</p>

<div class="dsdnote">〈EXPLANATION OF THAT JOB.〉</div>

<p>The true history of the affair was this: Being on the
Council of the Royal Society in 1827, I observed in our
accounts a charge of 381&#x200a;<i>l.</i> 5&#x200a;<i>s.</i> as paid to Mr. Murray for 500
copies of Sir Humphry Davy’s Discourses.</p>

<p>I asked publicly at the Council for an explanation of this
item. The answer given by Dr. Young and others <span class="nowrap">was—</span></p>

<p>“That the Council had agreed to purchase these volumes
at that price, in order to <i>induce</i> Mr. Murray to print the
President’s speeches.”</p>

<p>To this I replied that such an explanation was entirely
inadmissible. I then showed that even allowing a very high
price for composing, printing, and paper, if the Council had
wished to print 500 copies of those Discourses they could
have done it themselves for 150&#x200a;<i>l.</i> at the outside. I could not
extract a single word to elucidate this mystery, about which,
however, I had my own ideas.</p>

<p>It appeared by the papers put into my hands that Sir
Humphry Davy had applied to Mr. Murray, and had sold him
the copyright of the Discourses for 500 guineas, one of the
conditions being that the Royal Society should purchase of
him 500 copies at the trade price.</p>

<p>Mr. Murray paid Sir H. Davy the 500 guineas in three
bills at six, twelve, and eighteen months. These bills passed
through Drummond’s (Sir H. Davy’s banker), and I have
had them in my own hands for examination.</p>

<p>Thus it appears that Mr. Murray treated the whole affair
as a matter of business, and acted in this purchase in his
usual liberal manner. I have had in my hand a statement
of the winding-up of that account copied from Mr. Murray’s
books, and I find that he was a considerable
loser by his <span class="xxpn" id="p189">{189}</span>
purchase. Sir H. Davy, on the other hand, contrived to transfer
between three and four hundred pounds from the funds of the
Royal Society into his own pocket.<a class="afnanc" href="#fn35" id="fnanc35">35</a></p>

<p>It was my determination to have called for an explanation
of this affair at the election of our President and officers at
our anniversary on the 30th November if Sir H. Davy had
been again proposed as President in 1827.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc35" id="fn35">35</a>
See “Decline of Science in England,” p. 105. 8vo. 1830.</p></div>
</div><!--section-->

<div class="section">
<h3 class="h3herein"><i>The Thaumatrope.</i></h3>

<p>One day Herschel, sitting with me after dinner, amusing
himself by spinning a pear upon the table, suddenly asked
whether I could show him the two sides of a shilling at the
same moment.</p>

<p>I took out of my pocket a shilling, and holding it up before
the looking-glass, pointed out <i>my</i> method. “No,” said my
friend, “that won’t do;” then spinning my shilling upon the
table, he pointed out <i>his</i> method of seeing both sides at
once. The next day I mentioned the anecdote to the late
Dr. Fitton, who a few days after brought me a beautiful illustration
of the principle. It consisted of a round disc of card
suspended between the two pieces of sewing-silk. These
threads being held between the finger and thumb of each
hand, were then made to turn quickly, when the disc of card,
of course, revolved also.</p>

<p>Upon one side of this disc of card was painted a bird; upon
the other side, an empty bird-cage. On turning the thread
rapidly, the bird appeared to have got inside the cage. We
soon made numerous applications, as a rat on one side and a
trap upon the other, &amp;c. It was shown to Captain Kater,
Dr. Wollaston, and many of our friends, and was, after the
lapse of a short time, forgotten. <span class="xxpn" id="p190">{190}</span></p>

<div class="dsdnote">〈THE THAUMATROPE: ITS RETRIBUTION.〉</div>

<p>Some months after, during dinner at the Royal Society
Club, Sir Joseph Banks being in the chair, I heard Mr.
Barrow, then Secretary to the Admiralty, talking very loudly
about a wonderful invention of Dr. Paris, the object of which
I could not quite understand. It was called the thaumatrope,
and was said to be sold at the Royal Institution, in Albemarle-street.
Suspecting that it had some connection with our
unnamed toy, I went the next morning and purchased, for
seven shillings and sixpence, a thaumatrope, which I afterwards
sent down to Slough to the late Lady Herschel. It
was precisely the thing which her son and Dr. Fitton had
contributed to invent, which amused all their friends for a
time and had then been forgotten. There was however <i>one</i>
additional thaumatrope made afterwards. It consisted of the
usual disc of paper. On one side was represented a thaumatrope
(the design upon it being a penny-piece) with the motto,
“How to turn a penny.”</p>

<p>On the other side was a gentleman in black, with his
hands held out in the act of spinning a thaumatrope, the
motto being, “A new trick from Paris.”</p>

<p>After my contest for Finsbury was decided, Mr. Rogers the
banker, and the brother of the poet, who had been one of my
warmest supporters, proposed accompanying me to the hustings
at the declaration of the poll. He had also invited a
party of some of the most influential electors of his district to
dine with him in the course of the week, in order that they
might meet me, and consider about measures for supporting
me at the next opportunity.</p>

<div class="dsdnote">〈THE POET AND PHI­LOS­O­PHER AT A CROSSING.〉</div>

<p>On a cold drizzling rainy day in November the final state
of the poll was declared. Mr. Rogers took me in his carriage
to the hustings, and caught a cold, which seemed at first unimportant.
On the day of the dinner, when
we met at <span class="xxpn" id="p191">{191}</span>
Mr. Rogers’s, who resided at Islington, he was unable to leave
his bed. Miss Rogers, his sister, who lived with him, and his
brother the poet, received us, quite unconscious of the dangerous
condition of their relative, who died the next day.</p>

<p>Thus commenced a friendship with both of my much-valued
friends which remained unruffled by the slightest wave until
their lamented loss. Miss Rogers removed to a house in the
Regent’s Park, in which the paintings by modern artists collected
by her elder brother, and increased by her own judicious
taste, were arranged. The society at that house comprised
all that was most eminent in literature and in art. The adjournment
after her breakfasts to the delightful verandah
overlooking the Park still clings to my fading memory, and
the voices of her poet brother, of Jeffrey, and of Sidney
Smith still survive in the vivid impressions of their wisdom
and their wit.</p>

<p>I do not think the genuine kindness of the poet’s character
was sufficiently appreciated. I oc­ca­sion­al­ly walked home with
him from parties during the first years of our acquaintance.
In later years, when his bodily strength began to fail, I always
accompanied him, though sometimes not without a little contest.</p>

<p>I have frequently walked with him from his sister’s house,
in the Regent’s Park, to his own in St. James’s Place, and he
has sometimes insisted upon returning part of the way home
with me.</p>

<p>On one of those occasions we were crossing a street near
Cavendish Square: a cart coming rapidly round the corner, I
almost dragged him over. As soon as we were safe, the poet
said, very much as a child would, “There, now, that was all
your fault; you would come with me, and so I was nearly
run over.” However, I found less and less
resistance to my <span class="xxpn" id="p192">{192}</span>
accompanying him, and only regretted that I could not be
constantly at his side on those occasions.</p>

<p>Soon after the publication of the “Economy of Man­u­fac­tures,”
Mr. Rogers told me that he had met one evening, at a
very fashionable party, a young dandy, with whom he had had
some conversation. The poet had asked him whether he had
read that work. To this his reply was, “Yes: it is a very nice
book—just the kind of book that anybody could have written.”</p>

<div class="dsdnote">〈HOW TO LIVE FOR EVER.〉</div>

<p>One day, when I was in great favour with the poet, we
were talking about the preservation of health. He told me
he would teach me how to live for ever; for which I thanked
him in a compliment after his own style, rather than in mine.
I answered, “Only embalm me in your poetry, and it is
done.” Mr. Rogers invited me to breakfast with him the
next morning, when he would communicate the receipt. We
were alone, and I enjoyed a very entertaining breakfast. The
receipt consisted mainly of cold ablutions and the frequent
use of the flesh brush. Mr. Rogers himself used the latter to
a moderate extent regularly, three times every day—before
he dressed himself, when he dressed for dinner, and before he
got into bed. About six or eight strokes of the flesh-brush
completed each operation. We then adjourned to a shop,
where I purchased a couple of the proper brushes, which I
used for several years, and still use oc­ca­sion­al­ly, with, I believe,
considerable advantage.</p>

<div class="dsdnote">〈RAPIDITY OF COMPOSITION.〉</div>

<p>Once, at Mr. Rogers’s table, I was talking with one of his
guests about the speed with which some authors composed,
and the slowness of others. I then turned to our host, and,
much to his surprise, inquired how many lines a-day on the
average a poet usually wrote. My friend, when his astonishment
had a little subsided, very good-naturedly gave us the
result of his own experience. He said that he
had never written <span class="xxpn" id="p193">{193}</span>
more than four<a class="afnanc" href="#fn36" id="fnanc36">36</a>
lines of verse in any one day of his life.
This I can easily understand; for Mr. Rogers’ taste was the
most fastidious, as well as the most just, I ever met with.
Another circumstance also, I think, contributed to this slowness
of composition.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc36" id="fn36">36</a>
I am not quite certain that the number was four; but I am
absolutely certain that it was either four or six.</p></div>

<p>An author may adopt either of two modes of composing.
He may write off the whole of his work roughly, so as to get
upon paper the plan and general outline, without attending at
all to the language. He may afterwards study minutely every
clause of each sentence, and then every word of each clause.</p>

<p>Or the author may finish and polish each sentence as soon
as it is written.</p>

<p>This latter process was, I think, employed by Mr. Rogers,
at least in his poetry.</p>

<p>He then told us that Southey composed with much greater
rapidity than himself, as well in poetry as in prose. Of the
latter Southey frequently wrote a great many pages before
breakfast.</p>

<p>Once, at a large dinner party, Mr. Rogers was speaking of
an inconvenience arising from the custom, then commencing,
of having windows formed of one large sheet of plate-glass.
He said that a short time ago he sat at dinner with his back
to one of these single panes of plate-glass: it appeared to
him that the window was wide open, and such was the force
of imagination, that he actually caught cold.</p>

<div class="dsdnote">〈DIFFERENT EFFECTS OF IMAGINATION.〉</div>

<p>It so happened that I was sitting just opposite to the poet.
Hearing this remark, I immediately said, “Dear me, how odd
it is, Mr. Rogers, that you and I should make such a very
different use of the faculty of imagination. When I go to
the house of a friend in the country,
and unexpectedly <span class="xxpn" id="p194">{194}</span>
remain for the night, having no night-cap, I should naturally
catch cold. But by tying a bit of pack-thread tightly round
my head, I go to sleep imagining that I have a night-cap on;
consequently I catch no cold at all.” This sally produced
much amusement in all around, who supposed I had improvised
it; but, odd as it may appear, it is a practice I have
often resorted to. Mr. Rogers, who knew full well the respect
and regard I had for him, saw at once that I was relating a
simple fact, and joined cordially in the merriment it excited.</p>

<p>In the latter part of Mr. Rogers’s life, when, being unable
to walk, he was driven in his carriage round the Regent’s
Park, he frequently called at my door, and, when I was able,
I often accompanied him in his drive. On some one of these
occasions, when I was unable to accompany him, I put into his
hands a parcel of proof-sheets of a work I was then writing,
thinking they might amuse him during his drive, and that I
might profit by his criticism. Some years before, I had consulted
him about a novel I had proposed to write solely for
the purpose of making money to assist me in completing the
Analytical Engine. I breakfasted alone with the poet, who
entered fully into the subject. I proposed to give up a
twelvemonth to writing the novel, but I determined not to
commence it unless I saw pretty clearly that I could make
about 5,000&#x200a;<i>l.</i> by the sacrifice of my time. The novel was to
have been in three volumes, and there would probably have
been reprints of another work in two volumes. Both of these
works would have had graphic illustrations. The poet gave
me much information on all the subjects connected with the
plan, and amongst other things, observed that when he published
his beautifully illustrated work on Italy, that he had
paid 9,000&#x200a;<i>l.</i> out of his own pocket before he received any
return for that work.</p></div><!--section-->

<div class="section" id="p195">
<h2 class="h2herein">CHAPTER XIV.
<span class="hsmall">RECOLLECTIONS OF LAPLACE, BIOT, AND HUMBOLDT.</span></h2>

<div class="dsynopsis">
My First Visit to Paris&#x200a;—&#x200a;Anecdote of
the fifty-two Eggs&#x200a;—&#x200a;Mistake about
Woodhouse&#x200a;—&#x200a;Fourier&#x200a;—&#x200a;Biot&#x200a;—&#x200a;Drawings
of the Difference Engine&#x200a;—&#x200a;Strong char­ac­ter­is­tic
of Humboldt’s mind&#x200a;—&#x200a;English Clergyman at
Paris&#x200a;—&#x200a;Great Meeting of Phi­los­o­phers at
Berlin, 1828&#x200a;—&#x200a;Introduces the Author to Magnus
and Derichlet&#x200a;—&#x200a;Puts the Englishman upon the
Dining Committee&#x200a;—&#x200a;Conversation in the Linden
Walk&#x200a;—&#x200a;Humboldt’s study&#x200a;—&#x200a;Various
members of the family of Buonaparte&#x200a;—&#x200a;Lucien
and his Children&#x200a;—&#x200a;Louis, the King of
Holland&#x200a;—&#x200a;Joseph, the King of Spain&#x200a;—&#x200a;His
second Daughter married to a Son of Louis&#x200a;—&#x200a;Their
taste&#x200a;—&#x200a;Drawings and Lithographs&#x200a;—&#x200a;Her
Death.</div>

<p class="pfirst"><span class="smcap">M<b>Y</b></span>
first visit to Paris was made in company with my friend
John Herschel. On reaching Abbeville, we wanted breakfast,
and I undertook to order it. Each of us usually required a
couple of eggs. I preferred having mine moderately boiled,
but my friend required his to be boiled quite hard. Having
explained this matter to the waiter, I concluded by instructing
him that each of us required two eggs thus cooked,
concluding my order with the words, “pour chacun deux.”</p>

<p>The garçon ran along the passage half way towards the kitchen, and
then called out in his loudest <span class="nowrap">tone—</span></p>

<p>“Il faut faire bouillir cinquante-deux œufs pour Messieurs les
Anglais.” I burst into such a fit of un­con­trol­lable laughter at this
absurd mis­un­der­stand­ing of <i>chacun deux</i>, for <i>cinquante-deux</i>, that it
was some time before I could explain it to Herschel, and but for his
running into the kitchen to <span class="xxpn" id="p196">{196}</span>
coun­ter­mand it, the half hundred of eggs would have assuredly been
simmering over the fire.</p>

<p>A few days after our arrival in Paris, we dined with
Laplace, where we met a large party, most of whom were
members of the Institut. The story had already arrived at
at Paris, having rapidly passed through several editions.</p>

<div class="dsdnote">〈FIFTY-TWO EGGS.〉</div>

<p>To my great amusement, one of the party told the company
that, a few days before, two young Englishman being at
Abbeville, had ordered fifty-two eggs to be boiled for their
breakfast, and that they ate up every one of them, as well as
a large pie which was put before them.</p>

<p>My next neighbour at dinner asked me if I thought it
probable. I replied, that there was no absurdity a young
Englishman would not oc­ca­sion­al­ly commit.</p>

<p>One morning Herschel and I called on Laplace, who spoke
to us of various English works on math­e­mat­i­cal subjects.
Amongst others, he mentioned with approbation, “Un ouvrage
de vous deux.” We were both quite at a loss to know to what
work he referred. Herschel and I had not written any joint
work, although we had together translated the work of Lacroix.
The volume of the “Memoirs of the Analytical
Society,” though really our joint production, was not known
to be such, and it was also clear that Laplace did not refer
to that work. Perceiving that we did not recognise the name
of the author to whom he referred, Laplace varied the pronunciation
by calling him <i>vous deux</i>; the first word being pronounced
as the French word “vous,” and the second as the
English word “deuce.”</p>

<p>Upon further explanation, it turned out that Laplace meant
to speak of a work published by Woodhouse, whose name
is in the pronunciation of the French so very like <i>vous
deux</i>. <span class="xxpn" id="p197">{197}</span></p>

<div class="dsdnote">〈FOURIER AND BIOT.〉</div>

<p>Poisson, Fourier, and Biot were amongst my earliest friends
in Paris. Fourier, then Secretary of the Institute, had accompanied
the first Napoleon in his expedition to Egypt.
His profound acquaintance with analysis remains recorded
in his works. His unaffected and genial manner, the vast
extent of his acquirements, and his admirable taste conspicuous
even in the apartments he inhabited, were most felt by
those who were honoured by his friendship.</p>

<p>With M. Biot I became acquainted in early life; he was
then surrounded by a happy family. In my occasional visits
to Paris I never omitted an opportunity of paying my respects
to him: when deprived of those supports and advanced in
life, he still earnestly occupied himself in carrying out the
investigations of his earlier years.</p>

<p>His son, M. Biot, a profound oriental scholar, who did me
the honour of translating ‘The Economy of Man­u­fac­tures,’
died many years before his father.</p>

<p>In one of my visits to Paris, at a period when beards had
become fashionable amongst a certain class of my countrymen,
I met Biot. After our first greeting, looking me full in the
face, he said, “My dear friend, you are the best shaved man
in Europe.”</p>

<div class="dsdnote">〈BIOT AND THE DIFFERENCE ENGINE.〉</div>

<p>At a later period I took with me to Paris the complete
drawings of Difference Engine No. 2. As soon as I had hung
them up round my own apartments to explain them to my
friends I went to the College de France, where M. Biot
resided. I mentioned to him the fact, and said that if it was a
subject in which he was interested, and had leisure to look at
these drawings, I should have great pleasure in bringing them
to him, and giving him any explanation that he might desire.
I told him, however, that I was fully aware how much the
time of every man who really adds to
science must be <span class="xxpn" id="p198">{198}</span>
occupied, and that I made this proposal rather to satisfy my
own mind that I had not neglected one of my oldest friends
than in the expectation that he had time for the examination
of this new subject.</p>

<p>The answer of my friend was remarkable. After thanking
me in the warmest terms for this mark of friendship, he explained
to me that the effect of age upon his own mind was
to render the pursuit of any new inquiry a matter of slow
and painful effort; but that in following out the studies of
his youth he was not so much impeded. He added that in
those subjects he could still study with sat­is­fac­tion, and even
make advances in them, assisted in the working out of his
views experimentally by the aid of his younger friends.</p>

<p>I was much gratified by this unreserved expression of the
state of the case, and I am sure those younger men who so
kindly assisted the aged phi­los­o­pher will be glad to know
that their assistance was duly appreciated.</p>

<p>The last time during M. Biot’s life that I visited Paris I
went, as usual, to the College de France. I inquired of the
servant who opened the door after the state of M. Biot’s
health, which was admitted to be feeble. I then asked
whether he was well enough to see an old friend. Biot himself
had heard the latter part of this conversation. Coming
into the passage he seized my hand and said “My dear friend,
I would see you even if I were dying.”</p>
</div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Alexander Humboldt.</i></h3>

<p>One of the most remarkable char­ac­ter­is­tics of Humboldt’s mind was,
that he not merely loved and pursued science for its own sake, but that
he derived pleasure from assisting with his information and advice any
other inquirer, however humble, who might need it. <span class="xxpn"
id="p199">{199}</span></p>

<div class="dsdnote">〈HUMBOLDT AT PARIS.〉</div>

<p>In one of my visits to Paris, Humboldt was sitting with me
when a friend of mine, an English clergyman, who had just
arrived in Paris, and had only two days to spare for it, called
upon me to ask my assistance about getting access to certain
MSS. Putting into Humboldt’s hand a tract lying on my
table, I asked him to excuse me for a few minutes whilst I
gave what advice I could to my countryman.</p>

<p>My friend told me that he wanted to examine a MS., which
he was informed was in a certain library in a certain street
in Paris: that he knew nobody in the city to help him in his
mission.</p>

<p>Humboldt having heard this statement, came over to us
and said, “If you will introduce me to your friend, I can put
him in the way of seeing the MSS. he is in search of.” He
then explained that the MSS. had been removed to another
library in Paris, and proposed to give my friend a note of introduction
to the librarian, and mentioned other MSS. and
other libraries in which he would find information upon the
same subject.</p>

<p>Many years after, being at Vienna, I heard that Humboldt
was at Töplitz, a circumstance which induced me to visit that
town. On my arrival I found he had left it a few days before
on his return to Berlin. In the course of a few days, I
followed him to that city, and having arrived in the middle of
the day, I took apartments in the Linden Walk, and got all
my travelling apparatus in order; I then went out to call
on Humboldt. Finding that he had gone to dine with his
brother William, who resided at a short distance from Berlin,
I therefore merely left my card.</p>

<p>The next morning at seven o’clock, before I was out of bed,
I received a very kind note from Humboldt, to ask me to
breakfast with him at nine. In a postscript
he added, “What <span class="xxpn" id="p200">{200}</span>
are the moving molecules of Robert Brown?” These atoms
of dead matter in rapid motion, when examined under the
microscope, were then exciting great attention amongst phi­los­o­phers.</p>

<p>I met at breakfast several of Humboldt’s friends, with
whose names and reputation I was well acquainted.</p>

<div class="dsdnote">〈GREAT MEETING OF GERMAN PHI­LOS­O­PHERS.〉</div>

<p>Humboldt himself expressed great pleasure that I should
have visited Berlin to attend the great meeting of German
phi­los­o­phers, who in a few weeks were going to assemble in
that capital. I assured him that I was quite unaware of the
intended meeting, and had directed my steps to Berlin merely
to enjoy the pleasure of his society. I soon perceived that
this meeting of phi­los­o­phers on a very large scale, supported
by the King and by all the science of Germany, might itself
have a powerful influence upon the future progress of human
knowledge. Amongst my companions at the breakfast-table
were Derichlet and Magnus. In the course of the morning
Humboldt mentioned to me that his own duties required his
attendance on the King every day at three o’clock, and
having also in his hands the organization of the great
meeting of phi­los­o­phers, it would not be in his power to
accompany me as much as he wished in seeing the various
institutions in Berlin. He said that, under these circumstances,
he had asked his two young friends, Derichlet and
Magnus, to supply his place. During many weeks of my
residence in Berlin, I felt the daily advantage of this thoughtful
kindness of Humboldt. Accompanied by one or other,
and frequently by both, of my young friends, I saw everything
to the best advantage, and derived an amount of information
and in­struc­tion which under less favourable circumstances
it would have been impossible to have obtained.</p>

<p>The next morning, I again
breakfasted with Humboldt. <span class="xxpn" id="p201">{201}</span>
On the previous day I had mentioned that I was making a
collection of the signs employed in map-making. I now met
Von Buch and General Ruhl, both of whom were profoundly
acquainted with that subject. I had searched in vain for any
specimen of a map shaded upon the principle of lines of
equal elevation. Von Buch the next morning gave me an
engraving of a small map upon that principle, which was, I
believe, at that time the only one existing.</p>

<p>After breakfast we went into Humboldt’s study to look at
something he wished to show us. In turning over his papers,
which, like my own, were lying apparently in great disorder
upon the table, he picked up the cover of a letter on which
was written a number of names in different parallel columns.
“That,” he observed incidentally, “is for you.” After he had
shown us the object of our visit to his sanctum, he reverted to
the envelop which he put into my hands, explaining that he
had grouped roughly together for my use all the remarkable
men then in Berlin, and several of those who were expected.</p>

<p>These he had arranged in classes:—Men of science, men of
letters, sculptors, painters, and artists generally, instrument-makers,
&amp;c. This list I found very convenient for reference.</p>

<div class="dsdnote">〈THE AUTHOR PUT ON THE DINING COMMITTEE.〉</div>

<p>When the time of the great meeting approached, it became
necessary to prepare the arrangements for the convenience of
the assembled science of Europe. One of the first things, of
course, was the important question, how they were to dine?
A committee was therefore appointed to make experiment by
dining successively at each of the three or four hotels competing
for the honour of providing a table d’hôte for the
savans.</p>

<p>Humboldt put me on that committee, remarking, that an
Englishman always appreciates a good dinner. The committee
performed their agreeable duty in
a manner quite <span class="xxpn" id="p202">{202}</span>
sat­is­fac­tory to themselves, and I hope, also, to the digestions
of the Naturforschers.</p>

<div class="dsdnote">〈CONVERSATION IN THE LINDEN WALK.〉</div>

<p>During the meeting much gaiety was going on at Berlin.
One evening previous to our parties, I was walking in the
Linden Walk with Humboldt, discussing the singularities of
several of our learned acquaintance. My companion made
many acute and very amusing remarks; some of these were
a little caustic, but not one was ill-natured. I had contributed
a very small and much less brilliant share to this conversation,
when the clock striking, warned us that the hour for our
visits had arrived. I never shall forget the expression of
archness which lightened up Humboldt’s countenance when
shaking my hand he said, in English, “My dear friend, I
think it may be as well that we should not speak of each
other until we meet again.” We then each kept our respective
engagements, and met again at the most recherché
of all, a concert at Mendelssohn’s.</p>
</div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Of the Buonaparte Family.</i></h3>

<p>From my father’s house on the coast, near Teignmouth, we
could, with a telescope, see every ship which entered Torbay.
When the “Bellerophon” anchored, the news was rapidly
spread that Napoleon was on board. On hearing the rumour,
I put a small telescope into my pocket, and, mounting my
horse, rode over to Torbay. A crowd of boats surrounded the
ship, then six miles distant; but, by the aid of my glass, I
saw upon the quarter-deck that extraordinary man, with many
members of whose family I sub­se­quent­ly became acquainted.
Of those who are no more I may without impropriety say a
few words.</p>

<p>My first acquaintance with several branches of the family <span
class="xxpn" id="p203">{203}</span> of Napoleon Buonaparte arose under
the following <span class="nowrap">circumstances:—</span></p>

<div class="dsdnote">〈LUCIEN BUONAPARTE.〉</div>

<p>When his elder brother Lucien, to avoid the necessity of
accepting a kingdom, fled from his imperial brother, and took
refuge in England, his position was either not well understood,
or, perhaps, was entirely mistaken. Lucien seems to
have been looked upon with suspicion by our Government,
and was placed in the middle of England under a species of
espionage.</p>

<p>Political parties then ran high, and he did not meet with
those attentions which his varied and highly-cultivated tastes,
especially in the fine arts, entitled him to receive, as a stranger
in a foreign land.</p>

<p>A family connection of mine, residing in Worcestershire,
was in the habit of visiting Lucien Buonaparte. Thus, in
my occasional visits to my brother-in-law’s place, I became
acquainted with the Prince of Canino. In after-years,
when he oc­ca­sion­al­ly visited London, I had generally the
pleasure of seeing him.</p>

<p>In 1828 I met at Rome the eldest son of Lucien, who introduced
me to his sisters, Lady Dudley Stuart and the Princess
Gabrielli.</p>

<div class="dsdnote">〈LOUIS, THE KING OF HOLLAND.〉</div>

<p>In the same year I became acquainted, at Bologna, with
the Princess d’Ercolano, another daughter of Lucien, whom I
afterwards met at Florence, at the palace of her uncle Louis,
the former king of Holland. During a residence of several
months in that city I was a frequent guest at the family table
of the Compte St. Leu. One of his sons had married the
Princess Charlotte, the second daughter of the King of Spain,
a most accomplished, excellent, and charming person. They
reminded me much of a sensible English couple, in the best
class of English society. Both had great taste
in the fine <span class="xxpn" id="p204">{204}</span>
arts. The prince had a workshop at the top of the palace,
in which he had a variety of tools and a lithographic printing
press. Oc­ca­sion­al­ly, in the course of their morning drives,
some picturesque scene, in that beautiful country, would
arrest their attention. Stopping the carriage, they would
select a favourable spot, and the princess would then make a
sketch of it.</p>

<p>At other times they would spend the evening, the prince in
extemporizing an imaginary scene, which he described to his
wife, who, with admirable skill, embodied upon paper the
tasteful conceptions of her husband. These sketches then
passed up to the workshop of the Prince, were transferred to
stone, and in a few days lithographic impressions descended
to the drawing-room. I fortunately possess some of these
impressions, which I value highly, not only as the productions
of an amiable and most accomplished lady, but of one who
did not shrink from the severer duties of life, and died in fulfilling
them.</p>

<p>After the melancholy loss of her husband, the Princess Charlotte
remained with her father, who resided at one period in
the Regent’s Park, where I from time to time paid my respects
to them. Oc­ca­sion­al­ly I received them at my own house.
One summer letters from Florence reached them, announcing
the dangerous illness of the Comte de St. Leu. The daughter
of Joseph immediately set out alone for Florence to minister
to the comfort of her uncle and father-in-law. On her return
from Italy she was attacked by cholera and died in the
south of France.</p></div><!--section-->

<div class="section" id="p205">
<h2 class="h2herein">CHAPTER XV.
<span class="hsmall">EXPERIENCE BY WATER.</span></h2>

<div class="dsynopsis">
Shooting Sea-birds&#x200a;—&#x200a;Walking on the
Water&#x200a;—&#x200a;A Screw being loose&#x200a;—&#x200a;The
Author nearly drowned&#x200a;—&#x200a;Ad­ven­ture in the Thames
Tunnel&#x200a;—&#x200a;Descent in a Diving-bell&#x200a;—&#x200a;Plan
for Sub­ma­rine Nav­i­ga­tion.</div>

<p class="pfirst"><span class="smcap">T<b>HE</b></span> grounds
surrounding my father’s house, near Teignmouth, extended to the sea.
The cliffs, though lofty, admitted at one point of a descent to the
beach, of which I very frequently availed myself for the purpose of
bathing. One Christmas when I was about sixteen I determined to see if
I could manage a gun. I accordingly took my father’s fowling-piece, and
climbing with it down to the beach, I began to look about for the large
sea-birds which I thought I might have a chance of hitting.</p>

<p>I fired several charges in vain. At last, however, I was
fortunate enough to hit a sea-bird called a diver; but it fell
at some distance into the sea: I had no dog to get it out for
me; the sea was rough, and no boat was within reach; also it
was snowing.</p>

<p>So I took advantage of a slight recess in the rock to protect
my clothes from the snow, undressed, and swam out after my
game, which I succeeded in capturing. The next day, having
got the cook to roast it, I tried to eat it; but this was by no
means an agreeable task, so for the future I left the sea-birds
to the quiet possession of
their own dominion. <span class="xxpn" id="p206">{206}</span></p>

<div class="dsdnote">〈WALKING IN THE WATER.〉</div>

<p>Shortly after this, whilst residing on the beautiful banks of
the Dart, I constantly indulged in swimming in its waters.
One day an idea struck me, that it was possible, by the aid of
some simple mechanism, to walk upon the water, or at least
to keep in a vertical position, and have head, shoulders, and
arms above water.</p>

<p>My plan was to attach to each foot two boards closely connected
together by hinges themselves fixed to the sole of the
shoe. My theory was, that in lifting up my leg, as in the act
of walking, the two boards would close up towards each
other; whilst on pushing down my foot, the water would rush
between the boards, cause them to open out into a flat surface,
and thus offer greater resistance to my sinking in the water.</p>

<p>I took a pair of boots for my experiment, and cutting up
a couple of old useless volumes with very thick binding, I
fixed the boards by hinges in the way I proposed. I placed
some obstacle between the two flaps of each book to prevent
them from approaching too nearly to each other so as to
impede their opening by the pressure of the water.</p>

<p>I now went down to the river, and thus prepared, walked
into the water. I then struck out to swim as usual, and
found little difficulty. Only it seemed necessary to keep the
feet farther apart. I now tried the grand experiment. For
a time, by active exertion of my legs, I kept my head and
shoulders above water and sometimes also my arms. I was
now floating down the river with the receding tide, sustained
in a vertical position with a very slight exertion of force.</p>

<p>But unfortunately one pair of my hinges got out of order,
and refused to perform its share of the propulsion. The
result was that I became lop-sided. I was therefore obliged
to swim, which I now did with considerable exertion; but
another difficulty soon occurred,—the
instrument on the <span class="xxpn" id="p207">{207}</span>
disabled side refused to do its share in propelling me. The
tide was rapidly carrying me down the river; my own exertions
alone would have made me revolve in a small circle,
consequently I was obliged to swim in a spiral. It was very
difficult to calculate the curve I was describing upon the
surface of the water, and still more so to know at what point,
if at any, I might hope to reach its banks again. I became
very much fatigued by my efforts, and endeavoured to relieve
myself for a time by resuming the vertical position.</p>

<p>After floating, or rather struggling for some time, my feet
at last touched the bottom. With some difficulty and much
exertion I now gained the bank, on which I lay down in a
state of great exhaustion.</p>

<p>This experiment satisfied me of the danger as well as of
the practicability of my plan, and ever after, when in the
water, I preferred trusting to my own unassisted powers.</p>

<div class="dsdnote">〈DANGER IN THE THAMES TUNNEL.〉</div>

<p>At the close of the year 1827, as I anticipated a long
absence from England, I paid a visit to the Thames Tunnel,
in the construction of which I took a great interest. My
eldest son, then about twelve years of age, accompanied me
in this visit. I fortunately found the younger Brunel at the
works, who kindly took us with him into the workings.</p>

<p>We stood upon a timber platform, distant about fifty feet
from the shield, which was full of busy workmen, each actively
employed in his own cell. As we were conversing together,
I observed some commotion in the upper cell on the right
hand side. From its higher corner there entered a considerable
stream of liquid mud. Brunel ran directly to the shield
a line of workmen was instantly formed, and whatever tools
or timber was required was immediately conveyed to the spot.</p>

<div class="dsdnote">〈ON THE PROPER TIME FOR RUNNING AWAY.〉</div>

<p>I observed the progress with some anxiety, since but a
short time before a similar occurrence had
been the prelude <span class="xxpn" id="p208">{208}</span>
to the inundation of the whole tunnel. I remained watching
the fit time, if necessary, to run away; but also noticing what
effect the apparent danger had on my son. After a short
time it was clear that the ingress of liquid mud had been
checked, and in a few minutes more Brunel returned to me,
having this time succeeded in stopping up the breach. I then
inquired what was really the nature of the danger we had
escaped. Brunel told me that unless himself or Gravatt had
been present, the whole tunnel would in less than ten minutes
have been full of water. The next day I embarked for
Holland, and in about a week after I read in Galignani’s
newspaper, that the Thames had again broken into the
tunnel; that five or six of the workmen had been drowned,
and that Brunel himself had escaped with great difficulty by
swimming.</p>

<p>In 1818, during a visit to Plymouth, I had an opportunity
of going down in a diving-bell: I was accompanied by two
friends and the usual director of that machine.</p>

<p>The diving-bell in which I descended was a cast-iron vessel
about six feet long by four feet and a half wide, and five feet
eight inches high. In the top of the bell there were twelve
circular apertures, each about six inches in diameter, filled by
thick plate-glass fixed by water-tight cement. Exactly in
the centre there were a number of small holes through which
the air was continually pumped in from above.</p>

<p>At the ends of the bell are two seats, placed at such a
height, that the top of the head is but a few inches below the
top of the bell; these will conveniently hold two persons
each. Exactly in the middle of the bell, and about six
inches above its lower edge, is placed a narrow board, on
which the feet of the divers rest. On one side, nearly on a
level with the shoulders, is a small shelf, with
a ledge to <span class="xxpn" id="p209">{209}</span>
contain a few tools, chalk for writing messages, and a ring to
which a small rope is tied. A board is connected with this
rope; and after writing any orders on the board with a piece
of chalk, on giving it a pull, the superintendent above, round
whose arm the other end of the rope is fastened, will draw it
up to the surface, and, if necessary, return an answer by the
same conveyance.</p>

<p>In order to enter the bell, it is raised about three or four
feet above the surface of the water; and the boat, in which
the persons who propose descending are seated, is brought
immediately under it; the bell is then lowered, so as to
enable them to step upon the foot-board within it; and
having taken their seats, the boat is removed, and the bell
gradually descends to the water.</p>

<div class="dsdnote">〈SENSATIONS IN A DIVING-BELL.〉</div>

<p>On touching the surface, and thus cutting off the communication
with the external air, a peculiar sensation is perceived
in the ears; it is not, however, painful. The attention
is soon directed to another object. The air rushing in
through the valve at the top of the bell overflows, and
escapes with a considerable bubbling noise under the sides.
The motion of the bell proceeds slowly, and almost imperceptibly;
and, on looking at the glass lenses close to the
head, when the top of the machine just reaches the surface of
the water, it may be perceived, by means of the little impurities
which float about in it, flowing into the recesses containing
the glasses. A pain now begins to be felt in the ears,
arising from the increased external pressure; this may sometimes
be removed by the act of yawning, or by closing the
nostrils and mouth, and attempting to force air through the
ears. As soon as the equilibrium is established the pain
ceases, but recommences almost immediately by the continuance
of the descent. On returning, the
same sensation of <span class="xxpn" id="p210">{210}</span>
pain is felt in the ears; but it now arises from the dense air
which had filled them endeavouring, as the pressure is removed,
to force its way out.</p>

<div class="dsdnote">〈OBSERVATION IN DIVING BELL.〉</div>

<p>If the water is clear, and not much disturbed, the light in
the bell is very considerable; and, even at the depth of twenty
feet, was more than is usual in many sitting-rooms. Within
the distance of eight or ten feet, the stones at the bottom
began to be visible. The pain in the ears still continues to
occur at intervals, until the descent of the bell terminates by
its resting on the ground. The light is sufficient, after passing
through twenty feet of sea water, even for delicate experiments;
and a far less quantity is enough for the work which
is usually performed in those situations.</p>

<p>The temperatures of the hand and of the mouth, under the
tongue, were measured by a thermometer, but they did not
seem to differ from those which had been determined by the
same instrument previous to the descent; at least, the difference
did not amount to one-sixth of a degree of Fahrenheit’s
scale. The pulse was more frequent.</p>

<p>A small magnetic needle did not appear to have entirely
lost its directive power, when placed on the footboard in the
middle of the bell; but its direction was not the same as that
which it indicated on shore. This was determined by directing,
by means of signals, the workmen above to move the
bell in the direction of one of the co-ordinates; a stick then
being pressed against the bottom drew a line parallel to that
co-ordinate, its direction by compass was ascertained in the
bell, and the direction of the co-ordinate was determined on
returning to the surface after leaving the bell.</p>

<p>Signals are communicated by the workmen in the bell to
those above, by striking against the side of the bell with a
hammer. Those most frequently wanted
are indicated by <span class="xxpn" id="p211">{211}</span>
the fewest number of blows; thus a single stroke is to require
more air. The sound is heard very distinctly by those above;
but, it must be confessed, that to persons unaccustomed to it,
the force with which a weighty hammer is driven against so
brittle a material as cast iron is a little alarming.</p>

<p>After ascending a few inches from the bottom, the air in
the bell became slightly obscured. At the distance of a few
feet this appearance increased. Before it had half reached
the surface, it was evident that the whole atmosphere it contained
was filled with a mist or cloud, which at last began to
condense in large drops on the whole of the internal surface.</p>

<p>The explanation of this phenomenon seems to be, that on
the rising of the bell the pressure on the air within being
diminished by a weight equal to several feet of water, it began
to expand; and some portion of it escaping under the edges
of the bell, reduced the temperature of that which remained
so much, that it was unable to retain, in the state of invisible
vapour, the water which it had previously held in solution.
Thus the same principle which constantly produces clouds in
the atmosphere filled the diving-bell with mist.</p>

<div class="dsdnote">〈SUBMARINE NAVIGATION.〉</div>

<p>This first led me to consider the much more extensive
question of submarine navigation. I was aware that Fulton
had already descended in a diving-vessel, and remained under
water during several hours. He also carried down a copper
sphere containing one cubic foot of space into which he had
forced two hundred atmospheres. With these means he
remained under water and moved about at pleasure during
four hours.</p>

<div class="dsdnote">〈OPEN SUBMARINE VESSEL.〉</div>

<p>But a closed vessel is obviously of little use for the most
important purposes to which submarine navigation would be
applied in case of war. In the article Diving Bell, published
in 1826, in the ‘Encyclopedia Metropolitana,’
I gave a <span class="xxpn" id="p212">{212}</span>
description and drawings of an <i>open</i> submarine vessel which
would contain sufficient air for the consumption of four persons
during more than two days. A few years ago, I understand,
experiments were made in the Seine at Paris, on a
similar kind of open diving-vessel. Such a vessel could be
propelled by a screw, and might enter, without being suspected,
any harbour, and place any amount of explosive
matter under the bottoms of ships at anchor.</p>

<p>Such means of attack would render even iron and iron-clad ships
unsafe when blockading a port. For though chains were kept constantly
passing under their keels, it would yet be possible to moor explosive
magazines at some distance below, which would effectually destroy
them.</p></div><!--section-->

<div class="section" id="p213">
<h2 class="h2herein">CHAPTER XVI.
<span class="hsmall">EXPERIENCE BY FIRE.</span></h2>

<div class="dsynopsis">
Baked in an Oven&#x200a;—&#x200a;A Living
Volcano&#x200a;—&#x200a;Vesuvius in action&#x200a;—&#x200a;Carried
up the Cone of Ashes in a Chair&#x200a;—&#x200a;View of the Crater
in a Dark Night&#x200a;—&#x200a;Sunrise&#x200a;—&#x200a;Descent by
Ropes and Rolling into the great Crater&#x200a;—&#x200a;Watched the
small Crater in active eruption at intervals&#x200a;—&#x200a;Measured
a Base of 330 feet&#x200a;—&#x200a;Depth of great Crater 570
feet&#x200a;—&#x200a;Descent into small Crater&#x200a;—&#x200a;A
Lake of red-hot Boiling Lava&#x200a;—&#x200a;Regained the great
Crater with the sacrifice of my Boots&#x200a;—&#x200a;Lunched
on Biscuits and Irish Whisky&#x200a;—&#x200a;Visit to the
Hot Springs of Ischia&#x200a;—&#x200a;Towns destroyed by
Earthquake&#x200a;—&#x200a;Coronets of Smoke projected
by Vesuvius&#x200a;—&#x200a;Artificial Mode of producing
them&#x200a;—&#x200a;Fire-damp visited in Welsh Coal-mine in company
with Professor Moll.</div>

<h3 class="h3herein"><i>Baked in an Oven.</i></h3>

<p class="pfirst"><span class="smcap">C<b>ALLING</b></span> one morning
upon Chantrey, I met Captain Kater and the late Sir Thomas Lawrence,
the President of the Royal Academy. Chantrey was engaged at that period
in casting a large bronze statue. An oven of considerable size had been
built for the purpose of drying the moulds. I made several inquiries
about it, and Chantrey kindly offered to let me pay it a visit, and
thus ascertain by my own feelings the effects of high temperature on
the human body.</p>

<p>I willingly accepted the proposal, and Captain Kater
offered to accom­pany me. Sir Thomas Lawrence, who was
suffering from indis­po­si­tion, did not think it prudent to join
our party. In fact, he died on the second or third day after
our exper­i­ment.</p>

<p>The iron folding-doors of the small room
or oven were <span class="xxpn" id="p214">{214}</span>
opened. Captain Kater and myself entered, and they were
then closed upon us. The further <i>corner</i> of the room, which
was paved with squared stones, was visibly of a dull-red heat.
The thermometer marked, if I recollect rightly, 265°. The
pulse was quickened, and I ought to have counted but did
not count the number of inspirations per minute. Perspiration
commenced immediately and was very copious. We remained,
I believe, about five or six minutes without very great
discomfort, and I experienced no subsequent inconvenience
from the result of the experiment.</p>
</div><!--section-->

<div class="section">
<h3 class="h3herein"><i>A Living Volcano.</i></h3>

<p>I have never been so fortunate as to be <i>conscious</i> of having
experienced the least shock of an earthquake, although,
when a town had been destroyed in Ischia I hastened on from
Rome in the hope of getting a slight shake. My passion
was disappointed, so I consoled myself by a flirtation with a
volcano.</p>

<div class="dsdnote">〈VESUVIUS—CORONETS OF SMOKE.〉</div>

<p>The situation of my apartments during my residence at
Naples enabled me constantly to see the cone of Vesuvius,
and the continual projections of matter from its crater.
Amongst these were oc­ca­sion­al­ly certain globes of air, or of
some gas, which, being shot upwards to a great height above
the cone, spread out into huge coronets of smoke, having a
singular motion amongst their particles.</p>

<p>A similar phenomenon sometimes occurs on a small scale
during the firing of heavy ordnance. I have frequently
seen such at Plymouth and elsewhere; but I was not satisfied
about the cause of this phenomenon. I was told that it occurred
more frequently if the muzzle of the gun were rubbed
with grease; but this did not always succeed.</p>

<div class="dsdnote">〈ARTIFICIAL IMITATION.〉</div>

<p>Soon after my return to London I made a kind
of drum, by <span class="xxpn" id="p215">{215}</span>
stretching wet parchment over a large tin funnel. On directing
the point of the funnel at a candle placed a few feet distant,
and giving a smart blow upon the parchment, it is
observed that the candle is immediately extinguished.</p>

<p>This arises from what is called an air shot. In fact, the
air in the tubular part is projected bodily forward, and so
blows out the candle. The statements about persons being
killed by cannon balls passing close to but not touching
them, if true, are probably the results of air shots.</p>

<p>Wishing to trace the motions of such air shots, I added
two small tubes towards the large end of the tin funnel, in
order that I might fill it with smoke, and thus trace more distinctly
the progress of the ball of air.</p>

<p>To my great delight the first blow produced a beautiful
coronet of smoke, exactly resembling, on a small scale, the
explosions from cannon or the still more attractive ones from
Vesuvius.</p>

<p>If phosphoretted hydrogen or any other gas, which takes
fire in air, were thus projected upwards, a very singular kind
of fire-work would be produced.</p>

<p>It is possible in dark nights or in fogs that by such means
signals might be made to communicate news or to warn
vessels of danger.</p>

<p>Vesuvius was then in a state of moderate activity. It had
a huge cone of ashes on its summit, surrounding an extensive
crater of great depth. In one corner of this was a smaller
crater, quite on a diminutive scale, which from time to time
ejected red-hot fragments of lava oc­ca­sion­al­ly to the height of
from a thousand to fifteen hundred feet above the summit of
the mountain.</p>

<p>I had taken apartments in the Chiaja, just opposite the volcano,
in order that I might watch it with a
telescope. In fact, <span class="xxpn" id="p216">{216}</span>
as I lay in my bed I had an excellent view of the mountain.
My next step was to consult with Salvatori, the most experienced
of the guides, from whom I had purchased a good
many minerals, as to the possibility of getting a peep down
the volcano’s throat.</p>

<div class="dsdnote">〈ASCENT TO CRATER BY NIGHT.〉</div>

<p>Salvatori undertook to report to me from time to time
the state of the mountain, round the base of which I made
frequent excursions. After about a fortnight, the explosions
were more regular and uniform, and Salvatori assured me
that all the usual known indications led him to think that it
was a fit time for my expedition. As I wished to see as
much as possible, I made arrangements to economize my
strength by using horses or mules to carry me wherever they
could go. Where they could not carry me, as for instance,
up the steep slope of the cone of ashes, I employed men to
convey me in a chair.</p>

<p>By these means, I saw in the afternoon and evening of one
day a good deal of the upper part of the mountain, then took
a few hours’ repose in a hut, and reached the summit of the
cone long before sunrise.</p>

<p>It was still almost dark: we stood upon the irregular edge
of a vast gulf spread out below at the depth of about five
hundred feet. The plain at the bottom would have been
invisible but for an irregular network of bright-red cracks
spread over the whole of its surface. Now and then the
silence was broken by a rush upwards of a flight of red-hot
scoria from the diminutive crater within the large one.
These missiles, however, although projected high above the
summit of the cone, never extended themselves much beyond
the small cavity from which they issued.</p>

<p>Those who have seen the blood-vessels of their own eye by
the aid of artificial light, will have seen on a
small scale a <span class="xxpn" id="p217">{217}</span>
perfect resemblance of the plain which at that time formed
the bottom of the great crater of Vesuvius.</p>

<div class="dsdnote">〈SUNRISE FROM THE SUMMIT.〉</div>

<p>As the morning advanced the light increased, and some
time before sunrise we had completed the tour of the top of
the great crater. Then followed that glorious sight—the
sun when seen rising from the top of some lofty mountain.</p>

<p>I now began to speculate upon the means of getting a
nearer view of the little miniature volcano in action at one
corner of the gulf beneath us. We had brought ropes with
us, and I had observed, in our tour round the crater, every
dike of congealed lava by which the massive cone was split.
These presented buttresses with frequent ledges or huge steps
by which I hoped, with the aid of ropes, to descend into the
Tartarus below.</p>

<p>Having consulted with our chief guide Salvatori, I found
that he was unwilling to accompany us, and proposed remaining
with the other guides on the upper edge of the crater.
Upon the whole, I was not discontented with the arrangement,
because it left a responsible person to keep the other guides
in order, and also sufficient force to lift us up bodily by the
ropes if that should become necessary.</p>

<p>The abruptness of the rocky buttresses compelled us to use
ropes, but the attempt to traverse the steep inclines of light
ashes and of fine sand would have been more dangerous from
the risk of being engulfed in them.</p>

<div class="dsdnote">〈DESCENT INTO THE CRATER.〉</div>

<p>Having well examined the several disadvantages of these
rough-hewn irregular Titanic stairs, I selected one which
seemed the most promising for facilitating our descent into
the crater. I was encumbered with one of Troughton’s
heavy barometers, strapped to my back, looking much like
Cupid’s quiver, though probably rather heavier. In my pocket
I had an excellent box sextant, and in a rough
kind of basket <span class="xxpn" id="p218">{218}</span>
two or three thermometers, a measuring tape, and a glass
bottle enclosed in a leather case, commonly called a pocket-pistol,
accompanied by a few biscuits.</p>

<p>We began our descent by the aid of two ropes, each supported
above by two guides. I proceeded, trusting to my
rope to step wherever I could, and then cautiously holding on
by the rope to spring down to the next ledge. In this manner
we descended until we arrived at the last projecting ledge of
the dike. Nothing then remained for us but to slide down a
steep and lengthened incline of fine sand. Fortunately, the
sand itself was not very deep, and was supported by some solid
material beneath it. I soon found that it was impossible to
stand, so I sat down upon this moving mass, which evidently
intended to accompany us in our journey. At first, to my
great dismay, I was relieved from the care of my barometer,
of which the runaway sand immediately took charge. I then
found myself getting deeper and deeper in the sand, and still
accelerating my downward velocity.</p>

<p>Gravity had at last done its work and became powerless. I
soon dug myself out of my sandy couch, and rushed to my
faithful barometer lying at some distance from me with its
head just unburied. Fortunately, it was uninjured. My
companion, with more skill or good fortune, or with less incumbrances,
had safely alighted on the burning plain we now
stood upon.</p>

<p>The area of this plain, for it was perfectly flat, was in
shape somewhat elliptical. The surface consisted of a black
scoriacious rock, reticulated with ditches from one to three
feet wide, intersecting each other in every direction. From
some of these, fumes not of the most agreeable odour were
issuing. All those above two feet deep showed that at that
depth below us everything was of a dull-red
heat. It was <span class="xxpn" id="p219">{219}</span>
these ditches with red-hot bottoms which, in the darkness of
the night, had presented the singular spectacle I described
as having witnessed on the evening before.</p>

<div class="dsdnote">〈MEASUREMENT OF A BASE.〉</div>

<p>At one extremity of this oval plain there was a small cone,
from which the eruptions before described appeared to issue.</p>

<p>My first step, after examining the few instruments I had
brought with me, was to select a spot upon which to measure
a base for ascertaining the depth of the crater from its upper
edge.</p>

<p>Having decided upon my base line, I took with my sextant
the angle of elevation of the rim of the crater above a remarkable
spot on a level with my eye. Then fixing my walking-stick
into a little crack in the scoria, I proceeded to measure
with a tape a base line of 340 feet. Arrived at this point, I
again took the angle of elevation of the same part of the rim
from the same remarkable spot on a level with the eye.
Then, by way of verification, I remeasured my base line and
found it only differed from the former measure by somewhat
less than one foot. But my walking-stick, which had not
penetrated the crack more than a few inches, was actually in
flames.</p>

<p>Having noted down these facts, including the state of the
thermometer and barometer, in my pocket-book, I took first
a survey and then a tour about my fiery domain. I afterwards
found, from the result of this measurement, that our
base line was 570 feet below one of the lowest points of the
edge of the crater. Having collected a few mineral specimens,
I applied myself to observe and register the eruptions
of the little embryo volcano at the further extremity of the
elliptical plain.</p>

<div class="dsdnote">〈DESCENT INTO SMALL ACTIVE CRATER.〉</div>

<p>These periodical eruptions interested me very much. I proceeded
to observe and register them, and
found they occurred <span class="xxpn" id="p220">{220}</span>
at tolerably regular intervals. At first, I performed this
operation at a respectful distance and out of the reach of the
projected red-hot scoria. But as I acquired confidence in
their general regularity, I approached from time to time
more nearly to the little cone of scoria produced by its own
eruptions.</p>

<p>I now perceived an opening in this little cone close to the
perpendicular rock of the interior of the great crater. I was
very anxious to see real fluid lava; so immediately after an
eruption, I rushed to the opening and thus got within the
subsidiary crater. But my curiosity was not gratified, for I
observed, about forty or fifty feet below me, a huge projecting
rock, which being somewhat in advance, effectively prevented
me from seeing the lava lake, if any such existed. I
then retreated to a respectful distance from this infant volcano
to wait for the next explosion.</p>

<p>I continued to note the intervals of time between these
jets of red-hot matter, and found that from ten to fifteen
minutes was the range of the intervals of repose. Having
once more reconnoitred the descent into the little volcano, I
seized the opportunity of the termination of one of the most
considerable of its eruptions to run towards the gap and cautiously
to pick my way down to the rock which hid from me,
as I supposed, the liquid lava. I was armed with two phials,
one of common smelling salts, and the other containing a
solution of ammonia. On reaching the rock, I found it projected
over a lake which was really filled by liquid fiery lava.
I immediately laid myself down, and looking over its edge,
saw, with great delight, lava actually in a state of fusion.</p>

<div class="dsdnote">〈WAVES IN LAKE OF FLUID LAVA.〉</div>

<p>Presently I observed a small bubble swelling up on the
surface of the fluid lava: it became gradually larger and
larger, but did not burst. I had some
vague suspicion that <span class="xxpn" id="p221">{221}</span>
this indicated a coming eruption; but on looking at my watch,
I was assured that only one minute had elapsed since the termination
of the last. I therefore watched its progress; after a
time the bubble slowly subsided without breaking.</p>

<p>I now found the heat of the rock on which I was reposing,
and the radiation from the fluid lava, almost insupportable,
whilst the sulphurous effluvium painfully affected my lungs.
On looking around, I fortunately observed a spot a few feet
above me, from which I could, in a standing position, get a
better view of the lake, and perhaps suffer less inconvenience
from its vapours. Having reached this spot, I continued to
observe the slow formation and absorption of these vesicles of
lava. One of them soon appeared. Another soon followed
at a different part of the fiery lake, but, like its predecessor,
it disappeared as quietly.</p>

<p>Another swelling now arose about half way distant from
the centre of the cauldron, which enlarged much beyond
its predecessors in point of size. It attained a diameter of
about three feet, and then burst, but not with any explosion.
The waves it propagated in the fiery fluid passed on to
the sides, and were thence reflected back just as would have
happened in a lake of water of the same dimensions.</p>

<p>This phenomenon reappeared several times, some of the
bubbles being considerably larger in size, and making proportionally
greater disturbance in the liquid of this miniature
crater. I would gladly have remained a longer time, but the
excessive heat, the noxious vapours, and the warning of my
chronometer forbade it. I climbed back through the gap by
which I had descended, and rushed as fast as I could to a safe
distance from the coming eruption.</p>

<p>I was much exhausted by the heat, although I suffered
still greater inconvenience from the
vapours. From my <span class="xxpn" id="p222">{222}</span>
ob­ser­va­tions of the eruptions before my descent into this little
crater, I had estimated that I might safely allow myself six
minutes, but not more than eight, if I descended into the
crater immediately after an eruption.</p>

<p>If my memory does not fail me, I passed about six minutes
in examining it, and the next explosion occurred ten minutes
after the former one. On my return to Naples I found that
a pair of thick boots I had worn on this expedition were
entirely destroyed by the heat, and fell to pieces in my
attempt to take them off.</p>

<div class="dsdnote">〈BISCUITS AND WHISKY.〉</div>

<p>On my return from the pit of burning fire, I sat down
with my companion to refresh myself with a few biscuits
contained in our basket. Cold water would have been the
most refreshing fluid we could have desired, but we had none,
and my impatient friend cried out, “I wish I had a glass of
whisky!” It immediately occurred to me to feel in my own
basket for a certain glass bottle preserved in a tight leather
case, which fortunately being found, I presented to my
astonished friend, with the remark that it contained half a
pint of the finest Irish whisky. This piece of good luck for
my fellow-traveller arose not from my love but from my
dislike of whisky. Shortly before my Italian tour I had
been travelling in the north of Ireland, and having exhausted
my brandy, was unable to replace it by anything
but whisky, a drink which I can only tolerate under very
exceptional circumstances.</p>
</div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Hot Springs.</i></h3>

<p>During my residence at Naples in 1828, the government
appointed a commission of members of the Royal Academy of
Naples to visit Ischia and make a report upon the hot springs
in that island. Being a foreign member of
the Academy, they <span class="xxpn" id="p223">{223}</span>
did me the honour of placing my name upon that commission.
The weather was very favourable, the party was most agreeable,
and during three or four days I enjoyed the society of
my colleagues, the delightful scenery, and the highly interesting
natural phenomena of that singular island.</p>

<div class="dsdnote">〈HOT SPRINGS OF ISCHIA.〉</div>

<p>None of the hot springs were deep: in several we made
excavations which, in all cases, gave increased heat to the
water. In one or two, I believe if we had excavated to a
small depth or bored a few feet, we might have met with
boiling water.</p>

<p>I took the opportunity of this visit to view the devastations
made by the recent earthquake in the small town which had
been destroyed.</p>

<p>The greater part of the town consisted of narrow streets
formed by small houses built of squared stone. In some of
these streets the houses on one side were thrown down, whilst
those a few feet distant, on the opposite side, although severely
damaged, had their walls left standing.</p>

<p>The landlord of the hotel at which we took up our quarters
assured me the effects of the recent earthquake were entirely
confined to a small portion of the island which he pointed
out from the front of his hotel, and added that it was scarcely
felt in other parts.</p>
</div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Earthquakes.</i></h3>

<p>At the commencement of this chapter I mentioned that I
had never been <i>consciously</i> sensible of the occurrence of an
earthquake. I think it may perhaps be useful to state that
on a recent occasion I really perceived the effects of an
earthquake, although at the time I assigned them to a
different cause.</p>

<div class="dsdnote">〈UNCONSCIOUS WITNESS OF EARTHQUAKE.〉</div>

<p>On the 6th of last October, about
half-past three, a.m., <span class="xxpn" id="p224">{224}</span>
most of the inhabitants of London who were awake at that
hour perceived several shocks of an earthquake. I also was
awake, although not conscious of the shocks of an earthquake.</p>

<p>As soon as I read of the event in the morning papers, I was
forcibly struck by its coincidence with my own ob­ser­va­tions,
although I had attributed to them an entirely different cause.
In order to explain this, it is necessary to premise that I had
on a former occasion instituted some experiments for the
purpose of ascertaining how far off the passing of a cart or
carriage would affect the steadiness of a star observed by
reflection. Amongst other methods, I had fixed a looking-glass
of about 12 by 16 inches, by a pair of hinges, to
the front wall of my bedroom. It was usually so placed that,
as I lay in bed, at the distance of about 10 or 12 feet, I could
see by reflection a small gas-light burner, which was placed
on my left hand.</p>

<p>By this arrangement any tremors propagated through the
earth from passing carriages would be communicated to the
looking-glass by means of the front wall of the house, which
rose about 40 feet from the surface. The image of the small
gas-burner reflected in the looking-glass would be proportionally
disturbed. In this state of things, at about half-past
three o’clock of the morning in question, I observed the
reflected image of the gas-light move downwards and upwards
two or three times. I then listened attentively, expecting to
hear the sound of a distant carriage or cart. Hearing nothing
of the kind, I concluded that the earth wave had travelled
beyond the limit of the sound wave, arising from the carriage
which produced it. Presently the image of the gaslight again
vibrated up and down, and then suddenly fell about four or
five inches lower down in the glass, where it remained fixed
for a time. Still thinking the ob­ser­va­tion
of no consequence, <span class="xxpn" id="p225">{225}</span>
I shut my eyes, and after perhaps another minute, again saw
the image in its lower position. It then rose to its former
position, vibrated, and shortly again descended: it remained
down for some time and then resumed its first position.</p>
</div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Fire Damp.</i></h3>

<p>An opportunity presented itself several years after my
examination of Vesuvius of witnessing another form under
which fire oc­ca­sion­al­ly exerts its formidable power.</p>

<p>I was visiting a friend<a class="afnanc" href="#fn37" id="fnanc37">37</a>
at Merthyr Tydfil, who possessed
very extensive coal-mines. I inquired of my host
whether any fire-damp existed in them. On receiving an
affirmative answer, I expressed a wish to become personally
acquainted with the miner’s invisible but most dangerous
enemy. Arrangements were therefore made for my visit to
the subterranean world on the following day. Professor Moll
of Utrecht, who was also a guest, expressed a wish to accompany
me.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc37" id="fn37">37</a>
The late Sir John J. Guest, Bart.</p></div>

<p>The entrance to the mine is situated in the side of a mountain.
Its chief manager conducted our expedition to visit the
‘fire-king.’</p>

<p>We found a coal-waggon drawn by a horse, and filled
with clean straw, standing on the railway which led into the
workings.</p>

<p>The manager, Professor Moll, and myself, together with
two or three assistants, with candles, lanterns, and Davy-lamps,
got into this vehicle, which immediately entered the
adit of the mine. We advanced at a good pace, passing at
intervals doors which opened on our approach and then instantly
closed. Each door had an attendant boy, whose duty
was confined to the regulation of his own door. <span class="xxpn" id="p226">{226}</span></p>

<p>Many were the doors we passed before we arrived at the
termination of the tram-road. After travelling about a mile
and a half, our carriage stopped and we alighted. We now
proceeded on foot, each carrying his own candle, until we
reached a kind of chamber where one of our attendants was
left with the candles.</p>

<div class="dsdnote">〈DRIVE INTO THE MOUNTAIN.〉</div>

<p>We, each holding a Davy-lamp in our hand, advanced towards
a small opening in the side of this chamber, which was
so low that we were compelled to crawl, one after another, on
our hands and knees. A powerful current of air rushed
through this small passage. On reaching the end of it, we
found ourselves in a much larger chamber from which the
coal had been excavated. At a little distance opposite to the
path by which we entered was a continuation of the same
narrow hole which had led us to the waste in which we now
stood. From this opening issued the powerful stream of air
which seemed to pass in a direct course from one opening to
the other.</p>

<p>On our right hand the large chamber we had entered appeared
to spread to a very considerable distance, its termination
being lost in darkness. The floor was covered with fragments
which had fallen from the roof; so that, besides the risk
from explosion, there was also a minor one arising from the
possible fall of some huge mass of slate from the roof of the
excavation beneath which we stood: an accident which I had
already witnessed in the waste of another coal-mine. As we
advanced over this flaky flooring it was evident that we were
making a considerable ascent. We, in fact, now occupied a
vast cavern, which had been originally formed by the extraction
of the coal, and then partially filled up by the falling in
from time to time of portions of the slaty roof.</p>

<div class="dsdnote">〈TEMPLE OF THE FIRE-KING.〉</div>

<p>As we advanced cautiously with
our Davy-lamps beyond <span class="xxpn" id="p227">{227}</span>
the current of air which had hitherto accompanied us, it was
evident that a change had taken place in their light: for the
flames became much enlarged. Professor Moll and myself
mounted a huge heap of these fragments, and thus came into
contact with air highly charged with carburetted hydrogen.
At this point there was a very sensible difference in the atmosphere,
even by a change of three feet in the elevation of
the lamp.</p>

<p>Holding up the lamp at the level of my head, I could not
see the wick of the lamp, but a general flame seemed to fill
the inside of its wire-covering. On lowering it to the height
of my knee, the wick resumed its large nebulous appearance.</p>

<p>My companion, Professor Moll, was very much delighted
with this experiment. He told me he had often at his
lectures explained these effects to his pupils, but that this
was the first exhibition of them he had ever witnessed in their
natural home.</p>

<p>Although well acquainted with the miniature explosions
of the experimentalist, I found it very difficult to realize in
my own mind the effects which might result from an explosion
under the circumstances in which we were then placed.
I inquired of the manager, who stood by my side, what would
probably be the effect, if an explosion were to take place?
Pointing to the vast heap of shale from which I had just
descended, he said the whole of that would be blown through
the narrow channel by which we entered, and every door we
had passed through would be blown down.</p>

<p>We now retraced our steps, and crawling back through the
narrow passage, rejoined our carriage, and were rapidly conveyed
to the light of day.</p></div><!--section-->

<div class="section" id="p228">
<h2 class="h2herein">CHAPTER XVII.
<span class="hsmall">EXPERIENCE AMONGST WORKMEN.</span></h2>

<div class="dsynopsis">
Visit to Bradford&#x200a;—&#x200a;Clubs&#x200a;—&#x200a;Co-operative
Shops&#x200a;—&#x200a;The Author of the “Economy of
Man­u­fac­tures” welcomed by the Workmen&#x200a;—&#x200a;Visit
to the Temple of Eolus&#x200a;—&#x200a;The Phi­los­o­pher
moralises&#x200a;—&#x200a;Commiserates the unsuccessful
Statesman&#x200a;—&#x200a;Points to the Poet a Theme for his
Verse&#x200a;—&#x200a;Immortalises both.</div>

<p class="pfirst"><span class="smcap">D<b>URING</b></span> one of my
visits to Leeds, combinations and trades-unions were very prevalent.
A medical friend of mine, who was going to Bradford on a pro­fes­sion­al
visit, very kindly offered to take me over in his carriage and bring
me back again in the evening. He had in that town a friend engaged in
the manufactories of the place, to whom he proposed to introduce me,
and who would willingly give me every assistance. Unfortunately, on our
arrival we found that this gentleman was absent on a tour.</p>

<p>My medical friend was much vexed; but I assured him
that I was never at a loss in a manufacturing town, and we
agreed to meet at our hotel for dinner. I then went into
the town to pick up what information I might be able to
meet with.</p>

<div class="dsdnote">〈INTELLIGENT OPERATIVE.〉</div>

<p>Passing a small manufactory, I think it was of door-mats, I
inquired whether a stranger might be permitted to see it. The
answer being in the affirmative, one of the men accompanied
me round the works. Of course I asked him many questions
which he answered as far as he could; but
several of them <span class="xxpn" id="p229">{229}</span>
puzzled him, and he very good-humouredly tried to supply
the information I wanted by asking several of his fellow-workmen.
One question about which I was anxious to be informed,
puzzled them all. At last one of the men to whom
he applied said, “Why don’t you go and ask Sam Brown?”
My guide immediately went in search of his learned friend,
who gave me full information on the subjects of my inquiry.</p>

<p>Much pleased by the intelligence and acuteness of this
man, I thought it possible he might have read the “Economy
of Man­u­fac­tures.” On mentioning that work, I found he was
well acquainted with it, and he asked my opinion of its
merits. I told him that, having myself written the book,
I was not an impartial judge. On hearing that I was
its author, his delight was unbounded; he held out his
brawny hand, which I cordially grasped. The most gratifying
remark to me, however, amongst the many things in it to
which he referred with approbation, was the expression he
applied to it as a whole. “Sir,” said my new friend, “that
book made me think.” To make a man think for himself
is doing him far higher service than giving him much in­struc­tion.</p>

<p>I now told my new friend that I had studied a little the
effects of combinations, and also the results of co-operative
shops, and that I was very anxious to add to my stock of
information upon both subjects, but par­tic­u­lar­ly on the latter.
Knowing that there existed a co-operative shop in Bradford,
I asked whether it would be possible to see it and make some
inquiries as to its state and prospects. He said if he could
get permission for half an hour’s absence he would accompany
me to it, and give me whatever information I wished as to its
operation.</p>

<div class="dsdnote">〈CO-OPERATIVE SHOPS.〉</div>

<p>Mr. Brown accordingly accompanied
me to the <span class="xxpn" id="p230">{230}</span>
co-operative shop, where the information required was most readily
given.</p>

<p>As we were returning, my companion exclaimed, “Oh, how
lucky! there is ——, the secretary of all our clubs. He is
the man to tell you all about them.” We accordingly crossed
over to the other side: the secretary, as soon as he heard
my name, held out his hand and greeted me with a hearty
grasp.</p>

<p>Having told him the objects of my inquiry, he expressed
great anxiety to give me the fullest information. He proposed
to take me with him in the course of the evening to all
the clubs in Bradford, in each of which he promised me that
I should receive a most cordial welcome.</p>

<p>He offered to show me all their rules, with the exception
of certain ones which he assured me had no connection whatever
with the objects of my inquiries, and which the laws of
the respective clubs required to be kept secret. I think it
right to mention this fact; but I am bound also to add that
I have a strong conviction of the truth and sincerity of my
informant. I believe that the one or two rules which I understood
could not be communicated to a stranger, were merely
secret modes of recognition amongst the members of the different
societies by which fellow-members of the same societies
might recognize each other in distant places.</p>

<p>However, my limited time was now drawing to a close. It
was impossible to remain at Bradford that night, and my
previous arrangements called me in two days to a distant part
of the country. I parted with regret from these friendly
workmen, and joining my companion at the hotel, after a
hasty dinner we were soon on our way back to Leeds.</p>

<p>Our conversation turned upon the large ironworks we
should pass on our return, which
indeed were clearly <span class="xxpn" id="p231">{231}</span>
indicated by the columns of fire in front of us—tall chimneys
illumining the darkness of the night.</p>

<p>I was told by my friend that in one of the ironworks which
we should pass, there was a large tunnel through a rock which
had originally been intended for a canal: but that it was now
used as an air-chamber, to equalize the supply of the blast
furnaces. Also that an engine of a hundred horse-power
continually blew air into this stony chamber.</p>

<p>I inquired whether it would be possible to get admission
into this Temple of Æolus. As my friend, fortunately for me,
was acquainted with the proprietors, this was not difficult.
Our carriage drove up to the manager’s house, and my wish
was immediately gratified.</p>

<div class="dsdnote">〈A REVERIE.〉</div>

<p>A lantern was provided, a small iron door at the end of
the cavern was opened, and armed like Diogenes, I entered
upon <i>my</i> search after truth. I soon ascertained that there
was very little current, except close to the tuyeres which supplied
the several furnaces, and also at the aperture through
which tons of air were driven without cessation by the untiring
fiery horse.</p>

<p>I tried to think seriously; and reflecting on Shadrach,
Meshach, and Abed-nego, I speculated whether their furnace
might have been hotter than the one before me. I was within
a foot or two of a white heat, but I had no thermometer with
me, and if I had had one, its graduations might not have
been upon the same scale as theirs—so I gave up the
speculation.</p>

<p>The intensity of that fire was peculiarly impressive. It
recalled the past, disturbed the present, and suggested the
future. The contemplation of the fiery abyss, which had
recalled the history of those ancient Hebrews, naturally
turned my attention to the wonderful
powers of endurance <span class="xxpn" id="p232">{232}</span>
manifested by one of their modern rep­re­sen­ta­tives. Candour
obliges me to admit that my speculations on the future were
not entirely devoid of anxiety, though I trust they were
orthodox, for whilst I admired the humanity of Origen, I was
shocked by the heresy of Maurice.</p>

<p>I now began to moralize.</p>

<div class="dsdnote">〈EFFECT OF A DRAFT ON CONTEMPLATION.〉</div>

<p>Blown upon by a hundred horse-power, I sympathised
with Disraeli refrigerated by his <i>friends</i>. Turning from that
painful contemplation, I was calmed by the freshness of the
breeze. The action of the pumps, the <i>cool</i>ness of the place
and of the time, for it was <i>evening</i>, recalled to my recollection
M....... M.....; so I hoped, for the sake of in­struc­tion,
that he would in his own adamantine verses snatch if
possible from oblivion the moral anatomy of that unsuccessful
statesman. Yet, lest even the poet himself should be forgotten,
I resolved to give each of them his last chance of
celebrity preserved in the modest amber of my own simple
prose.</p>

<p>Emerging from my reverie, I made the preconcerted
signal; the iron door was opened, and we were again on our
road to Leeds.</p></div><!--section-->

<div class="section" id="p233">
<h2 class="h2herein">CHAPTER XVIII.
<span class="hsmall">PICKING LOCKS AND DECIPHERING.</span></h2>

<div class="dsynopsis">
Interview with Vidocq&#x200a;—&#x200a;Remarkable Power of altering his
Height&#x200a;—&#x200a;A Bungler in picking Locks&#x200a;—&#x200a;Mr.
Hobbs’s Lock and the Duke of Wellington&#x200a;—&#x200a;Strong
belief that certain Ciphers are inscrutable&#x200a;—&#x200a;Davies
Gilbert’s Cipher&#x200a;—&#x200a;The Author’s Cipher both
deciphered&#x200a;—&#x200a;Classified Dictionaries of the English
Language&#x200a;—&#x200a;Anagrams&#x200a;—&#x200a;Squaring
Words&#x200a;—&#x200a;Bishop not easily squared&#x200a;—&#x200a;Lesser
Dignitaries easier to work upon.</div>

<p class="pfirst"><span class="smcap">T<b>HESE</b></span> two subjects
are in truth much more nearly allied than might appear upon a
superficial view of them. They are in fact closely connected with each
other as small branches of the same vast subject of <i>combinations</i>.</p>

<p>Several years ago, the celebrated thief-taker, Vidocq, paid
a short visit to London. I had an interview of some duration
with this celebrity, who obligingly conveyed to me much
information, which, though highly interesting, was not of a
nature to become personally useful to me.</p>

<p>He possessed a very remarkable power, which he was so good
as to exhibit to me. It consisted in altering his height to about
an inch and a half less than his ordinary height. He threw
over his shoulders a cloak, in which he walked round the room.
It did not touch the floor in any part, and was, I should say,
about an inch and a half above it. He then altered his
height and took the same walk. The cloak then touched the
floor and lay upon it in some part or other
during the whole <span class="xxpn" id="p234">{234}</span>
walk. He then stood still and altered his height alternately,
several times to about the same amount.</p>

<p>I inquired whether the altered height, if sustained for
several hours, produced fatigue. He replied that it did not,
and that he had often used it during a whole day without any
additional fatigue. He remarked that he had found this gift
very useful as a disguise. I asked whether any medical man
had examined the question; but it did not appear that any
sat­is­fac­tory explanation had been arrived at.</p>

<div class="dsdnote">〈PICKING LOCKS, VIDOCQ, HOBBS.〉</div>

<p>I now entered upon a favourite subject of my own—the art
of picking locks—but, to my great disappointment, I found
him not at all strong upon that question. I had myself
bestowed some attention upon it, and had written a paper,
‘On the Art of Opening all Locks,’ at the conclusion of which
I had proposed a plan of partially defeating my own method.
My paper on that subject is not yet published.</p>

<p>Several years after Vidocq’s appearance in London, the
Exhibition of 1851 occurred. On one of my earliest visits, I
observed a very curious lock of large dimensions with its internal
mechanism fully exposed to view. I found, on inquiry,
that it belonged to the American department. Having discovered
the exhibitor, I asked for an explanation of the lock.
I listened with great interest to a very profound disquisition
upon locks and the means of picking them, conveyed to me
with the most unaffected simplicity.</p>

<p>I felt that the maker of that lock surpassed me in knowledge
of the subject almost as much as I had thought I excelled
Vidocq. Having mentioned it to the late Duke of
Wellington, he proposed that we should pay a visit to the
lock the next time I accompanied him to the Exhibition.
We did so a few days after, when the Duke was equally
pleased with the lock and its inventor.
Mr. Hobbs, the <span class="xxpn" id="p235">{235}</span>
gentleman of whom I am speaking, and whose locks have now
become so celebrated, was good enough to explain to me from
time to time many difficult questions in the science of constructing
and of picking locks. He informed me that he
had devised a system for defeating all these methods of picking
locks, for which he proposed taking out a patent. I was,
however, much gratified when I found that it was precisely
the plan I had previously described in my own unpublished
pamphlet.</p>
</div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Deciphering.</i></h3>

<p>Deciphering is, in my opinion, one of the most fascinating
of arts, and I fear I have wasted upon it more time than it
deserves. I practised it in its simplest form when I was at
school. The bigger boys made ciphers, but if I got hold of
a few words, I usually found out the key. The consequence
of this ingenuity was oc­ca­sion­al­ly painful: the owners of the
detected ciphers sometimes thrashed me, though the fault
really lay in their own stupidity.</p>

<p>There is a kind of maxim amongst the craft of decipherers
(similar to one amongst the locksmiths), that every cipher can
be deciphered.</p>

<div class="dsdnote">〈BELIEF IN AN INSCRUTABLE CIPHER.〉</div>

<p>I am myself inclined to think that deciphering is an affair
of time, ingenuity, and patience; and that very few ciphers
are worth the trouble of unravelling them.</p>

<p>One of the most singular char­ac­ter­is­tics of the art of deciphering
is the strong conviction possessed by every person,
even moderately acquainted with it, that he is able to construct
a cipher which nobody else can decipher. I have also
observed that the cleverer the person, the more intimate is
his conviction. In my earliest study of the subject I shared
in this belief, and maintained it
for many years. <span class="xxpn" id="p236">{236}</span></p>

<div class="dsdnote">〈THE PRESIDENT OF ROYAL SOCIETY’S CIPHER
DECIPHERED.〉</div>

<p>In a conversation on that subject which I had with the late
Mr. Davies Gilbert, President of the Royal Society, each
maintained that he possessed a cipher which was absolutely
inscrutable. On comparison, it appeared that we had both
imagined the same law, and we were thus confirmed in our
conviction of the security of our cipher.</p>

<p>Many years after, the late Dr. Fitton, having asked my
opinion of the possibility of making an inscrutable cipher, I
mentioned the conversation I had had with Davies Gilbert,
and explained the law of the cipher, which we both thought
would baffle the greatest adept in that science. Dr. Fitton
fully agreed in my view of the subject; but even whilst I
was explaining the law, an indistinct glimpse of defeating it
presented itself vaguely to my imagination. Having mentioned
my newly-conceived doubt, it was entirely rejected by
my friend. I then proposed that Dr. Fitton should write a
few sentences in a cipher constructed according to this law,
and that I should make some attempts to unravel it. I
offered to give a few hours to the subject; and if I could
see my way to a solution, to continue my researches; but if
not on the road to success, to tell him I had given up the
task.</p>

<p>Late in the evening of that day I commenced a preparatory
inquiry into the means of unravelling this new cipher, and I
soon arrived at a tolerable certainty that I should succeed.
The next night, on my return from a party, I found Dr.
Fitton’s cipher on my table. I immediately commenced my
attempt. After some time I found that it would not yield to
my means of treating it; and on further examination I succeeded
in proving that it was not written according to the
law agreed upon. At first my friend was very positive that
I was mistaken; and having taken it to his
sister, by whose <span class="xxpn" id="p237">{237}</span>
aid it was composed, he returned and told me that it <i>was</i>
constructed upon the very law I had proposed. I then
assured him that they <i>must</i> have made some mistake, and
that my evidence was so irresistible, that if my life depended
upon the result I should have no hesitation in making my
election.</p>

<p>Dr. Fitton again retired to consult his sister; and after the
lapse of a considerable interval of time again returned, and
informed me that I was right—that his sister had inadvertently
mistaken the enunciation of the law. I now remarked
that I possessed an absolute demonstration of the fact I had
communicated to him; and added that, having conjectured
the origin of the mistake, I would decipher the cipher with
the erroneous law before he could send me the new cipher to
be made according to the law originally proposed. Before
the evening of the next day both ciphers had been translated.</p>

<p>This cipher was arranged upon the following principle:—Two
concentric circles of cardboard were formed, each divided
into twenty-six or more divisions.</p>

<p>On the outer were written in regular order the letters of
the alphabet. On the inner circle were written the same
twenty-six letters, but in any irregular manner.</p>

<p>In order to use this cipher, look for the first letter of the
word to be ciphered on the outside circle. Opposite to it, on
the inner circle, will be another letter, which is to be written
as the cipher for the former.</p>

<p>Now turn round the inner circle until the cipher just
written is opposite the letter <i>a</i> on the <i>outer</i> circle. Proceed
in the same manner for the next, and so on for all succeeding
letters.</p>

<p>Many varieties of this cipher may be
made by inserting <span class="xxpn" id="p238">{238}</span>
other characters to represent the divisions between words,
the various stops, or even blanks. Although Davies Gilbert,
I believe, and myself, both arrived at it from our own efforts,
I have reason to think that it is of very much older date. I
am not sure that it may not be found in the “Steganographia”
of Schott, or even of Trithemius.</p>

<div class="dsdnote">〈NEW DICTIONARY OF ENGLISH LANGUAGE.〉</div>

<p>One great aid in deciphering is, a complete analysis of the
language in which the cipher is written. For this purpose
I took a good English dictionary, and had it copied out into
a series of twenty-four other dictionaries. They comprised
all words of</p>

<div class="nowrap">
<p class="pcontinue">One letter,</p>
<p class="pcontinue">Two letters,</p>
<p class="pcontinue">Three letters,</p>
<div>&amp;c. &amp;c.:</div>
<p class="pcontinue">Twenty-six letters.</p>
</div><!--nowrap-->

<p>Each dictionary was then carefully examined, and all the
modifications of each word, as, for instance, the plurals of
substantives, the comparatives and superlatives of adjectives,
the tenses and participles of verbs, &amp;c., were carefully indicated.
A second edition of these twenty-six dictionaries was
then made, including these new derivatives.</p>

<p>Each of these dictionaries was then examined, and every
word which contained any two or more letters of the same kind
was carefully marked. Thus, against the word <i>tell</i> the numbers
3 and 4 were placed to indicate that the third and fourth
letters are identical. Similarly, the word <i>better</i> was followed
by the numbers 25, 34. Each of these dictionaries was then
re-arranged thus:—In the first or original one each word was
arranged according to the alphabetical order of its <i>initial</i>
letter.</p>

<p>In the next the words
were arranged alphabetically <span class="xxpn" id="p239">{239}</span>
according to the <i>second</i> letter of each word, and so in the other
dictionaries on to the last letter.</p>

<p>Again, each dictionary was divided into several others,
according to the numerical char­ac­ter­is­tics placed at the end
of each word. Many words appeared repeatedly in several of
these subdivisions.</p>

<p>The work is yet unfinished, although the classification
already amounts, I believe, to nearly half a million words.</p>

<div class="dsdnote">〈QUEER COINCIDENCES.〉</div>

<p>From some of these, dictionaries were made of those words
only which by transposition of their letters formed anagrams.
A few of these are <span class="nowrap">curious:—</span></p>

<div class="dtablebox">
<table class="tafmono" summary="">
<tr>
 <th scope="col">Opposite.</th>
 <th scope="col">Similarity.</th>
 <th scope="col">Satirical.</th></tr>
<tr>
 <td class="tdcntr">vote veto</td>
 <td class="tdcntr">fuel flue</td>
 <td class="tdcntr">odes dose</td></tr>
<tr>
 <td class="tdcntr">acre care</td>
 <td class="tdcntr">taps pats</td>
 <td class="tdcntr">bard drab</td></tr>
<tr>
 <td class="tdcntr">evil veil</td>
 <td class="tdcntr">tubs buts</td>
 <td class="tdcntr">poem mope</td></tr>
<tr>
 <td class="tdcntr">ever veer</td>
 <td class="tdcntr">vast vats</td>
 <td class="tdcntr">poet tope</td></tr>
<tr>
 <td class="tdcntr">lips slip</td>
 <td class="tdcntr">note tone</td>
 <td class="tdcntr">trio riot</td></tr>
<tr>
 <td class="tdcntr">cask sack</td>
 <td class="tdcntr">cold clod</td>
 <td class="tdcntr">star rats</td></tr>
<tr>
 <td class="tdcntr">fowl wolf</td>
 <td class="tdcntr">evil vile</td>
 <td class="tdcntr">wive view</td></tr>
<tr>
 <td class="tdcntr">gods dogs</td>
 <td class="tdcntr">arms mars</td>
 <td class="tdcntr">nabs bans</td></tr>
<tr>
 <td class="tdcntr">tory tyro</td>
 <td class="tdcntr">rove over</td>
 <td class="tdcntr">tame mate</td></tr>
<tr>
 <td class="tdcntr">tars rats</td>
 <td class="tdcntr">lips lisp</td>
 <td class="tdcntr">acts cats</td></tr>
</table></div>

<p>There are some verbal puzzles costing much time to solve
which may be readily detected by these dictionaries. Such,
for instance, is the sentence,</p>

<div>I tore ten Persian MSS.,</div>

<p class="pcontinue">which it is required to form into one word of
eighteen letters.</p>

<p>The first process is to put opposite each letter the number of
times it occurs, <span class="nowrap">thus:—</span> <span class="xxpn"
id="p240">{240}</span></p>

<div class="dtablebox">
<table summary="">
<tr>
 <th scope="row">i</th>
 <td class="tdleft">&#x2007;2</td></tr>
<tr>
 <th scope="row">t</th>
 <td class="tdleft">&#x2007;2</td></tr>
<tr>
 <th scope="row">o</th>
 <td class="tdleft">&#x2007;1</td></tr>
<tr>
 <th scope="row">r</th>
 <td class="tdleft">&#x2007;2</td></tr>
<tr>
 <th scope="row">e</th>
 <td class="tdleft">&#x2007;3</td></tr>
<tr>
 <th scope="row">n</th>
 <td class="tdleft">&#x2007;2</td></tr>
<tr>
 <th scope="row">p</th>
 <td class="tdleft">&#x2007;1</td></tr>
<tr>
 <th scope="row">s</th>
 <td class="tdleft">&#x2007;3</td></tr>
<tr>
 <th scope="row">a</th>
 <td class="tdleft">&#x2007;1</td></tr>
<tr>
 <th scope="row">m</th>
 <td class="tdleft">&#x2007;1</td></tr>
<tr>
 <th scope="row" title="sum"></th>
 <td class="tdleft"><span class="bor10">18</span></td></tr>
</table></div>

<p class="pcontinue">It contains—</p>
<ul>
<li>&#x2007;2 triplets.</li>
<li>&#x2007;4 pairs.</li>
<li>&#x2007;4 single letters.</li>
<li><span class="bor10">18</span></li></ul>

<p class="pcontinue">Now, on examining the dictionary of all
words of eighteen letters, it will be observed that they amount
to twenty-seven, and that they may be arranged in six <span
class="nowrap">classes:—</span></p>

<ul>
<li>&#x2007;7 having five letters of the same kind.</li>
<li>&#x2007;5 having four letters of the same kind.</li>
<li>&#x2007;3 having three triplets.</li>
<li>&#x2007;7 having two triplets.</li>
<li>&#x2007;3 having one triplet.</li>
<li>&#x2007;2 having seven pairs.</li>
<li><span class="bor10">27</span></li></ul>

<div class="dsdnote">〈ANAGRAMS.〉</div>

<p class="pcontinue">Hence it appears that the word sought must
be one of those seven having two triplets, and also that it must
have four pairs; this reduces the question to the two <span
class="nowrap">words—</span></p>

<div class="nowrap">
<p class="pcontinue">misinterpretations,</p>
<p class="pcontinue">misrep­re­sen­ta­tions.</p></div>

<p class="pcontinue">The latter is the one sought, because its triplets
are e and s, whilst those of the former are i and t.</p>

<p>The reader who has leisure may try to find out the
word of eighteen letters formed by the following <span
class="nowrap">sentence:—</span></p>

<div>Art is not in, but Satan.</div>

<div class="dsdnote">〈SQUARING A DEAN.〉</div>

<p>Another amusing puzzle may be greatly assisted by these <span
class="xxpn" id="p241">{241}</span> dic­tion­aries. It is called
squar­ing words, and is thus prac­tised:—Let the given word to be squared
be Dean. It is to be writ­ten hor­i­zon­tally, and also ver­ti­cally, <span
class="nowrap">thus:—</span></p>

<div class="nowrap tafmono">
<p class="pcontinue">D&#x202f;e&#x202f;a&#x202f;n.</p>
<p class="pcontinue">e&#x202f;.&#x202f;.&#x202f;.</p>
<p class="pcontinue">a&#x202f;.&#x202f;.&#x202f;.</p>
<p class="pcontinue">n&#x202f;.&#x202f;.&#x202f;.</p></div>

<p class="pcontinue">And it is required to fill up the blanks with
such letters that each vertical column shall be the same as its
corresponding horizontal column, <span class="nowrap">thus:—</span></p>

<div class="nowrap tafmono">
<p class="pcontinue">D&#x202f;e&#x202f;a&#x202f;n</p>
<p class="pcontinue">e&#x202f;a&#x202f;s&#x202f;e</p>
<p class="pcontinue">a&#x202f;s&#x202f;k&#x202f;s</p>
<p class="pcontinue">n&#x202f;e&#x202f;s&#x202f;t</p>
</div>

<p>The various ranks of the church are easily squared; but it
is stated, I know not on what authority, that no one has yet
succeeded in squaring the word bishop.</p>

<p>Having obtained one squared word, as in the case of Dean,
it will be observed that any of the letters in the two diagonals,
d, a, k, t,—n, s, s, n, may be changed into any other letter
which will make an English word.</p>

<p>Thus Dean may be changed into such words as</p>

<div class="tafmono">
dear&nbsp;&nbsp;peas&nbsp;&nbsp;weak&nbsp;&nbsp;beam<br />
fear&nbsp;&nbsp;seas&nbsp;&nbsp;lead&nbsp;&nbsp;seal<br />
deaf&nbsp;&nbsp;bear&nbsp;&nbsp;real&nbsp;&nbsp;team</div>

<p class="pcontinue">In fact there are upwards of sixty substitutes:
possibly some of these might render the two diagonals, d, a, k, t, and
n, s, s, n, also English words.</p></div><!--section-->

<div class="section" id="p242">

<h2 class="h2herein">CHAPTER XIX.
<span class="hsmall">EXPERIENCE IN ST. GILES’S.</span></h2>

<div class="dsynopsis">
Deep-snow&#x200a;—&#x200a;Beggar in Belgravia wanted
work&#x200a;—&#x200a;He said he was a Watchmaker&#x200a;—&#x200a;Gave
his address&#x200a;—&#x200a;It was false&#x200a;—&#x200a;Met him
months after&#x200a;—&#x200a;The same story&#x200a;—&#x200a;The
same untruth&#x200a;—&#x200a;Children hired for the
purpose of Begging&#x200a;—&#x200a;Cellar in St.
Giles’s&#x200a;—&#x200a;Inquired for a Poor Woman and
Child&#x200a;—&#x200a;Landlady told me of a Man almost starving in
her back kitchen&#x200a;—&#x200a;He turned out to be an accomplished
Swindler&#x200a;—&#x200a;Pot-boys&#x200a;—&#x200a;Caught him at
last&#x200a;—&#x200a;Took him to Bow Street.</div>

<p class="pfirst"><span class="smcap">S<b>OON</b></span> after
taking up my residence in London, I met with many applications from
street-beggars, with various tales of distress. I could not imagine
that all these were fictitious, and found great difficulty in selecting
the few objects on whom I could bestow my very moderate means of
charity. One severe winter I resolved on making my own personal
ob­ser­va­tions on the most promising cases which presented themselves.</p>

<p>The first general principle at which I arrived was, <span class="nowrap">that—</span></p>

<p>In whatever part of London I might be, if I asked for the
residence of a mendicant, it was pretty sure to be in a
quarter very remote from the one in which he asked relief.</p>

<p>The next was, <span class="nowrap">that—</span></p>

<p>Those mendicants who professed to want work and not
charity, always belonged to trades in which it was scarcely
possible to give them employment without trusting them with
valuable property. <span class="xxpn" id="p243">{243}</span></p>

<p>One example will suffice. During a very severe winter,
the ground being covered with snow, whilst passing through
Belgrave Square, a man accosted me, declaring that he could
get no work, and that himself and family were starving.</p>

<div class="dsdnote">〈BEGGAR, A WATCHMAKER.〉</div>

<p>I inquired his trade: he was a watchmaker. I asked for
his address. I wrote down in my pocket-book his name, the
street, and the number, and read it to him: it was in Clerkenwell.
The next day I went there, made particular inquiries
of the landlord, and was informed that no person of that
name lodged in the house, or ever had lodged in it. I spoke
to several respectable female lodgers also, who gave me the
same information, as far as their knowledge went.</p>

<p>Several months after, I met the same pro­fes­sion­al mendicant
in Portland Road. He did not recollect me, and again
told the same story, and again gave me the same address.
On this, I recalled to his memory that I had seen him before:
that he had given me the same address; and that, having
myself been there to inquire, I had found that his story was
untrue. This statement had allowed him time to invent a
new tale.</p>

<p>With well-feigned surprise he suddenly remembered that
his wife, about three months ago, had told him that a strange
gentleman had called, and had par­tic­u­lar­ly inquired for him;
that his wife, knowing that a writ was out against him, and
that he was liable to be arrested, had denied that any person
of his name resided in the house.</p>

<p>A few days after I went again to Clerkenwell, and received
from the residents the answer they had given me three
months before. I then went to one of the large shops for
tools used by watchmakers near that locality, and having
mentioned the subject to the master, he very readily asked
amongst his shopmen whether they knew of
such a person. <span class="xxpn" id="p244">{244}</span></p>

<p>He assured me that, even allowing the man had not usually
dealt at his shop, it was impossible that he should not have
been several times there for some trifling article necessary in
the hurry of his business. I then went to two or three other
shops of a similar kind, and found that his name was entirely
unknown. I therefore concluded that he was an impostor.</p>

<p>I will mention one other case, because it arose entirely out
of an accident, and could not have been foreseen.</p>

<p>Living at that time much in society, I usually walked
home from the hot rooms of an evening party wrapped in a
stout cloak, even though it sometimes rained. On these
occasions I was often placed in a most painful situation.</p>

<div class="dsdnote">〈BEGGARS WITH CHILDREN.〉</div>

<p>A half-clad miserable female, with an infant in her arms,
and sometimes accompanied by another just able to walk,
followed me through a drizzling rain to ask charity for her
starving children.</p>

<p>I confess it was to me a most painful effort to resist such
an application; yet my better reason informed me that in all
probability these miserable children were hired for the purpose
of exciting the feelings of the charitable. To give
money to their heartless conductors could only be considered
charitable, inasmuch as it might contribute to shorten the
lives of their wretched victims.</p>

<p>I fear I gave wrongfully many a sixpence. I inquired into
some cases, but without any result which could enable me to
alter the opinion I have expressed. It was in one of these
inquiries that the singular case I am now about to relate
occurred.</p>

<p>In one of the densest of London fogs on a November night,
or rather at between one and two o’clock in the morning, I
was inquiring, in one of the most disreputable streets in
London—George Street, St. Giles’s, long
ago pulled down, <span class="xxpn" id="p245">{245}</span>
enlarged, and rebuilt—for a female with an infant, who had
represented herself to me as a miserable mother, and into
the truth of whose story I was anxious to inquire.</p>

<p>I had been into several of the lowest lodging-houses, and
into the cellars of that nest of misery and guilt, and was unsuccessful
in finding the object I sought.</p>

<div class="dsdnote">〈THE LANDLADY IN GEORGE STREET, ST. GILES’S.〉</div>

<p>Only a few of these abodes of wretchedness remained unvisited,
when I inquired after the poor woman I was seeking
of a somewhat decently clothed woman, who rented one of
them.</p>

<p>She was the weekly tenant of one of these houses, and told
me that on the preceding night a poor woman, with a child
wrapped up in a miserably torn shawl, had applied for a
lodging at about eleven o’clock. It was raining hard, and the
poor woman possessed only twopence, and the price of a bed
in the cellar was at this house threepence. The poor woman
went away, remarking that she must then go and pawn the
remnant of the shawl that covered her infant. She went, but
returned no more.</p>

<p>The ancient weekly tenant then thought it necessary to
defend, or rather to explain, her own apparently cruel conduct.
I told her that it was unnecessary, and that even in
my inmost thoughts I had not cast a reproach upon her. I
told her that, from my knowledge of the misery suffered by
poor people, I could readily imagine circumstances which
might fully explain her conduct.</p>

<p>Her heart, however, was too full, so I sat down and listened
to her tale. She was a widow advanced in years, having no
relatives, or even friends, to assist her in her old age. She
was the weekly tenant of a small house in that villanous
street, and was entirely supported by letting out every foot of
floor which could be made available for a
human being to <span class="xxpn" id="p246">{246}</span>
sleep upon. But the stern necessity which hung over her
with its iron hand was <span class="nowrap">this:—</span></p>

<p>Her weekly rent became due on each Monday, and if not
paid on that night, the next morning would see her inexorably
turned out of her only home, and deprived of her only means
of sustaining life.</p>

<div class="dsdnote">〈A STARVING MAN IN HER KITCHEN.〉</div>

<p>She was pleased at my attention to her sad tale, and, with
a little encouragement, mentioned some of the experience she
had had in her painful vocation.</p>

<p>“At this moment,” she said, “there is lying on a rug in the
back kitchen a young man, who has tasted nothing during the
last two days but water from the pump on the opposite side
of the street. He appears,” she said, “to have been in better
circumstances in other times.”</p>

<p>It was now two o’clock in the morning, in the midst of a
dense fog. I inquired whether it would be possible at this
hour to get some soup or meat, or anything to sustain life. I
went down into the close unventilated room, and beheld,
stretched on a kind of thing like a couple of sacks, a pale,
emaciated man, apparently about two or three and thirty
years of age. I desired him to call on me the next morning;
and, leaving my address with his landlady, left also a
small sum of money to procure for him, if possible, present
necessaries.</p>

<p>The next morning this half-starved man called at my
house, in garments scarcely covering him. I inquired into
his history, and he told me one probably as fabulous as that
with which he afterwards deluded me, during my own short
acquaintance with him.</p>

<p>I supplied him with a few clothes, shoes, and other things,
just to replace the worn-out rags in which I had found him,
and desired him in a day or two, when he got
them into a <span class="xxpn" id="p247">{247}</span>
serviceable form, to come to me, that I might see what his
capacity was, and by what means he could best earn a subsistence.</p>

<div class="dsdnote">〈AN ACCOMPLISHED ROGUE.〉</div>

<p>It is unnecessary to enter into the long and artful stories
he invented. The short result was this: that he had been a
steward of a merchant ship—had been in the West Indies,
and on other voyages; that having, on his return from some
voyage, been reduced by illness to spend all his little earnings,
and even to sell his clothes, and having no friends in
London, he could not go amongst the merchant captains for
want of decent clothes to appear in. This difficulty was
partially removed by my giving him a suit. He called one
day to tell me that he had succeeded in getting the situation
of steward in a small West Indiaman, and that he did not like
to sell or exchange a pair of top-boots which I had given him
without asking my permission, which, of course, I gave. He
told me that if he sold the boots, and purchased light, gaudy-coloured
waistcoating, he might do a little profitable business
with the niggers. He showed me the card of the shop in
Monmouth Street at which he had commenced a negotiation
about the sale of the boots, and another, in the same street,
at which he proposed to purchase the waistcoats. He gave
me the name of his ship, and of its captain, and the day of
sailing. I flattered myself that he was now in a fair position
to get a fresh start in life.</p>

<p>A few evenings after the ship was supposed to have sailed
he called at my house, in the midst of heavy rain, apparently
much agitated, and stated that, in raising their anchor, an
accident had happened, by which the captain’s leg had been
broken.</p>

<p>He also said that, being sent up with the ship’s boat to
fetch the new captain, he could not resist calling
at my house <span class="xxpn" id="p248">{248}</span>
once more to express all his gratitude. I confess I entertained
some suspicion about this story; but I said nothing.</p>

<p>The next morning I found that during his visit he had
extracted something more from my female servants, upon
whose sympathy he had worked, and who had previously
contributed very liberally to his wants.</p>

<div class="dsdnote">〈CONSULTATION AT BOW STREET.〉</div>

<p>I now went to search for him in his old haunts, and with
much difficulty ascertained that he had been living riotously
at some public-house in another quarter, and had been continually
drunk.</p>

<p>My next step was to go to Bow Street and consult Sir
Richard Birnie. Having explained the case, he consulted
several of his most skilful officers; but none were acquainted
with the man. Sir Richard remarked that he was a very
adroit fellow, and that it was doubtful whether he had actually
committed an act of swindling. I inquired what I should do
in case I found him. The magistrate replied, “Bring him
before me;” but he did not indicate the slightest expectation
of my accomplishing that object.</p>

<p>Having thanked Sir Richard, I withdrew, determined, if
the fellow were in London, I would catch him.</p>

<p>I now renewed my inquiries, which at first were ineffectual.
One day it occurred to me that, as he had shown me
two cards of shopkeepers in Monmouth Street, I might possibly,
by cautious inquiry, get some clue to his whereabouts.</p>

<p>Although it was Sunday when this idea occurred, I immediately
commenced at one end of the street to knock at each
door, apologize to the landlord or landlady, and, shortly
stating my case, to inquire if they could throw any light
upon the subject. I went up one side of the street, and
down part of the other, having at two places gained some
traces of the fellow. <span class="xxpn" id="p249">{249}</span></p>

<div class="dsdnote">〈MORNING VISIT TO ST. GILES’S.〉</div>

<p>I will say, to the credit of the then residents, some of
whom I intruded upon at their dinner hour, that I received
in no one instance the slightest incivility, nor even coldness.</p>

<p>The most important information I obtained was, that a
certain pot-boy (name and name of his public-house both
unknown) would probably be able to give me some clue.</p>

<p>I next took my station at the northern end of Monmouth
Street, and during three hours accosted every pot-boy who
passed. At last I got hold of the right one, and so ultimately
obtained the information I wanted.</p>

<p>The fellow was then arrested, and brought before Sir R.
Birnie. The magistrate was much surprised that so clever a
fellow should not have been known to any of his officers.
After a long examination, I stated to the magistrate, that
though I was very reluctant to appear before the public in
such a case, yet that if he thought it a public duty, I should
not shrink from it. Sir Richard remarked, that the inconvenience
of my attending two or three days to prosecute would
be very great—that the fellow was so accomplished an artist,
that it was very doubtful if he could be convicted. He then
added, that the best thing to be done for the man himself
would be, if I could produce any new evidence, that he
should be remanded for a week, to hear it, and then be discharged
with a caution from the bench.</p>

<p>As my servants could give additional evidence, the fellow
was remanded for a week, then duly lectured and discharged.</p>

<p>In the course of my efforts to inform myself of the real
wants of those around me, I profited much by the experience
of one or two friends, both most excellent and kind-hearted
men, whose official duties rendered them far more conversant
than myself with the subject. Mr. Walker and Mr. Broderip,
both of them magistrates, were amongst
my intimate friends. <span class="xxpn" id="p250">{250}</span>
Mr. Walker, the author of “The Original,” maintained that
no one ever was actually starved in London, except through
his own folly or fault.</p>

<div class="dsdnote">〈VALUABLE MAGISTRATES.〉</div>

<p>The result of my own experience leads me to recommend
all those who do not possess time and the requisite energies
for personal inquiries, to place the means they wish to devote
to charity in the hands of some sensible and kind-hearted
magistrate.</p>

<p>I have been present, in the course of my life, at many cases
brought before our London police magistrates. They possess
an immense power of doing good—a power of making the law
respected, not by its punishments, but by their own kindliness
of manner and thoughtful consideration for the feelings
of those brought into close contact with them.</p>

<p>Plain common sense, a kind heart, and, above all, the feelings of
a thorough gentleman, are invaluable qualities in a magistrate. They
give dignity to the court over which he presides, as well as an example
which will be insensibly followed by all its officers. I have seen
cases from which my own avocations have imperatively called me away,
when I would gladly have remained to admire the kindness and the tact
with which entangled questions have been gradually brought to a humane
and just conclusion.</p></div><!--section-->

<div class="section" id="p251">
<h2 class="h2herein">CHAPTER XX.
<span class="hsmall">THEATRICAL EXPERIENCE.</span></h2>

<div class="dsynopsis">
The Phi­los­o­pher in a Tableau at the Feet of
Beauty&#x200a;—&#x200a;Tableau encored&#x200a;—&#x200a;Phi­los­o­pher at
the Opera of ‘Don Juan’&#x200a;—&#x200a;Visits the Water-works above
and the dark expanse below the Stage&#x200a;—&#x200a;Seized by two
Devils on their way up to fetch Juan&#x200a;—&#x200a;Cheated the Devils
by springing off to a beam at an infinite distance, just as his head
appeared to the Audience through the trap-door&#x200a;—&#x200a;The
Phi­los­o­pher writes a Ballet&#x200a;—&#x200a;Its
rehearsal&#x200a;—&#x200a;Its high moral tone&#x200a;—&#x200a;Its
rejection on the ground of the probable combustion of the
Opera-house.</div>

<p class="pfirst">I <span class="smmaj">WAS</span> never par­tic­u­lar­ly
devoted to theatrical rep­re­sen­ta­tions. Tragedy I disliked, and comedy,
which I enjoyed, frequently excited my feelings more than the dignity
of the philosophic character sanctioned. In fact, I could not stand the
reconciliation scenes.</p>

<p>I did, however, oc­ca­sion­al­ly, in one or two rare instances,
<i>assist</i> in a tableau. I still remember my delight when personating
a dead body, with my head towards the audience, I
lay motionless at the feet of three angels, entranced by their
beauty, and whose charms still fascinate my imagination, and
still retain their wonted power over my own sex.</p>

<p>We enacted the scene so admirably that our performance
was twice encored. But though thus “thrice slain,” the near
proximity of beauty speedily revived the ‘caput mortuum’
at its feet.</p>

<p>On one occasion having joined a party of friends in their
box at the opera of ‘Don Juan,’ I escaped, by
half a second, <span class="xxpn" id="p252">{252}</span>
a marvellous adventure. Somewhat fatigued with the opera,
I went behind the scenes to look at the mechanism. One of
the scene-shifters of whom I had made an inquiry, found out
that I, like himself, was a workman. He immediately offered
to take me all over the theatre, and show me every part.</p>

<div class="dsdnote">〈ADVENTURE AT THE OPERA.〉</div>

<p>We ascended to the roof to examine the ventilation, by
which, if stopped, the spectators, in case of accident or of a row,
might be suffocated. Also, the vast water-tanks by which,
in case of fire, they might be drowned. After long rambling
and descending endless steps, I found myself in a vast dark
and apparently boundless area; the flat wooden roof high
above my head was supported by upright timbers, some having
intermediate stages like large dissecting-tables. Here and
there three lamps, rivalling rushlights, made the obscurity
more visible, and the carpentry more in­com­pre­hen­sible.</p>

<p>Suddenly a little bell rang—the signal for my scene-shifting
friend to take his post. He pointed to one of the dismal
imitations of a rushlight, and said: “You see that light; on
its left is a door, go through that, and straight on until you
arrive at daylight.” Instantly my friend became invisible in
the surrounding gloom.</p>

<p>My first step when thus suddenly abandoned, was to mount
on a large oblong platform about six feet above the floor.
Here I was philosophically contemplating the surrounding
obscure vacuity, in order that I might fully “comprehend the
situation.”</p>

<p>Suddenly a flash of lightning occurred. On looking up,
high above my head I saw an opening as large as the platform
on which I stood. All there was brightness. Whilst I was
admiring this new light, and seeking my way to the upper and
outer world, two devils with long forked tails jumped upon the
platform, one
at each end. <span class="xxpn" id="p253">{253}</span></p>

<div class="dsdnote">〈ESCAPE FROM THE DEVILS.〉</div>

<p>“What do you do here?” said Devil No. 1.</p>

<p>Before I could invent a decent excuse, Devil No. 2 exclaimed:</p>

<p>“You must not come with us.”</p>

<p>This was consolatory and reassuring, so I <span class="nowrap">replied—</span></p>

<p>“Heaven forbid.”</p>

<p>During this colloquy, the table, the phi­los­o­pher, and the
devils, were all slowly moving upward to the open trap-door
of the stage above. Seeing a beam some feet higher at a
moderate distance, I inquired whether it was fixed and would
bear my weight? “Yes,” said Devil No. 1.</p>

<p>“But you cannot reach it at a jump,” added Devil No. 2.</p>

<p>“Trust that to me,” said I, “to get out of your clutches.”</p>

<p>We had now reached the level of the desired beam, though
not near enough for a jump. However, still ascending, we
passed it: then stooping my head and bending my body to
avoid the floor of the stage, which we were fast approaching,
I sprang down on the beam of refuge. My two missionary
companions continued their course to the world above in
order to convey the wicked Juan to the realms below. My
transit through the dark, subterranean abyss to my own
world above was rapid. I soon rejoined my companions, who
congratulated me on what they represented as my ‘undeserved
escape:’ kindly hoping that I might be equally fortunate
upon some future occasion.</p>

<p>Presence of mind frequently arises from having previously
considered a variety of possible events. I had never contemplated
such a situation, and have often asked myself and
others what should have been my conduct, in case I had not
escaped from my satanic companions; but no sat­is­fac­tory
conclusion has yet presented itself.</p>

<div class="dsdnote">〈STALL AT THE OPERA.〉</div>

<p>During one season, I had a stall at
the German Opera. <span class="xxpn" id="p254">{254}</span>
One evening, in the cloister scene by moonlight, in the
convent, I observed that the white bonnet of my companion
had a pink tint: so also had the paper of our books and every
white object around us.</p>

<p>This contrast of colour suggested to me the direct use of
coloured lights. The progress of science in producing intense
lights by the oxy-hydrogen blowpipe, and by electricity under
its various forms, enabled me to carry out the idea of producing
coloured lights for theatrical rep­re­sen­ta­tions. I made
many experiments by filling cells formed by pieces of parallel
plate glass with solutions of various salts of chrome of
copper, and of other substances.</p>

<p>The effects were superb. I then devised a dance, in which
they might be splendidly exhibited. This was called the
rainbow dance. I proposed to abolish the foot-lights, and
instead of them to substitute four urns with flowers. These
urns would each conceal from the audience an intense light of
one of the following colours: blue, yellow, red, or any others
which might be preferable.</p>

<p>The rays of light would be projected from the vases towards
the stage, and would form four cones of red, blue, yellow, and
purple light passing to its further end.</p>

<p>Four groups, each of fifteen danseuses in pure white, would
now enter on the stage. Each group would assume the colour
of the light in which it was placed. Thus four dances each of
a different colour would commence. Oc­ca­sion­al­ly, a damsel
from a group of one colour would spring into another group,
thus resembling a shooting star.</p>

<p>After a time, the coloured lights would expand laterally
and overlap each other, thus producing all the colours of the
rainbow. In the mean time the sixty damsels in pure white
forming one vast ellipse, would dance round,
each in turn <span class="xxpn" id="p255">{255}</span>
assuming, as it passed through them, all the prismatic
colours.</p>

<p>I had mentioned these experiments and ideas to a few of my
friends, one of whom spoke of it to Mr. Lumley, the lessee of
the Italian Opera House. He thought it promised well, and
ultimately I made a series of experiments in the great concert-room.</p>

<p>Ropes were stretched across the room, on which were hung
in innumerable forms large sheets of patent net. The various
folds and bendings displayed the lights under endless modifications.
Some brilliant greens, some fiery reds, blues of the
brightest hue. Another of these was an almost perfect resemblance
of the dead purple powdery coating of the finest
grapes.</p>

<div class="dsdnote">〈THE PHI­LOS­O­PHER WRITES A BALLET.〉</div>

<p>Things being thus prepared, I had a consultation with the
eminent <i>chef-de-ballet</i> as to the kind of dance and the
nature of the steps to be adapted to these gorgeous colours.
Thus having invented the “Rainbow Dance” I became still
more ambitious, and even thought of writing a story to introduce
it, and to give it a moral character. Hence arose the
beautiful ballet of ‘Alethes and Iris.’</p>

<div class="dsdnote">〈ALETHES AND IRIS.〉</div>

<p>Alethes, a priest of the Sun, surrounded by every luxury
that earth can lay at the feet of its god, feels, like all before
him, that the most glorious life is sad without a companion to
sympathize with his feelings and share in his enjoyments.
He makes, therefore, a magnificent sacrifice to the god of
this visible creation, and prays for the gratification of his
solitary desire.</p>

<p>Apart from all the inferior orders of his class, in the midst
of clouds of incense, the high priest himself becomes entranced.</p>

<p>He beholds in a vision a distant and lonely
spot of bright <span class="xxpn" id="p256">{256}</span>
light. Advancing towards him, it assumes a circular form,
having a small yellow centre surrounded by a deep blue confined
within a brilliant red circle.</p>

<p>Retaining its shape, but slowly enlarging in size, it becomes
a circular rainbow, out of which emerges a form of beauty
more resplendent than mortal eyes might bear. Approaching
the Book of Fate, which lies closed upon a golden pedestal in
this the deepest and most sacred portion of the Temple of the
Sun, she opens it and inscribes in purple symbols these
mystic signs.</p>

<div class="nowrap tafmono">
<p class="pcontinue">·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·</p>
<p class="pcontinue">·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·</p>
<p class="pcontinue">·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·</p>
<p class="pcontinue">·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·&nbsp;&nbsp;·</p>
</div>

<p class="pcontinue">Then waving her graceful arm over the entranced high
priest, she re-enters the aërial circle: it closes and retires.</p>

<p>Alethes, recovering from the magic spells his powerful art
had wrought, rushes to the Book of Fate, opens, and reads the
revelation it unfolds.</p>

<div class="dpoemctr fsz6"><div class="dstanzactr">
<div class="dpp00">Through ocean’s depths to southern ice-fields roam,</div>
<div class="dpp01">Through solid strata seek earth’s central fire,</div>
<div class="dpp00">Cull from each wondrous field, each distant home,</div>
<div class="dpp01">An offering meet for her thy soul’s desire.</div>
</div></div>

<p>This gives rise to a series of moving and most instructive
dioramas, in which the travels of Alethes are depicted.</p>

<ul>
<li>1. A rep­re­sen­ta­tion of all the inhabitants of the ocean,
comprising big fishes, lobsters, and various crustacea,
mollusca, coralines, &amp;c.</li>

<li>2. A view of the antarctic regions,—a continent of ice
with an active volcano and a river of boiling water,
supplied by geysers cutting their way through cliffs of
blue ice.</li>

<li>3. A diorama representing the
animals whose various <span class="xxpn" id="p257">{257}</span>
remains are contained in each successive layer of the
earth’s crust. In the lower portions symptoms of
increasing heat show themselves until the centre is
reached, which contains a liquid trans­par­ent sea,
con­sis­ting of some fluid at a white heat, which, how­ever,
is filled up with little infin­i­tes­i­mal eels, all of
one sort, wriggling eternally.</li></ul>

<div class="dsdnote">〈HIGH MORAL VIEW.〉</div>

<p>This would have produced a magnificent spectacle considered
merely as a show, but the moralist might, if he
pleased, have discovered in it a profound philosophy.</p>

<p>The ennui and lassitude felt by the priest of the Sun arose
from the want of occupation for his powerful mind. The
remedy proposed in the ballet was—look into all the works
of creation.</p>

<p>The central ocean of frying eels was added to assist the
teaching of those ministers who prefer the doctrine of the
eternity of bodily torments.<a class="afnanc" href="#fn38" id="fnanc38">38</a></p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc38" id="fn38">38</a>
An ancestor of mine, Dr. Burthogge, a great friend of
John Locke, wrote, I regret to say it, a book to prove the eternity of
torments; so I felt it a kind of hereditary duty to give him a lift.
The arguments, such as they are, of my wealthy and therefore revered
ancestor are contained in a work whose title is “Causa Dei; or, an
Apology for God,” wherein the perpetuity of infernal torments is
evinced, and Divine justice (that not­with­stand­ing) defended. By Richard
Burthogge, M.D. London: Imprinted at the Three Daggers, Fleet Street,
1675.</p>

<p>The learned Tobias Swinden, M.A., late rector of Cuxton, in his
“Enquiry into the Nature and Place of Hell,” 2nd edition, 1727, has
discovered that its locality is in the Sun. The accurate map he gives
of that luminary renders it highly probable that the red flames so
well observed and photographed by Mr. De La Rue during a recent total
eclipse have a <i>real</i> existence.</p></div>

<p>The night proposed for the experiment of the dance at
length arrived. Two fire-engines duly prepared were placed
on the stage under the care of a portion of the fire brigade.</p>

<p>About a dozen danseuses in their white dresses danced
and attitudinized in the rays of powerful oxy-hydrogen
<span class="xxpn" id="p258">{258}</span>
blowpipes. The various brilliant hues of coloured light had an
admirable effect on the lovely fire-flies, especially as they
flitted across from one region of coloured light to another.</p>

<div class="dsdnote">〈COMBUSTION THE ENEMY OF GENIUS.〉</div>

<p>A few days after I called on Mr. Lumley, to inquire what conclusion
he had arrived at. He expressed great admiration at the brilliancy of
the colours and the effect of the Rainbow Dance, but much feared the
danger of fire. I tried to reassure him; and to show that I apprehended
no danger from fire, added, that I should myself be present every
night. Mr. Lumley remarked that if the house were burnt his customers
would also be burnt with it. This certainly was a valid objection, for
though he could have insured the building, he could not have insured
his audience.</p></div><!--section-->

<div class="section" id="p259">
<h2 class="h2herein">CHAPTER XXI.
<span class="hsmall">ELECTIONEERING EXPERIENCE.</span></h2>

<div class="dsynopsis">
The late Lord Lyndhurst candidate for the University of
Cambridge&#x200a;—&#x200a;The Phi­los­o­pher refuses to vote for
him&#x200a;—&#x200a;The reason why&#x200a;—&#x200a;Example of
unrivalled virtue&#x200a;—&#x200a;In 1829 Mr. Cavendish was
a Candidate for that University&#x200a;—&#x200a;The Author
was Chairman of his London Committee&#x200a;—&#x200a;Motives
for putting men on Committees&#x200a;—&#x200a;Of the pairing
Sub-Committee&#x200a;—&#x200a;Motives for Voting&#x200a;—&#x200a;Means
of influencing Voters&#x200a;—&#x200a;Voters brought from Berlin
and from India&#x200a;—&#x200a;Elections after the Reform Bill,
1832&#x200a;—&#x200a;The Author again requested to be Chairman of
Mr. Cavendish’s Committee&#x200a;—&#x200a;Reserves three days in
case of a Contest for Bridgenorth&#x200a;—&#x200a;It occurs, but is
arranged&#x200a;—&#x200a;Bridgenorth being secure, the Author gets
up a Contest for Shropshire&#x200a;—&#x200a;Patriotic Fund sends
500&#x200a;<i>l.</i> to assist the Contest&#x200a;—&#x200a;It lasts three
days&#x200a;—&#x200a;Reflections on Squibs&#x200a;—&#x200a;Borough of
Finsbury&#x200a;—&#x200a;Adventure in an Omnibus&#x200a;—&#x200a;A
judicious Loan&#x200a;—&#x200a;Subsequent invitation to stand for
Stroud&#x200a;—&#x200a;Declined&#x200a;—&#x200a;Reflections on improper
influence on Voters.</div>

<p class="pfirst"><span class="smcap">W<b>HEN</b></span> the
late Lord Lyndhurst was a candidate for the rep­re­sen­ta­tion of the
University of Cambridge, I met Mr. <span class="nowrap">——,</span>
a Whig in politics, and a great friend of Dr. Wollaston. After the
usual salutation, he said, “I hope you will go down to Cambridge
and vote for our friend Copley.” I made no answer, but, looking
full in his face, waited for some explanation. “Oh,” said Mr. <span
class="nowrap">——,</span> “I see what you mean. You think him a Tory;
Copley still is what he always has been—a republican.” I replied that
I was equally unable to vote for him upon that ground, and wished my
friend good morning. <span class="xxpn" id="p260">{260}</span></p>

<p>A few evenings after I met the beautiful Lady Copley,
who also canvassed me for my vote for her husband. I had
the energy to resist even this temptation, which I should not
have ventured to mention did not the poll-book enable me to
refer to it as a witness of my unrivalled virtue.</p>

<div class="dsdnote">〈CAMBRIDGE UNIVERSITY ELECTION.〉</div>

<p>Some years after, in 1829, a vacancy again arose in the
rep­re­sen­ta­tion of the University of Cambridge. Mr. Cavendish
having recently waived the privilege of his rank, which
entitled him, after a residence of two years, to take the
degree of Master of Arts, had entered into competition with
the whole of the young men of his own standing, and had
obtained the distinguished position of second wrangler and
senior Smith’s prize man. Under such circumstances, it was
quite natural that all those who felt it important that the
accidental aristocracy of birth should be able to maintain its
position by the higher claim of superior knowledge; as well
as all those who took a just pride in their Alma Mater, should
wish to send such a man as their rep­re­sen­ta­tive to the House
of Commons.</p>

<p>A very large meeting of the electors was held in London,
over which the Earl of Euston presided. It was unanimously
resolved to nominate Mr. Cavendish as a proper person to
represent the University of Cambridge in the House of
Commons. A committee was appointed to carry on the
election, of which I was nominated chairman. Similar proceedings
took place at Cambridge. The family of the young
but distinguished candidate were not at first very willing to
enter upon the contest. As it advanced, the committee-room
became daily more and more frequented. Ultimately, in the
midst of the London season, and during the sitting of the
House of Commons, this single election excited an intense
interest amongst men of all parties,
whilst those who <span class="xxpn" id="p261">{261}</span>
supported Mr. Cavendish upon higher grounds were not less
active than the most energetic of his political supporters.</p>

<div class="dsdnote">〈MOTIVES FOR BEING ON A COMMITTEE.〉</div>

<p>At all elections some few men, perhaps from four or five
up to ten or twelve, do all the difficult and real work of the
committee. The committee itself is, for several reasons,
generally very numerous.</p>

<p>All who are supposed to have weight are, of course, put
upon it.</p>

<p>Many who wish to appear to have weight get their names
upon it.</p>

<p>Some get put upon it thinking to establish a political claim
upon the <i>party</i>.</p>

<p>Others because they like to see their names in the newspapers.</p>

<p>Others again, who, if not on <i>his</i> committee, would vote
against the candidate.</p>

<p>There are also idlers and busybodies, who go there to talk
or to carry away something to talk about, which may give
them importance in their own circle.</p>

<p>Young lawyers, of both departments of the profession, are
very numerous, possessing acute perceptions of pro­fes­sion­al
advantage.</p>

<p>A jester and a good story-teller are very useful; but a
jolly and enterprising professor of rhodomontade is on some
occasions invaluable—more especially if he is not an Irishman.</p>

<p>Oc­ca­sion­al­ly a few simply honest men are found upon
committees. These are useful as adjuncts to give a kind of
high moral character to the cause; but the rest of the committee
generally think them bores, and when they differ
upon any point from the worldly members, it is invariably
whispered that they
are crotchety fellows. <span class="xxpn" id="p262">{262}</span></p>

<p>When any peculiarly delicate question arises, it is sometimes
important to eliminate one or more of them temporarily from
the real committee of management. This is accomplished (as
in graver matters) by sending him on an embassy, usually to
one of the adepts, with a confidential mission on a subject represented
to him as of great importance. The adept respectfully
asks for his view of the subject, rather opposes it, but
not too strongly; is at last convinced, and ultimately entirely
adopts it. The adept then enters upon the honest simpleton’s
crotchet, trots it out in the most indulgent manner, and
at length sends him back, having done the double service of
withdrawing him from a consultation at which he might have
impeded the good cause, and also of enabling him at any
future time to declare truly, if necessary, that he never was
present at any meeting at which even a questionable course
had been proposed.</p>

<div class="dsdnote">〈OF THE PAIRING COMMITTEE.〉</div>

<p>One of the most difficult as well as of the most important
departments of some elections is the pairing sub-committee.
When I had myself to arrange it, I generally picked out two
of the cleverest and most quick-witted of the committee. I
told them I had perfect confidence in their judgment and
discretion, and therefore constituted them a sub-committee,
with absolute power on all questions of pairing. I also
entirely forbade any appeal to myself. I then advised them
to have attached to them a couple of good and entertaining
talkers, to hold in play the applicants while they retired to
ascertain the policy of the proposed pair.</p>

<p>Upon one occasion, when both my persuasive gentlemen
were absent, I was obliged to officiate myself. I soon discovered
that the adverse vote was very lukewarm in his own
cause, and was also very averse to the prospect of missing a
great cricket-match if he went to the
poll. Whilst my <span class="xxpn" id="p263">{263}</span>
pairing committee were making the necessary inquiries, I
was so fortunate as to secure the promise of his vote for my
own candidate at the succeeding election. In the meantime
the pairing committee had kindly taken measures to save him
from missing his cricket-match without, however, wasting a
pair.</p>

<div class="dsdnote">〈PRIMITIVE PURITY—IT WON’T DO.〉</div>

<p>Yet not­with­stand­ing all my efforts to introduce primitive
virtue into electioneering, I did not always succeed. About
a dozen years had elapsed after one of the elections I had
managed, when the subject was mentioned at a large dinner-table.
A supporter of the adverse political party, referring
to the contest, stated as a <i>merit</i> in his friends that they had
succeeded in outwitting their opponents, for on one occasion
they had got a man on their side who had unluckily just
broken his arm, whom they succeeded in pairing off against
a sound man of their adversaries. Remembering my able
coadjutors in that contest, I had little doubt that a good
explanation existed; so the next time I met one of them I
mentioned the circumstance. He at once admitted the fact,
and said, “We knew perfectly well that the man’s arm was
broken; but our man, whom we paired off against him, had
<i>no vote</i>.” He then added, “We were afraid to tell you of
our success.” To which I replied, “You acted with great
discretion.”</p>

<p>University elections are of quite a different class from all
others. The nature of the influences to be brought to bear
upon the voters is of a peculiar kind: the clerical element is
large, and they are for the greater part expectant of something
better hereafter.</p>

<div class="dsdnote">〈MATERIALS FOR CANVASSING.〉</div>

<p>The first thing to be done in any election contest is to get as
exact a list as possible of the names and addresses of the voters.
In a university contest the chairman should adopt <span class="xxpn"
id="p264">{264}</span> certain letters or other signs to be used in
his own private copy attached to the names of the clerical voters.
These should <span class="nowrap">indicate—</span></p>

<ul class="ulindenta fsz6">
<li>The books such voter may have written.</li>
<li>The nature of his preferment.</li>
<li>The source whence derived.</li>
<li>The nature of his expectations.</li>
<li>The source whence expected.</li>
<li>The age of the impediment.</li>
<li>The state of its health.</li>
<li>The chance of its promotion.</li></ul>

<p>Possessed of a full knowledge of all these circumstances, a
paragraph in a newspaper regretting the alarming state of
health of some eminent divine will frequently decide the
oscillation even of a cautious voter.</p>

<p>This dodge is the more easily practised because some
eminent divines, on the approach of an university election,
oc­ca­sion­al­ly become ill, and even take to their bed, in order
to avoid the bore of being canvassed, or of committing
themselves until they see “how the land lies.”</p>

<p>The motives which induce men to act upon election committees
are various. The hope of advancement is a powerful
motive. It was stated to me by some of my committee, that
every really working member of the committee which a few
years before had managed the election of Copley for the
University of Cambridge had already been rewarded by place
or advancement.</p>

<p>My two most active lieutenants in the two contests for
Cambridge, to which I have referred, were not neglected.
One of them shortly after became a Master in Chancery, and
the other had a place in India, producing
£10,000 a year. <span class="xxpn" id="p265">{265}</span></p>

<p>The highest compliment, however, that party can pay to
those who thus assist them is entirely to ignore their service,
and pass them over on every occasion. This may be done
with impunity to the very few who have such strong convictions
that no amount of neglect or ill-usage can cause them
to desert those principles of the soundness of which their
reason is convinced. This course has also the great advantage
of economizing patronage.</p>

<p>Always ascertain who are the personal enemies of the
opposing candidate. If skilfully managed, you may safely
depend upon their becoming the warmest friends of your own.
Their enthusiasm can be easily stimulated: their zeal in the
cause may shame some of your own lukewarm friends into
greater earnestness. Men will always give themselves tenfold
more trouble to crush a man obnoxious to their hatred than
they will take to serve their most favoured ally.</p>

<p>When I have been chairman of an election committee I
have found it advantageous to commence my duties early in
the morning, and to remain until late at night. There is
always something to be done for the advancement of the
cause. In the first Cambridge election in which I took part
I invariably remained at my post until midnight; and in the
second, I was seldom absent at that hour.</p>

<div class="dsdnote">〈GOT A VOTER FROM BERLIN.〉</div>

<p>One evening, being alone, I employed myself in looking
through our lists to find the names of all voters at that period
unaccounted for. The first name which attracted my attention
was that of a liberal with whom I was personally unacquainted.
The next day I set at work one of my investigating
committee. In the course of the following day, he had traced
out the voter, who at that time was at Berlin. As there was
ample time for his return, a friend was employed to write to
him, and he returned and voted
for our candidate. <span class="xxpn" id="p266">{266}</span></p>

<div class="dsdnote">〈NEGLECT NO CHANCE.〉</div>

<p>On another evening, the name of Minchin turned up on
the list. I remembered the man, whom I had met very
frequently at the rooms of one of my most intimate friends;
but I had not seen him for nearly twenty years.</p>

<p>The next day, after many inquiries, I found that he
had been lost sight of for a long time, and it was believed
that he had gone out to India. I immediately sent a note
to a friend of mine, Captain Robert Locke, who commanded
an Indiaman, to beg of him to look in upon me at the
committee-room. In two hours he called and informed me
that Minchin was a barrister at Calcutta, and was about to
return to England. On my expressing a wish for further
particulars, he kindly went into the City to procure information,
and on his return told me that Minchin was on his
voyage home in the “Herefordshire,” an excellent ship. It
was due on a certain day, about a fortnight thence, and would
in all probability not be three days behind its time.</p>

<p>In the evening, being again alone in the committee-room,
I resumed the Minchin question, and found that he might
possibly arrive on the second of the three days’ polling. I
therefore wrote the following <span class="nowrap">letter:—</span></p>

<div class="dblockquote">
<p class="pfirst"><span class="smcap">D<b>EAR</b></span>
<span class="smcap">M<b>INCHIN,</b></span></p>

<p>If twenty years have not altered your political principles,
we have now an opportunity of getting in a Liberal to
represent our University.</p>

<p>The three days of polling are ——&nbsp;&nbsp;——&nbsp;&nbsp;——</p>

<p>If you arrive in time, pray come immediately to my committee-room
in Cockspur Street.</p>

<p class="pcompclose">Yours truly,</p>

<p class="psignature">C. <span class="smcap">B<b>ABBAGE</b>.</span></p></div>

<p>I addressed this letter to Minchin
at Portsmouth, and <span class="xxpn" id="p267">{267}</span>
making two copies of it, directed them to two other seaports.
When I put these letters into the basket, I smiled
at my own simplicity in speculating on the triple <span class="nowrap">improbability—</span></p>

<ul>
<li>1. That Minchin should ever get my letter.</li>

<li>2. That his ship, which was expected, should really
arrive on the second or third of the three days of
polling.</li>

<li>3. That a young lawyer should not have changed his
political principles in twenty years.</li></ul>

<p>However, I considered that the chance of this election
lottery-ticket winning for us a vote, although very small,
was at least worth the three sheets of letter-paper which it
cost our candidate.</p>

<div class="dsdnote">〈GOT A VOTER FROM INDIA.〉</div>

<p>Amidst the bustle of the election this subject was entirely
forgotten. The first day of polling arrived, and was concluded,
and as usual I was sitting, at midnight, alone in the
large committee-room, when the door opened, and there
entered a man enveloped in a huge box-coat, who advanced
towards me. He held out his hand, and grasping mine, said,
“I have not altered my political principles.” This was
Minchin, to whom the pilot, cruizing about on the look-out
for the “Herefordshire,” had delivered a packet of letters.</p>

<p>The first letter Minchin opened was mine. He immediately
went below, told his wife that he must get into the
boat which had just put the pilot on board, and hasten to
Cambridge, whilst she remained with the children to pursue
their voyage to London. Minchin returned in the pilot-boat
to Portsmouth, found a coach just ready to start, got up on
the roof, borrowed a box-coat, and on arriving in London,
drove directly to the committee-room.
Finding that it <span class="xxpn" id="p268">{268}</span>
would be most convenient to Minchin to start immediately
for Cambridge, I sent off a note to the Temple for the most
entertaining man<a class="afnanc" href="#fn39" id="fnanc39">39</a>
upon the committee; I introduced him to
Minchin, and they posted down to Cambridge, and voted on
the second day.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc39" id="fn39">39</a>
My friend, John Elliott Drinkwater, afterwards Bethune.</p></div>

<p>Greatly to the credit and to the advantage of the University,
Mr. Cavendish was elected on this occasion.</p>

<hr class="hrblk" />

<div class="dsdnote">〈ELECTION AFTER THE REFORM BILL.〉</div>

<p>In May, 1832, after the passing of the Reform Bill, there
was a dissolution of Parliament. At the general election
which ensued, Lord Palmerston and Mr. Cavendish, the two
former members, again became candidates. Two of the most
active members of Mr. Cavendish’s former committee called
upon me, one of whom began speaking in somewhat complimentary
phrases of our young candidate. I was listening
attentively to all that could be said in favour of the Cavendish
family, when his companion, suddenly interrupting him, said,
“No, <span class="nowrap">——</span> that won’t do for Babbage.”
He then continued,
in terms which I have no wish to repeat, to speak of our
candidate, and concluded by saying, that they expressed
the opinion of all the working members of the former committee,
and came by their desire to request me again to take
the chair during the approaching contest; stating, also, that
there was no other man under whom they would all willingly
act. He then entreated me to be their chairman, not for the
sake of the Cavendishes, but for the sake of the cause.</p>

<p>This appeal was irresistible. I immediately acceded to
their request, but with one reservation, in case my brother-in-law’s
seat was contested, that I should have three days to
help him at Bridgenorth.</p>

<p>Under such circumstances the contest
commenced. I can <span class="xxpn" id="p269">{269}</span>
truly add, that amongst the many elections in which I have
taken an active working share, none was ever carried on
with greater zeal, nor were greater efforts ever made to attain
success.</p>

<p>I had good reason at its commencement to doubt the
success of our candidate: not from any defect on his part,
but entirely on political grounds. The same reasons induced
me to suppose that Lord Palmerston’s seat was equally in
danger. Of course, a tone of perfect confidence was sustained,
and, but for a very inopportune petition signed by a
considerable number of members of the University, I believe
that we might have managed, by a compromise with the
other party, to have secured one seat for our own. As it
was, however, both the Liberal candidates were defeated.</p>

<div class="dsdnote">〈BRIDGENORTH BEING SAFE.〉</div>

<p>The contingency I had anticipated did occur. I was sent
for, and went down by the mail to assist Mr. Wolryche Whitmore.
On my arrival, I found that circumstances had entirely
changed, and not only my brother-in-law, but also Mr. Foster,
a large iron-master, was to be returned for Bridgenorth without
a contest.</p>

<div class="dsdnote">〈A CONTEST FOR SHROPSHIRE STARTED.〉</div>

<p>As soon as I was informed of this arrangement, I took immediate
measures for rejoining my committee in Cockspur
Street. On reaching Bridgenorth, it appeared that four hours
would elapse before the mail to London could arrive. I
fortunately found a great number of Mr. Foster’s most influential
supporters assembled at the hotel, comprising amongst
them many of the largest iron-masters and man­u­fac­turers in
the county. They were naturally elated at the success of
their friend, which secured to their class a certain amount of
influence in the House of Commons. In the course of conversation,
mention was made of the utter neglect of the manufacturing
interests of the district by
their county members. <span class="xxpn" id="p270">{270}</span>
I remarked, that it depended upon themselves to remedy this
evil, and inquired whether they were seriously disposed to
work. One of the party, who had greatly assisted me when I
was managing another contest, and who had ridden over four
counties in search of votes for us, appealed to my own experience
of their energy. After some discussion, I suggested
that they should start a rival candidate of their own for the
county.</p>

<p>I then proposed to retire into another room and draw up
an address to the freeholders, and also placards, to be stuck up
in every town and village in the county. I desired them, in
the mean time, to divide the county into districts, of such
size that one of our party could in the course of a day go to
every town and large village in his district, and arrange with
one or more tradesmen in our interest to exhibit the address
in their shop-windows. I also desired them to make an estimate
of the number of large and small placards necessary for
each town and village, in order that we might ascertain how
many of each need be printed.</p>

<p>I returned with the addresses to the freeholders. In these
the characters of their late members were lightly sketched,
and the public were informed that a committee in the liberal
interest was sitting in every town in the county, and that at
the proper time the name of a fit candidate would be announced.</p>

<p>My friends cordially concurring in these sentiments, unanimously
adopted the addresses, undertook to publish them
in the newspapers, to arrange their distribution, and organize
committees throughout the county. They were, of course,
very anxious to know who was to be their candidate. I told
them at once that it was not to be expected that they could
succeed in their first attempt, but that such
a course would <span class="xxpn" id="p271">{271}</span>
assuredly secure for them in future much more attention to
their interests from their county members. With respect to
a candidate, if they could not themselves find one, these placards
and advertisements would without doubt produce one.</p>

<p>I may here mention that a member of the Cambridge
committee in Cockspur Street had taken rooms at the Crown
and Anchor, and, in conjunction with many other Liberals,
instituted the Patriotic Fund, for the purpose of collecting
subscriptions for the support of liberal candidates at the first
elections under the Reform Bill. A very large sum was soon
subscribed.</p>

<p>In the broadsides and placards issued in Shropshire, I had
taken care to allude to this fund in large capitals.</p>

<p>I now got into the mail for London, amidst the hearty
con­grat­u­la­tions of my Shropshire friends. During the few
minutes’ rest at Northampton, I had an opportunity of seeing
a member of the Liberal committee and of informing him of
our proceedings in Shropshire, and afterwards of conveying
his report of the prospects of the contest in that town to our
friends in London.</p>

<p>Two or three days after every town, and almost every
village in Shropshire, was enlightened by my placards; and
in the course of a few days more, three candidates were in
the field.</p>

<div class="dsdnote">〈PATRIOTIC FUND AIDS IT WITH £500.〉</div>

<p>On my return to London I communicated with the Patriotic
Fund, who sent down 500&#x200a;<i>l.</i> to support the party in Shropshire.
After a short contest the Liberal party was of course beaten;
but the diversion produced the intended effect.</p>

<hr class="hrblk" />

<p>One portion of electioneering tactics is thought to consist
in the man­u­fac­ture of squibs. These should never give pain
nor allude to any personal defect or
inevitable evil. They <span class="xxpn" id="p272">{272}</span>
ought either to produce a broad laugh or that involuntary smile
which true wit usually provokes. They are productive of
little effect except the amusement of the supporters engaged
in carrying on the contest.</p>

<p>My own share in elections has generally been in more
serious departments. I remember, however, a very harmless
squib which I believed equally amused both parties, and
which, I was sub­se­quent­ly informed, was concocted in Mr.
Cavendish’s committee-room.</p>

<p>High math­e­mat­i­cal knowledge is by no means a very great
qualification in a candidate for the House of Commons, nor
is the absence of it any disparagement. In the contest to
which I refer, the late Mr. Goulburn was opposed to Mr.
Cavendish. The following paragraph appeared in the
‘Morning <span class="nowrap">Post:’—</span></p>

<div class="dblockquote">
<p>“The Whigs lay great stress on the academical distinction attained by
Mr. Cavendish. Mr. Goulburn, it is true, was not a candidate for university
honours; but his scientific attainments are by no means insignificant. He
has succeeded in the exact rectification of a circular arc; and he has likewise
discovered the equation of the lunar caustic, a problem likely to prove
of great value in nautical astronomy.”</p></div>

<p>It appears that late one evening a cab drove up in hot
haste to the office of the ‘Morning Post,’ delivered the copy
as coming from Mr. Goulburn’s committee, and at the same
time ordered fifty <i>extra</i> copies of the ‘Post’ to be sent next
morning to their committee-room.</p>

<hr class="hrblk" />

<div class="dsdnote">〈CONTEST FOR FINSBURY.〉</div>

<p>During my own contest for the borough of Finsbury few
incidents worth note occurred. One day, as I was returning
in an omnibus from the City, an opportunity presented itself
by which I acquired a few votes. A gentleman at the extreme
end of the omnibus being about to leave
it, asked the <span class="xxpn" id="p273">{273}</span>
conductor to give him change for a sovereign. Those around
expressed their opinion that he would acquire bad silver by
the exchange. On hearing this remonstrance, I thought it
a good opportunity to make a little political capital, which
might perhaps be improved by a slight delay. So I did not
volunteer my services until a neighbour of the capitalist
who possessed the sovereign had offered him the loan of a
sixpence. It was quite clear that the borrower would ask
for the address of the lender, and tolerably certain that it
would be in some distant locality. So, in fact, it turned out:
Richmond being the abode of the benevolent one. Other
liberal individuals offered their services, but they only possessed
half-sovereigns and half-crowns.</p>

<div class="dsdnote">〈A JUDICIOUS LOAN—SIXPENCE.〉</div>

<p>In the mean time I had taken from my well-loaded breast-pocket
one of my own charming addresses to my highly-cultivated
and independent constituents, and having also a
bright sixpence in my hand, I immediately offered the latter
as a loan, and the former as my address for repayment. I
remarked at the same time that my committee-room on
Holborn Hill, at which I was about to alight, would be open
continually for the next five weeks. This offer was immediately
accepted, and further extensive demands were instantly
made upon my pocket for other copies of my address.</p>

<p>My immediate neighbour, having read its fascinating contents,
applied to me for more copies, saying that he highly
agreed with my sound and patriotic views, would at once
promise me six votes, and added that he would also immediately
commence a canvass in his own district. On arriving
at my committee-room I had already acquired other supporters.
Indeed, I am pretty sure I carried the whole of my
fellow-passengers with me: for I left the omnibus amidst the
hearty cheers of
my newly-acquired friends. <span class="xxpn" id="p274">{274}</span></p>

<div class="dsdnote">〈REPAID WITH COMPOUND INTEREST.〉</div>

<p>About a year or two after this long-forgotten loan, I received
a letter from a gentleman whose name I did not
recognize as being one of my too numerous cor­res­pon­dents.
It commenced thus:—“Sir, I am the gentleman to whom
you lent sixpence in the omnibus.” He then went on
to state, in terms too flattering for me to repeat, that he
had watched the Finsbury election with the greatest interest,
and much deplored the taste of the electors in rejecting
so, &amp;c. &amp;c., a candidate. My friend then informed me of an
approaching vacancy in the borough of Stroud, in which town
he resided. He proceeded to give me an outline of the state
of opinion, and of the wants of the electors, and concluded
by saying he was certain that my opinions would be very
favourably received. He also assured me, if I decided on
offering my services to the constituency, that he should have
great pleasure in giving me every support in his power. In
reply, I cordially thanked him for his generous offer, but
declined the proposed honour. In fact, I was not peculiarly
desirous of wasting my time for the benefit of my country.
The constituency of Finsbury had already expressed their
opinion that Mr. Wakley and Mr. Thomas Duncombe were
fitter than myself to represent them in Parliament, and in
that decision I most cordially concurred.</p>

<hr class="hrblk" />

<p>During some of the early contests for the borough of Marylebone,
it too frequently occurred that ladies drove round to
their various tradesmen to canvass for their votes, threatening,
in case of refusal, to withdraw their custom. This unfeminine
conduct oc­ca­sion­al­ly drew upon them unpleasant
though well-deserved rebukes.</p>

<div class="dsdnote">〈DISGRACEFUL CANVASSING.〉</div>

<p>In one of those contests I took a considerable interest in
favour of a candidate whom I shall call Mr. A.  Meeting <span class="xxpn" id="p275">{275}</span>
a very respectable tradesman—a plumber and painter, whom
I had employed in decorating my own house—I asked him
how he intended to vote. He replied that he wished to vote
for Mr. A., but that one of his customers had been to his shop
and asked him to vote for Mr. Z., threatening, in case he
declined, never to employ him again.</p>

<p>I inquired whether his customer’s house was larger than
mine, to which he replied that mine was twice the size of the
other. I then asked whether his customer was a younger
man than myself, to this he replied, “He is a much older
man.”</p>

<p>I then asked him what he would do if I adopted the same
line of conduct, and insisted on his voting for my friend
Mr. A. This query was unanswerable. Of course I did not
attempt to make him violate his extorted promise.</p>

<p>Such conduct is disgraceful, and if of frequent occurrence
would have a tendency to introduce the vote by ballot; a
mode of voting for rep­re­sen­ta­tives which, in my opinion,
nothing short of the strongest necessity could justify.</p>

<p>The election for Finsbury gave occasion to the
following <i>jeu d’esprit</i>, which, as a specimen of the
electioneering <i>squibs</i> of the day, I give <i>in</i> <span
class="nowrap"><i>extenso:</i>—</span></p></div><!--section-->

<div class="section" id="p276">
<h2 class="h2herein">CHAPTER XXII.
<span class="hsmall">
SCENE FROM A NEW AFTER-PIECE,</span>
<span class="hsmaller">
CALLED</span>
<span class="hsmall">
“<i>Politics and Poetry</i>;” <i>or</i>, “<i>The
 Decline of Science</i>.”</span></h2>

<hr class="hr20" />

<div>DRAMATIS PERSONÆ.</div>

<ul>
<li class="li0">
<i>PEOPLE OF</i> <span class="nowrap"><i>FASHION</i>:—</span>
<ul class="ullha">
<li><span class="smcap">T<b>URNSTILE</b>,</span> <i>a retired Phi­los­o­pher, M.P. for Shoreditch</i>.</li>
<li><span class="smcap">L<b>ORD</b></span> <span class="smcap">F<b>LUMM</b>,</span> <i>a Tory nobleman of ancient family</i>.</li>
<li><span class="smcap">C<b>OUNTESS</b></span> <span class="smmaj">OF</span> <span class="smcap">F<b>LUMM</b>,</span> <i>his wife</i>.</li>
<li><span class="smcap">L<b>ADY</b></span> <span class="smcap">S<b>ELINA</b>,</span> <i>their daughter</i>.</li>
<li><span class="smcap">H<b>ON.</b></span> <span class="smcap">M<b>RS.</b></span> <span class="smcap">F<b>UBSEY</b>,</span> <i>sister of the Countess</i>.</li>
</ul></li>

<li class="li0"><i>WHIGS</i>:—
<ul class="ullha">
<li><span class="smcap">L<b>ORD</b></span> A., <i>Prime Minister</i>.</li>
<li><span class="smcap">C<b>LOSEWIND</b>,</span> <i>First Lord of the Admiralty</i>.</li>
<li><span class="smcap">S<b>HIFT</b>,</span> <i>Secretary at War</i>.</li>
<li><span class="smcap">S<b>MOOTH</b>,</span> <i>Secretary for the Colonies; also M.P. for Shoreditch</i>.</li>
</ul></li>

<li class="li0"><i>TORIES</i> (<i>Members of the Conservative</i>
 <span class="nowrap"><i>Club</i>):—</span>
<ul class="ullha">
<li><span class="smcap">L<b>ORD</b></span> <span class="smcap">G<b>EORGE</b>,</span></li>
<li><span class="smcap">L<b>ORD</b></span> <span class="smcap">C<b>HARLES</b>,</span></li>
<li><span class="smcap">M<b>ARQUIS</b></span> <span class="smmaj">OF</span> <span class="smcap">F<b>LAMBOROUGH</b>,</span></li>
<li><span class="smcap">D<b>ICK</b></span> <span class="smcap">T<b>RIM</b>,</span> <i>a former Whipper-in</i>,</li>
</ul></li>

<li class="li0"><i>SHOREDITCH</i> <span class="nowrap"><i>ELECTORS</i>:—</span>
<ul class="ullha">
<li><span class="smcap">H<b>IGHWAY</b>,</span> <i>a Radical</i>.</li>
<li><span class="smcap">G<b>RISKIN</b>,</span> <i>Colonel of the Lumber Troop</i>.</li>
<li><span class="smcap">T<b>RIPES</b>,</span> <i>his Lieutenant</i>.</li>
</ul></li>

<li class="li0"><i>PHI­LOS­O­PHERS</i>:—
<ul class="ullha">
<li><span class="smcap">S<b>IR</b></span> <span class="smcap">O<b>RLANDO</b></span> <span class="smcap">W<b>INDFALL</b>,</span> Knt. R. Han. Guelph. Order, <i>an Astronomical Observer</i>.</li>
<li><span class="smcap">S<b>IR</b></span> <span class="smcap">S<b>IMON</b></span> <span class="smcap">S<b>MUGG</b>,</span> Knt. R. Han. Guelph. Order, <i>Professor of Botanism</i>.</li>
<li><span class="smcap">A<b>TALL</b>,</span> <i>an Episcopizing Mathematician, Dean of Canterbury</i>.</li>
<li><span class="smcap">B<b>YEWAYS</b>,</span> <i>a Calculating Officer</i>.</li></ul></li>

<li class="li0">&nbsp;<ul class="ullha" id="ulp276">
<li class="pcenter"><i>Other Lords—Conservative and Whig.</i></li>
</ul></li>
</ul>

<hr class="hr10" />

<p>The Scene is laid in London; principally at the West-end of the Town.</p>

<div>The time is near the end
of May, 1835. <span class="xxpn" id="p277">{277}</span></div>
</div><!--section-->

<div class="section">
<div class="padtopa fsz4">SCENES,
&amp;c., <span class="smcap">E<b>XTRACTED</b>.</span></div>

<h3 class="h3herein">ACT I.</h3>

<p class="pscenea"><span class="smcap">S<b>CENE</b></span>
I.—<i>Committee-room of the Conservatives, Charles-street</i>;
<span class="smcap">L<b>ORD</b></span>
<span class="smcap">F<b>LUMM</b>;</span>
<span class="smcap">M<b>ARQUIS</b></span>
<span class="smmaj">OF</span>
<span class="smcap">F<b>LAMBOROUGH</b>;</span>
<span class="smcap">L<b>ORD</b></span>
<span class="smcap">G<b>EORGE</b>;</span>
<span class="smcap">L<b>ORD</b></span>
<span class="smcap">C<b>HARLES</b>;</span> <i>other Tory Lords, and</i>
<span class="smcap">T<b>RIM</b>.</span>
<i>A table covered with papers</i>;
<span class="smcap">L<b>ORD</b></span>
<span class="smcap">C<b>HARLES</b></span> <i>smoking a
cigar</i>;
<span class="smcap">L<b>ORD</b></span>
<span class="smcap">G<b>EORGE</b></span> <i>half asleep in an arm-chair</i>;
<span class="smcap">T<b>RIM</b></span>
<i>busy in looking over a list of the House of Commons</i>.</p>

<p><i>Trim.</i> It will be a devilish close run I see!—yet I think we
might manage some of them (<i>Pause</i>). Does anybody know
<i>Turnstile</i>?</p>

<p><i>Marquis.</i> Never heard of him!</p>

<p><i>Lord George.</i> (<i>Mumbling</i>). The reform Member for Puddledock,
isn’t he?—the author of a book on Pinmaking, and
things of that kind. An ironmonger in Newgate-street!</p>

<p><i>Trim.</i> No, no! Member for Shoreditch;—with Smooth,
the Colonial Secretary!</p>

<p><i>Lord Charles.</i> (<i>Taking the cigar from his mouth.</i>) I think
I’ve heard something of him at Cambridge: he was Newtonian
Professor of Chemistry when I was at College.</p>

<p><i>Trim.</i> Can’t we talk him over?</p>

<p><i>Lord Charles.</i> No, no! he is too sharp for that.</p>

<p><i>Trim.</i> Will anybody speak to him?—and if he won’t vote
with us, keep him out of the way.</p>

<p><i>Marquis.</i> Perhaps a hint at an <span class="nowrap">appointment!—</span></p>

<p><i>Lord Charles.</i> Nor that either; he is a fellow of some
spirit; and devilish proud. <span class="xxpn" id="p278">{278}</span></p>

<p><i>Lord Flumm.</i> But what are his tastes?—how does he
employ himself?—who are his friends?</p>

<p><i>Trim.</i> Why he’s—a sort of a—phi­los­o­pher,—that wants to
be a man of the world!</p>

<p><i>Lord Flumm.</i> Oh!—now I begin to recollect;—I must
have seen him at Sir Phillip’s. Leave him to me;—I think
Lady Flumm and my daughter can manage to keep him
quiet on Thursday night.</p>

<p><i>Trim.</i> But for Tuesday,—my Lord?</p>

<p><i>Lord Flumm.</i> Two nights!—Then I must try what I can
do for you, myself.
<span class="stgdira">[<i>Exit.</i></span></p>
</div><!--section-->

<div class="section">
<p class="psceneb clearfix"><span class="smcap">S<b>CENE</b></span>
IV.—<i>Grosvenor-square.</i></p>

<div><i>Enter</i>
<span class="smcap">T<b>URNSTILE</b>,</span> <i>musing</i>.</div>

<p><i>Turnstile.</i> This will never do! They make use of
me, and laugh at me in their sleeves;—push me round and go by. That
break down <i>was</i> a devil of a business! They didn’t laugh out to be
sure; but they coughed and looked unutterably!! And where is this to
end? What shall I have to show for it? Confounded loss of time;—to hear
those fellows prosing, instead of seeing the oc­cul­ta­tion last night.
And that book of Ls.’; so much that <i>I</i> had begun upon,—and might have
finished! It never will do! (<i>Rousing himself after a pause.</i>) But
knowledge, after all, <i>is</i> power! That at least is certain,—power—to do
what? to refuse Lord Doodle’s invitation; and to ask Lord Humbug for a
favour, which it is ten to one he will refuse! But the Royal Society
is defunct! That I <i>have</i> accomplished. Gilbert, and the Duke! and the
Secretaries! I have driven them all before me!—and, now, though <i>I</i>
must not be a knight of the Guelphic order, (yet a riband is a pretty
looking thing! and <span class="xxpn" id="p279">{279}</span> a star
too!—) I will show that I can teach <i>them</i> how to make knights; and
describe the decorations that other men are to wear. But here comes
Lord Flumm, and I am saved the bore of calling upon him.</p>

<div class="dkeeptgth">
<p class="psceneb clearfix"><span class="smcap">S<b>CENE</b></span>
V.</p>

<div><i>Enter</i> <span class="smcap">L<b>ORD</b></span>
<span class="smcap">F<b>LUMM.</b></span></div>

<p><i>Lord Flumm.</i> Mr. Turnstile, if I do not mistake! My
dear Turnstile: how glad I am to see you again! it <i>was</i> kind of Sir
Phillip to introduce me. You know that you are near our house; and Lady
Flumm will be so <span class="nowrap">happy——</span></p></div>

<p><i>Turnstile.</i> In truth, my Lord, I was about to call upon you.
After what you were so good as to say last night, I took the
first opportunity.</p>

<p><i>Lord Flumm.</i> Well, that <i>is</i> kind. But you did not speak
last night. How came that? I don’t find you in the paper,
yet the subject was quite your own. Tallow and bar-iron,
raw materials and machinery. Ah, my dear sir! when
science condescends to come among us mortals, the effects to
be expected <i>are</i> wonderful indeed!</p>

<p><i>Turnstile.</i> My Lord, you flatter. But we have reached
your door. (<i>Aside.</i>) [Confound him!—But I am glad he was
not in the house. It’s clear he hasn’t heard of the break
down.]</p>

<p><i>Lord Flumm.</i> While I have you to myself, Turnstile,
remember that you dine with me on Tuesday. I am to have
two friends, Lord <span class="nowrap">S——</span> and Sir George
<span class="nowrap">Y——,</span> who wish
very much to be acquainted with you. Half-past seven.</p>

<p><i>Turnstile.</i> You are very good, my lord. I dare not refuse
so kind an invitation.
<span class="stgdira">[<i>Exeunt.</i></span></p>

<div class="xxpn" id="p280">{280}</div>

<div class="dkeeptgth">
<p class="pscenea clearfix"><span class="smcap">S<b>CENE</b></span>
VI.—<span class="smcap">L<b>ADY</b></span>
<span class="smcap">F<b>LUMM’S</b></span> <i>drawing-room</i>.
<span class="smcap">L<b>ADY</b></span>
<span class="smcap">F<b>LUMM</b></span>
<i>at the writing-table</i>.
<span class="smcap">M<b>RS.</b></span>
<span class="smcap">F<b>UBSEY</b></span> <i>at work on a sofa</i>.</p>

<div><i>Enter</i>
<span class="smcap">L<b>ORD</b></span>
<span class="smcap">F<b>LUMM</b></span> <i>and</i>
<span class="smcap">T<b>URNSTILE</b>.</span></div>

<p><i>Lord Flumm.</i> Lady Flumm, this is Mr. Turnstile, whom
you have so long wished to know. Mr. Turnstile,—Lady
Flumm.</p></div>

<p><i>Lady Flumm.</i> <i>The</i> Mr. Turnstile. My dear sir, I am too
happy to see you. We had just been speaking of your
delightful book. Selina! (<i>Calling.</i>) [<i>Enter</i>
<span class="smcap">L<b>ADY</b></span>
<span class="smcap">S<b>ELINA</b>.</span>]
This is Mr. Turnstile.</p>

<p><i>Lady Selina.</i> Indeed!</p>

<p><i>Lady Flumm.</i> Yes, indeed! You see he is a mortal man
after all. Bring me, my love, the book you will find open
on the table in the boudoir. I wish to show Mr. Turnstile
the passages I have marked this morning.</p>

<p><i>Lady Selina.</i> (<i>Re­turn­ing with the book, and run­ning over
the leaves.</i>) “Lace made by ca­ter­pil­lars.”—“Steam-engines
with fairy fingers.”—“Robe of na­ture.”—“Sun of science.”—“Fal­ter­ing
wor­ship­per.”—“Al­tar of truth.” It <i>is, in­deed</i>,
de­light­ful! The taste, the poet­i­cal imag­i­na­tion, are sur­pris­ing.
I hope, Mr. Turn­stile,—in­deed I am sure, that you
love music?</p>

<p><i>Turnstile.</i> Not <i>very</i> par­tic­u­lar­ly, I must ac­knowl­edge
(<i>smiling</i>); a bar­rel-organ is the in­stru­ment most in my way.</p>

<p><i>Lady Flumm.</i> (<i>Smiling.</i>) Music and machinery, Mr. Turnstile.
Polite literature and mathematics. You <i>do</i> know how
to combine. Others must judge of the pro­founder parts of
your works; but the style, and the fancy, are what I should
most admire.—You dine with Lord Flumm, he tells me, on
Tuesday. Now you <i>must</i> come to <i>me</i> on Thursday night.</p>

<p><i>Turnstile.</i> I am sorry to say, that, on recollection,
I <i>ought</i> to <span class="xxpn" id="p281">{281}</span>
have apologized to Lord Flumm. The Pottery Question
stands for Tuesday; and I should be there, as one of the
Committee; and Thursday, your Ladyship knows, is the
second reading of the Place and Pension Bill.</p>

<p><i>Lady Flumm.</i> Oh, we are Staffordshire people! <i>that</i> will
excuse you to the pottery folks; and, for Thursday, I <i>will</i>
absolutely take no excuse. We have Pasta and Donzelli!
perhaps a quadrille afterwards—(you dance, Mr. Turnstile?)—and
Lady Sophia <span class="nowrap">C——</span> and her cousin, Lord
<span class="nowrap">F——,</span> have
said <i>so much</i> about those beautiful passages at the end of your
book, that they will be quite disappointed if I do not keep
my promise to introduce them. (<i>Touching his arm with her
finger.</i>)</p>

<p><i>Turnstile.</i> Your Ladyship knows how to conquer: I feel
that I <i>cannot</i> refuse.
<span class="stgdira">[<i>Exit.</i></span></p>

<div class="dkeeptgth">
<p class="psceneb clearfix"><span class="smcap">S<b>CENE</b></span>
VII.—<i>Grosvenor-square; before</i>
<span class="smcap">L<b>ORD</b></span>
<span class="smcap">F<b>LUMM’S</b></span>
<i>house</i>.</p>

<div><i>Enter</i>
<span class="smcap">T<b>URNSTILE</b>,</span> <i>from the house</i>.</div>

<p><i>Turnstile.</i> This is all very delightful; but what will they
say at Shoreditch?—twice in one week absent from the
House, and at two Tory parties.</p></div>

<div><i>Enter</i>
<span class="smcap">G<b>RISKIN</b>,</span> <i>hastily, heated; his hat in his left hand; a
pocket-handkerchief in his right</i>.</div>

<p><i>Griskin.</i> Mr. Turnstile, I’m glad to find you; just called
on you, as I came to this quarter to look after a customer—long
way from the City—sorry not to hear from you.</p>

<p><i>Turnstile.</i> Why, really, Mr. Griskin, I am very sorry;
but I am not acquainted with the Commander-in-chief. And
I must say that I should not know how to
press for the <span class="xxpn" id="p282">{282}</span>
contract, knowing that your nephew’s prices are thirty per cent.,
at least, above the market.</p>

<p><i>Griskin.</i> That’s being rather nice, I should say, Mr. Turnstile.
My nephew is as good a lad as ever stood in shoe-leather;
and has six good wotes in Shoreditch,—and, as to
myself, Mr. Turnstile, I must say that, after all I did at
your election—and in such wery hot weather—I did not
expect you’d be so wery particular about a small matter.—Sir,
I wish you a good morning.</p>

<p><i>Turnstile.</i> (<i>Bowing and looking after him.</i>) So this fellow,
like the rest of them, thinks that I am to do his jobs, and to
neglect my own. And this is your <i>reformed</i> Parliament.</p>

<div class="dkeeptgth">
<p class="psceneb clearfix"><span class="smcap">S<b>CENE</b></span>
IX.—<i>The street, near</i>
<span class="smcap">T<b>URNSTILE’S</b></span> <i>house</i>.</p>

<div><i>Enter</i>
<span class="smcap">T<b>RIPES</b></span> <i>and</i>
<span class="smcap">S<b>MOOTH</b>,</span> <i>meeting</i>.</div>

<p><i>Smooth.</i> (<i>Taking both</i>
<span class="smcap">T<b>RIPES’</b></span> <i>hands</i>). My dear Tripes,
how d’ye do?—Pray, how is your good lady?—What a jolly
party at your house last night! and Mrs. Tripes, I hope, is
none the worse for it?</p></div>

<p><i>Tripes.</i> Oh dear sir, no! Mrs. Tripes and my daughters
were <i>so</i> pleased with your Scotch singing.</p>

<p><i>Smooth.</i> And your boys, how are they?—fine, promising,
active fellows.—You’ve heard from MacLeech?</p>

<p><i>Tripes.</i> Just received the note as I left home.</p>

<p><i>Smooth.</i> All is quite right, you see, your cousin has the
appointment at the Cape. I knew MacLeech was just the
man for the details. A ship, I find, is to sail in about three
weeks; and (<i>significantly</i>) I don’t think your cousin need be
<i>very</i> scrupulous about freight and passage.</p>

<p><i>Tripes.</i> You are too good, Mr. Smooth. I’m sure if anything
that I can do,—my sense of
all your <span class="nowrap">kindness——</span>
<span class="xxpn" id="p283">{283}</span></p>

<p><i>Smooth.</i> I was thinking, when I saw those fine lads of
yours, that another assistant to my under secretary’s deputy—but
(between you and me) Hume thinks that one is more
than enough. We must wait a little.</p>

<div><i>Takes</i>
<span class="smcap">T<b>RIPES’</b></span> <i>arm</i>.
<span class="stgdira">[<i>Exeunt.</i></span></div>

<div class="dkeeptgth clearfix">
<p class="pscenea"><span class="smcap">S<b>CENE</b></span>
X.—<span class="smcap">T<b>URNSTILE’S</b></span> <i>parlour</i>, 11½
<span class="smmaj">A.M.</span> <i>Breakfast on the table; pamphlets
and newspapers. In the corners of the room, books and philosophical
instruments, dusty and thrown together; heaps of Parliamentary Reports
lying above them.</i> <span class="smcap">T<b>URNSTILE</b></span> <i>alone,
musing, and looking over some journals</i>.</p>

<p><i>Turnstile.</i> This headache! Impossible to sleep when one
goes to bed by daylight. Experiments by Arago! Ah! a
paper by Cauchy, on my own subject. But here is this
cursed committee in Smithfield to be attended; and it is
already past eleven. (<i>Rising</i>).</p></div>

<div>[<i>Knock at the hall door.</i>]</div>

<div><i>Enter Servant.</i></div>

<p><i>Servant.</i> Mr. Tripes, sir.</p>

<p><i>Turnstile.</i> Show him in. He comes, no doubt, to say that
my election is arranged. A good, fat-headed, honest fellow.</p>

<div><i>Enter</i>
<span class="smcap">T<b>RIPES</b>.</span></div>

<p>Well Mr. Tripes, I’m glad to see you. Pray take a chair.</p>

<p><i>Tripes.</i> We hoped to have seen you at the meeting yesterday,
sir. Capital speech from Mr. Smooth. You know, of
course, that Mr. Highway is a candidate; and Mr. MacLeech
is talked of;—very sorry, indeed, you weren’t there.</p>

<p><i>Turnstile.</i> A transit of Venus, Mr. Tripes, is a thing that
does not happen every day. Besides,
my friend, Stellini <span class="xxpn" id="p284">{284}</span>
from Palermo, is here; and I had promised to go with him to
Greenwich.</p>

<p><i>Tripes.</i> Almost a pity, sir, to call off your attention from
such objects. But in the City we are men of business, you
know,—plain, every-day people.</p>

<p><i>Turnstile.</i> It was unlucky; but I could not help it. The
committee, I hope, is by this time at work?</p>

<p><i>Tripes.</i> It was just that, I called about. I wished to tell
you myself how very sorry I am that I cannot be your chairman.
But—my large family—press of business,—in short,—you
must excuse me;—and, if I should be upon Mr.
Smooth’s committee, I don’t well see how I can attend to
both.</p>

<p><i>Turnstile.</i> Smooth!—but he and I go together, you know,—at
least, I understood it so.</p>

<p><i>Tripes.</i> I’m glad to hear it; I feared there might be some
mistake. And, if Mr. MacLeech comes forward,—being a
fellow-townsman of Mr. Smooth, and a good deal in the
Glasgow interest;—a commercial man too, Mr. Turnstile;—a
<i>practical</i> man—Mr. Turnstile;—I am not quite sure that you
can count upon Mr. Smooth’s assistance;—and Government,
you know, is strong.</p>

<p><i>Turnstile.</i> Assistance, Mr. Tripes,—from Smooth!—why
I came in on my own ground;—on the <i>Independent</i>
interest.—Assistance from Smooth!—Besides,—Smooth knows very
well that <i>our</i> second votes secured him.</p>

<p><i>Tripes.</i> Very true, sir; but these Independent people are
hard to deal with; and Mr. Highway, I assure you, hit very
hard in his speech at the meeting yesterday. He talked of
amateur politicians,—attention to the business of the
people,—dinners with the opposite party. In short, I fear, they
will say,—like the others,—that what they
want is something <span class="xxpn" id="p285">{285}</span>
of “a <i>practical man</i>” Mr. Turnstile.—I’m sorry that I must
be going.—Sir, your servant.</p>

<p><i>Turnstile.</i> (<i>Rising and ringing.</i>) [<i>Enter servant.</i>] Open
the door for Mr. Tripes. [<i>Exit</i>
<span class="smcap">T<b>RIPES</b>.</span>]
<span class="nowrap">D——d,</span> double-faced,
selfish blockhead!</p>

<div class="dkeeptgth">
<p class="psceneb"><span class="smcap">S<b>CENE</b></span>
XI.—<i>The street, as before.</i></p>

<div><i>Enter</i>
<span class="smcap">T<b>RIPES</b>,</span> <i>from</i>
<span class="smcap">T<b>URNSTILE’S</b></span> <i>house</i>.</div>

<p><i>Tripes.</i> (<i>Putting on his hat.</i>) He might have been more
civil, too;—though he did count upon me for his chairman. But I’ll
show him that I’m not to be insulted; and if, MacLeech manages
the matter well for Charles, this <i>Mr. Phi­los­o­pher Turnstile</i>,
though he thinks himself so clever, may go to the devil. <span
class="stgdira">[<i>Exit.</i></span></p></div>
</div><!--section-->

<div class="section">
<h3 class="h3herein">ACT II.</h3>

<p class="pscenea"><span class="smcap">S<b>CENE</b></span>
I.—<i>Downing-street, after a Cabinet Meeting.</i>
<span class="smcap">L<b>ORD</b></span>
A.;
<span class="smcap">C<b>LOSEWIND</b>;</span>
<span class="smcap">S<b>HIFT</b>;</span>
<span class="smcap">S<b>MOOTH</b>;</span> <i>and
other Members of the Cabinet</i>.</p>

<p><i>Lord A.</i> That point being settled, gentlemen, the sooner
you are at your posts the better. The King comes down to
dissolve on Friday.<a class="afnanc" href="#fn40" id="fnanc40">40</a>
But, before we part,
we had better <span class="xxpn" id="p286">{286}</span>
decide about this Presidency of the Board of Man­u­fac­tures.
The appointment requires an able man; of <i>rather</i> peculiar
attainments. Mr. Turnstile has been mentioned to me; and
his claims I am told, are strong:—long devotion to science,—great
expense and loss of time for public objects,—high reputation,
and weight of opinion, as a man of science.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc40" id="fn40">40</a>
Parliament is ordinarily dissolved by Proclamation, after
having been previously prorogued. However, there is at least one
modern instance to justify the historical consistency of the text,
namely, that which occurred on the 10th June, 1818, when the Prince
Regent, afterwards George IV., dissolved the Parliament in person. The
Dramatist cannot therefore be properly accused of drawing heedlessly
upon his imagination, though even had he thus far transgressed the
boundaries of historical truth, Horace’s maxim might have been pleaded
in <span class="nowrap">excuse:—</span></p>

<div class="dpoemctr"><div class="dstanzactr">
<div class="dpp08">“Pictoribus atque Poetis</div>
<div class="dpp00">Quidlibet audendi semper fuit æqua potestas.”</div>
</div></div>
</div>

<p><i>Smooth.</i> I believe that he has left <i>science</i>; at least, he
wishes it to be so considered. He is my colleague at Shoreditch;
and, of course, I wish to support him;—but,—when
business is to be done;—and men,—and things, to be brought
together,—I own,—I <i>doubt</i>—whether a more practical man,—might
<span class="nowrap">not——</span></p>

<p><i>Shift.</i> And <i>that</i> poor Turnstile certainly is not. He must
always have <i>a reason</i>;—nothing but the <i>quod erat demonstrandum</i>;
a romancer; if you have anything to do, his first object
is <i>to do it well</i>. I am quite sure he will not answer our purpose.</p>

<p><i>Closewind.</i> He talks too much about consistency; and on
party questions, you are never sure of him: last week he did
not divide with us, on either night.</p>

<p><i>Lord A.</i> Well; <i>I</i> am quite indifferent. I did hear of his
being at Lord Flumm’s; and after what had just passed in
the Lords, a personal friend of mine would, perhaps, have
kept away from that quarter. Is there no other person?</p>

<p><i>Smooth.</i> (<i>Hesitatingly.</i>) Davies Gilbert.</p>

<p><i>Shift.</i> (<i>Laughing.</i>) Pooh! Pooh! Poor Gilbert! No,
that will never do.</p>

<p><i>Smooth.</i> Or—Warburton?</p>

<p><i>Shift.</i> (<i>Sneering.</i>) Worse and worse!—if <i>ever</i> there was
an <span class="nowrap">impracticable——</span></p>

<p><i>Closewind.</i> But we don’t know that Turnstile is sure of his
seat. Smooth, hasn’t MacLeech been talked
of for Shoreditch? <span class="xxpn" id="p287">{287}</span></p>

<p><i>Smooth.</i> He’s <i>certain</i> of succeeding! The independent
gentlemen don’t quite like Turnstile—they wish for Highway—and
the split will foil them both. MacLeech—now that
he has been mentioned—I must acknowledge, does seem to
me to be the <i>very</i> man for the man­u­fac­tures,—a practical,
persevering man of business,—never absent from the House,—excellent
Scotch connections,—a cousin of the Duke of
<span class="nowrap">Y.’s——.</span></p>

<p><i>Lord A.</i> That is a good point, certainly. An appointment
given there would be candid and liberal;—it might
<span class="nowrap">conciliate——</span></p>

<p><i>Closewind.</i> A very civil, excellent fellow, too. MacLeech,
<i>I</i> should say, is the man.</p>

<p><i>Shift.</i> I quite agree with you.</p>

<p><i>Smooth.</i> I confess, I think he will fill the office well. And
if it is thought quite necessary that Hume’s motion to reduce
the salary,—though it is not <span class="nowrap">large——</span></p>

<p><i>Closewind.</i> Oh, no! The salary had better remain;—2000&#x200a;<i>l.</i>
is not too much. Besides, the <i>principle</i> of giving way
is bad.</p>

<p><i>Lord A.</i> Well, gentlemen, let it be so. Smooth, you
will let MacLeech know that he has the office.</p>

<p><i>Smooth.</i> And at the present salary?</p>

<p><i>Lord A.</i> Agreed.
<span class="stgdira">[<i>Exeunt.</i></span></p>

<div class="dkeeptgth clearfix">
<p class="pscenea"><span class="smcap">S<b>CENE</b></span>
IV.—<i>The Athenæum Club.</i>
<span class="smcap">S<b>MOOTH</b></span> <i>and</i>
<span class="smcap">A<b>TALL</b></span> <i>at
a table</i>.</p>

<p><i>Smooth.</i> I saw it this morning on the breakfast-table at
Lord A’s; it is an admirable article, and I was told is yours.</p></div>

<p><i>Atall.</i> (<i>Decliningly.</i>) These things, you know, are always
supposed to be anonymous. But I am not sorry that you
liked the paper. Did his lordship
speak of it? <span class="xxpn" id="p288">{288}</span></p>

<p><i>Smooth.</i> The book was open at the article upon the table.
It does you honour. Hits <i>just</i> the happy point,—hints probable
<i>intentions</i>, without giving any pledge,—enough to please
the Liberals,—and full room for <i>explanation</i>, if any change
becomes expedient. The true plan, believe me, for a ministry,
in times like these, is to proceed <i>en tâtonnant</i>.—Pray, Mr.
Dean, how is the Bishop of Hereford?</p>

<p><i>Atall.</i> I didn’t know that he was par­tic­u­lar­ly ill. He has
long been feeble.</p>

<p><i>Smooth.</i> These complainers do sometimes hold out. But
they cannot last for ever.—We meet I hope to-morrow at the
levee. You <i>ought</i> to be there.</p>

<p><i>Atall.</i> I have come to town for the purpose; having
secured, I think, Closewind’s election at Cambridge.</p>

<p><i>Smooth.</i> Well done, my very good friend! Men of talent
should always pull together. Sorry that I must go; but we
meet to-morrow. (<i>Shaking hands very cordially.</i>)
<span class="stgdira">[<i>Exit.</i></span></p>

<div class="dkeeptgth clearfix">
<p class="psceneb"><span class="smcap">S<b>CENE</b></span>
VI.—<span class="smcap">B<b>YEWAYS’</b></span> <i>lodgings</i>.
<span class="smcap">B<b>YEWAYS</b></span> <i>alone, writing</i>.</p>

<div><i>Enter</i>
<span class="smcap">T<b>URNSTILE</b>.</span></div>

<p><i>Turnstile.</i> My dear Byeways; I want your assistance.
Deserted by those shabby dogs the Radicals, and tricked, I
fear, by the Whigs, I find I have no chance of a decent show
of numbers at the next election, if my scientific friends do
not support me with spirit. Even so, it <i>can</i> be only an
honourable retreat. I count upon <i>you</i>,—you understand the
world;—and as soon as we can muster a committee, you
must be my chairman.</p></div>

<p><i>Byeways.</i> My good friend, don’t be in a hurry; sit down
and tell me all about it. I know you don’t care much about
your seat,—and after all,—it is,—to you,
a waste of <span class="xxpn" id="p289">{289}</span>
time;—but, with the Independents at your back, you are secure. As
to me, my dear fellow, you know that I <span class="nowrap">am——</span></p>

<p><i>Turnstile.</i> But man! the Independents, as you call them,
have taken up Highway; he blusters, and goes any length.</p>

<p><i>Byeways.</i> But Smooth, you know, is strong in Shoreditch,—Government
interest,—you brought him in last time; and
you and he, <span class="nowrap">together——</span></p>

<p><i>Turnstile.</i> I know it; but he says he is not <i>strong enough</i>
to run any risk. If you will be my chairman, with a good
committee, we may at least die game.</p>

<p><i>Byeways.</i> My dear Turnstile, you know how glad I always
am to serve you—and you know what <i>I think</i>;—but in my
situation, my dear fellow, it is quite impossible that I can
<i>oppose</i> the ministers. MacLeech too, they say, is a candidate;
and his brother-in-law’s uncle was very civil, last year, in
Scotland, to my wife’s cousin.—But I <i>have</i> a plan for you.
There is Atall, just come to town; make <i>him</i> your chief, and
bring the Cambridge men together. The clergy were always
strong in Shoreditch. Atall can speak to them.—I am
obliged to go to the War Office.—And you had better lose no
time in seeing Atall. Sorry to bid you good-bye.
<span class="stgdira">[<i>Exit.</i></span></p>

<p class="clearfix"><i>Turnstile.</i> Well, this <i>is</i> strange!
yet I thought I might have counted upon Byeways. <span
class="stgdira">[<i>Exit.</i></span></p>

<div class="dkeeptgth clearfix">
<p class="psceneb"><span class="smcap">S<b>CENE</b></span>
VIII.—<span class="smcap">L<b>ADY</b></span>
<span class="smcap">F<b>LUMM’S</b></span> <i>Drawing-room</i>.
<span class="smcap">L<b>ADY</b></span>
<span class="smcap">F<b>LUMM</b>;</span>
<span class="smcap">L<b>ADY</b></span>
<span class="smcap">S<b>ELINA</b>;</span>
<span class="smcap">H<b>ON.</b></span>
<span class="smcap">M<b>RS.</b></span>
<span class="smcap">F<b>UBSEY</b>.</span></p>

<p><i>Mrs. Fubsey.</i> But, my dear sister; how <i>can</i> you so beflatter
that poor man? You don’t know all the mischief you
may do to him.</p></div>

<p><i>Lady Flumm.</i> “Poor man!” I cannot pity him. His
maxim is, that knowledge is power; and
he thinks <i>his</i> <span class="xxpn" id="p290">{290}</span>
knowledge is all that can be known. He has to learn that <i>our</i>
knowledge, also, is power; and that we know how to use it
too.</p>

<div><i>Enter</i>
<span class="smcap">L<b>ORD</b></span>
<span class="smcap">F<b>LUMM</b>.</span></div>

<p><i>Lord Flumm.</i> There, Lady Selina, so much for your
philosophic friend. Poor Turnstile! What a business he
<i>has</i> made of it. Here is the “Times,” with the report of the
Shoreditch election meeting. Turnstile has no chance. The
Scotchmen coalesce; Highway none of us can think of; and
Smooth and MacLeech walk over the ground in triumph;
and then, the Presidency of Man­u­fac­tures, the <i>very</i> appointment
for which poor Turnstile was fitted (and, to do the
poor devil justice, he could have filled it well), is given to
MacLeech, a Scotch hanger on, or distant cousin of Smooth’s,
and with the old salary, in spite of all that Hume could say
against it.—Bravo! Reform, and the Whigs for ever!—We
Tories could not have done the business in a better style.</p>

<div><i>Enter a Footman.</i></div>

<p><i>Footman.</i> Mr. Turnstile, my Lady, sends up his card.</p>

<p><i>Lady Flumm.</i> Oh, not at home! And Sleek, put a memorandum
in the visiting-book, that we are “out of town,”
whenever Mr. Turnstile calls.</p>

<div class="dkeeptgth clearfix">
<p class="psceneb"><span class="smcap">S<b>CENE</b></span>
XII.—<span class="smcap">T<b>URNSTILE’S</b></span> <i>Parlour. Night.</i>
<span class="smcap">T<b>URNSTILE</b></span>
<i>alone</i>.</p>

<p><i>Turnstile.</i> Then all is up. What a fool have I been to embark
upon this sea of trouble! Two years of trifling and lost time; while
others have been making discoveries and adding to their reputation.
Those <i>rascal</i> Whigs, my blood boils to think of them. I can forgive
the Shoreditch <span class="xxpn" id="p291">{291}</span> people—the
greasy, vulgar, money-getting beasts;—but my friends, the men of
principle<span class="nowrap">——</span> (<i>Getting up and walking
about.</i>)</p></div>

<div class="dkeeptgth">
<p>Is it still too late to return? (<i>Looking round upon his
books and instruments.</i>) There you are, my old friends, whom
I <i>have</i> treated rather ungratefully. What a scene at that
cursed meeting! Highway’s bullying; and the baseness of
Smooth; the sleek, sly, steering of that knave MacLeech;
and yet they <i>must</i> succeed. There’s no help for it. I <i>am</i>
fairly beaten—thrown overboard, with not a leg to stand
upon; and all I have to do is to go to bed now, to sleep off
this fever; and to-morrow, take leave of politics, and try to
be myself once more.</p>

<div class="fsz7 padtopa">END OF THE EXTRACTS.</div>

<p class="fsz7 padtopa">
<i>Note.</i>—The reader will doubtlessly have already discovered that
“Byeways,” with the other <i>dramatis personæ</i> of this squib, are
living characters not unknown in fashionable and political circles.
In a future edition, if it can be done without offence, I may perhaps
be induced to present them to the public without their masks and
buskins.</p></div></div><!--section-->

<div class="section" id="p292">
<h2 class="h2herein">CHAPTER XXIII.
<span class="hsmall">EXPERIENCE AT COURTS.</span></h2>

<div class="dsynopsis">
Pension to Dr. Dalton&#x200a;—&#x200a;Inhabitants of Manchester
subscribe for a Statue by Chantrey&#x200a;—&#x200a;The Author proposed
that he should appear at a Levee&#x200a;—&#x200a;Various difficulties
suggested and removed&#x200a;—&#x200a;The Chancellor approves and
offers to present him&#x200a;—&#x200a;Mentions it to King William
IV.&#x200a;—&#x200a;Difficulties occur&#x200a;—&#x200a;Dalton as a
Quaker could not wear a Sword&#x200a;—&#x200a;Answer, he may go in
his Robes as Doctor of Laws of Oxford&#x200a;—&#x200a;As a Quaker
he could not wear Scarlet Robes&#x200a;—&#x200a;Answer, Dalton is
afflicted with Colour-blindness&#x200a;—&#x200a;Crimson to him
is dirt-colour&#x200a;—&#x200a;Dr. Dalton breakfasts with the
Author&#x200a;—&#x200a;First Rehearsal&#x200a;—&#x200a;Second Rehearsal
at Mr. Wood’s&#x200a;—&#x200a;At the Levee&#x200a;—&#x200a;The
Church in danger&#x200a;—&#x200a;Courtiers jealous of the
Quaker&#x200a;—&#x200a;Conversation at Court sometimes interesting,
oc­ca­sion­al­ly profitable.</div>

<p class="pfirst"><span class="smcap">T<b>HE</b></span>
following letter was ad­dressed by me to Dr. Henry, the
bi­og­ra­pher of Dal­ton, in reply to in­quiries re­spect­ing the part
I had taken in pro­curing a pen­sion for that dis­tin­guished
phi­los­o­pher. It was printed in the “Life of Dalton,” and is
now reprinted from its il­lus­tra­tion of the subject of this
<span class="nowrap">chapter:—</span></p>

<p class="padtopb">“<span class="smcap">M<b>Y</b></span> <span
class="smmaj">DEAR</span> <span class="smcap">S<b>IR</b>,</span>—I have
now examined my papers, as far as I can, to find any traces of Dalton
amongst them. I find only two letters, of which I send you copies.</p>

<p>“I well remember taking a great interest in Dalton’s pension, as you
will see by several passages in ‘The Decline of Science,’ pp. 20 and
22, and note; but I have no recollection of any of the circumstances,
or through what channel it was applied for. <span class="xxpn"
id="p293">{293}</span></p>

<p>“I find several letters of that date from Mr. Wood,<a class="afnanc"
href="#fn41" id="fnanc41">41</a> and it appears from them that I
went with him to Poulett Thomson;<a class="afnanc" href="#fn42"
id="fnanc42">42</a> but I only gather this fact from those letters. I
send them in the enclosure, as they may be of use. You can return them
at your own convenience.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc41" id="fn41">41</a>
Member for South Lancashire.</p>

<p class="pfirst padtopc"><a class="afnlabel" href="#fnanc42" id="fn42">42</a>
Afterwards Lord Sydenham.</p></div>

<div class="dsdnote">〈STATUE OF DALTON.〉</div>

<p>“When the inhabitants of Manchester had subscribed
2,000&#x200a;<i>l.</i> for a statue of Dalton, he came up to London, and
was the guest of Mr. Wood. He sat to Chantrey for the
statue. I consequently saw much of my friend. It occurred
to me that, as his townsmen were having a statue of him—as
the University of Oxford had given him the honorary degree
of Doctor of Laws—and as the Government had given him a
pension—if it were not incompatible with his feelings, it would
be a fit thing that he should be presented at a levee. It
appeared to me that if William the Fourth were informed of
it, it would afford him an opportunity of saying a few words
to the venerable phi­los­o­pher, which would be gratifying to
the inhabitants of Manchester, the University of Oxford, and
the world of science.</p>

<p>“Accordingly I wrote a note to Mr. Wood, suggesting the
idea, and proposing that he should ascertain from Doctor
Dalton whether it would be unpleasant to him to go through
the usual forms.</p>

<p>“Dalton not objecting, my note was sent on by Mr. Wood
to Lord Brougham, who at that time was Lord Chancellor.
He approved highly of the plan, and offered to present
Doctor Dalton. He also mentioned the circumstance to the
King.</p>

<p>“I had had some conversation with Mr. Wood upon the subject, when
several difficulties presented themselves to him. Doctor Dalton, as a
Quaker, could not appear in a <span class="xxpn" id="p294">{294}</span>
court-dress, because he must wear a sword. To this I replied, that
being aware of the difficulty, I had proposed to let him wear the robes
of a Doctor of Laws of Oxford.</p>

<p>“Mr. Wood remarked, that those robes being <i>scarlet</i>, they
were not of a colour admissible by Quakers.</p>

<p>“To this I replied, that Doctor Dalton had a kind of
<i>colour-blindness</i>, and that all red colours appeared to him to
be the colour of dirt. Besides, I had found that our friend
entertained very reasonable views of such mere matters of
form. The velvet cap of the Doctor again was not an
obstacle, as he was informed that it was usually held in the
hand, and was rather a mark of office than a covering for
the head.</p>

<p>“These difficulties being surmounted, Doctor Dalton came
one morning to breakfast with me. We were alone; and
after breakfast he went up with me into the drawing-room, in
order to see the Difference Engine. After we had made
several series of calculations, he recollected that he had in his
pocket a note to me from Mr. Wood. On hastily looking
it over, I found that it was to announce to me that our friend
acquiesced in the plan.</p>

<div class="dsdnote">〈FIRST REHEARSAL OF A LEVEE.〉</div>

<p>“I now mentioned the forms usual at a levee, and placing
several chairs in order to represent the various officers in the
Presence-chamber, I put Doctor Dalton in the middle of the
circle to represent the King. I then told my friend that I
should represent a greater man than the King; that I intended
to personate Doctor Dalton, and would re-enter at the
further door, go round the circle, make my obeisance to the
King, and thus show him the kind of ceremony at which he
was to assist.</p>

<p>“On passing the third chair from the King’s, I put my
card on the chair, at the same time
informing Doctor Dalton <span class="xxpn" id="p295">{295}</span>
that this was the post of a Lord in Waiting, who takes the
cards, and gives them to the next officer, who announces them
to the King.</p>

<p>“On passing the phi­los­o­pher I kissed his hand, and then
passing round the rest of the circle of chairs, I thus gave him
his first lesson as a courtier.</p>

<p>“It was arranged that I should take Doctor Dalton with
me to the levee, and put on his card, ‘Doctor Dalton, presented
by the Lord Chancellor.’</p>

<div class="dsdnote">〈FULL DRESS REHEARSAL OF LEVEE.〉</div>

<p>“When the morning arrived I went to Mr. Wood’s residence,
and found Doctor Dalton quite ready for the expedition.
In order to render the chief actor perfect in his part,
we again had a rehearsal; Mrs. Wood personating the King,
and the rest of the family, with the assistance of sundry chairs
and stools, representing the great Officers of State. I then
entered the room, preceding my excellent friend, who followed
his in­struc­tions as perfectly as if he had been repeating
an experiment.</p>

<p>“Being now quite satisfied with the performance, we
drove off to St. James’s. The robes of a Doctor of Laws are
rarely made use of, except at a University Address: consequently
Dr. Dalton’s costume attracted much attention, and
compelled me to gratify the curiosity of many of my friends,
by explaining who he was. The prevailing opinion had been
that he was the Mayor of some corporate town come up to get
knighted. I informed my inquirers, that he was a much
more eminent person than any Mayor of any city, and having
won for himself a name which would survive when orders of
knighthood should be forgotten, he had no ambition to be
knighted.</p>

<div class="dsdnote">〈THE CHURCH IN DANGER.〉</div>

<p>“At a short distance from the Presence-chamber, I observed
close before me several dignitaries of
the church, in <span class="xxpn" id="p296">{296}</span>
the full radiance of their vast lawn sleeves. The Bishop
of Gloucester,<a class="afnanc" href="#fn43" id="fnanc43">43</a>
who was nearest, accidentally turning his
head, I recognized a face long familiar to me from its
cordiality and kindness. A few words were interchanged
between us, and also by myself with the rest of the party,
the remotest of whom, if I remember rightly, was the Archbishop
of Dublin. The dress of my friend seemed to strike
the Bishop’s attention; but the quiet costume of the Quaker
beneath his scarlet robe was entirely unnoticed. I therefore
confided to the Bishop of Gloucester the fact that I had a
Quaker by my side, at the same time assuring him that my
peaceful and philosophic friend was very far from meditating
any injury to the Church. The effect was electric upon the
whole party; episcopal eyes had never yet beheld such a
spectacle in such society, and I fear, not­with­stand­ing my assurance,
some portion of the establishment thought the Church
really in danger.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc43" id="fn43">43</a>
Dr. Monk.</p></div>

<p>“We now entered the Presence-chamber, and having
passed the King, I retired very slowly, in order that I might
observe events. Doctor Dalton having kissed hands, the
King asked him several questions, all which the phi­los­o­pher
duly answered, and then moved on in proper order to join
me. This reception, however, had not passed with sufficient
rapidity to escape jealousy, for I heard one officer say to
another, ‘Who the d—l is that fellow whom the King keeps
talking to so long?’</p>

<div class="dsdnote">〈INTERESTING CONFIDENCES AT A LEVEE.〉</div>

<p>“Conversations at Courts are not always thought to be
the most interesting things in the world; although, doubtless,
they must be so to the parties engaged in them. In the
midst of crowded levees and drawing-rooms, one is often
compelled to become the confidant of
strangers around us. <span class="xxpn" id="p297">{297}</span>
The amusement derived from this source predominates over
the in­struc­tion. I have heard much anxious inquiry as to
certain pieces of clerical preferment—who is to have certain
military or colonial commands, and what promotions will
take place from the consequent vacancies?—many political
queries have been proposed, and how ‘the party’ would act
in certain contingent cases? I once heard a gentleman
receive at a levee the first announcement of a legacy; on
another occasion, on my return from the Continent, I was
myself informed at a levee of a similarly gratifying, and to
me entirely unexpected, event.</p>

<p>“Doctor Dalton having now passed through the formal
part of a levee, had a better opportunity of viewing the
details. He inquired the names of several of the portraits,
and I took the opportunity of pointing out to him many of
the living celebrities.</p>

<div class="dkeeptgth">
<p>“We then returned to Mr. Wood’s residence, and the whole party were
highly gratified at the success of the undertaking.</p>

<p class="pcompclose"> “I am, my dear Sir, very truly yours,</p>

<p class="psignature">“C. <span class="smcap">B<b>ABBAGE</b>.</span></p>

<p class="phanga fsz7">“<i>Dorset Street, Manchester Square,<br />
February 7, 1854.</i>”</p></div></div><!--section-->

<div class="section" id="p298">
<h2 class="h2herein">CHAPTER XXIV.
<span class="hsmall">EXPERIENCE AT COURTS.</span></h2>

<div class="dsynopsis">
The Author invited to a Meeting at Turin of the Phi­los­o­phers
of Italy, 1840&#x200a;—&#x200a;The King, Charles
Albert&#x200a;—&#x200a;Reflections on Shyness&#x200a;—&#x200a;Question
of Dress&#x200a;—&#x200a;Electric Telegraph&#x200a;—&#x200a;Theory
of Storms&#x200a;—&#x200a;Remark of an Italian Friend in the evening
at the Opera&#x200a;—&#x200a;Various Instruments taken to the
Palace, and shown to the young Princes&#x200a;—&#x200a;The Queen
being absent&#x200a;—&#x200a;The reason why&#x200a;—&#x200a;The
young Princes did great credit to their Governor&#x200a;—&#x200a;The
General highly gratified&#x200a;—&#x200a;The Phi­los­o­pher proposes
another difficult question&#x200a;—&#x200a;It is referred to the King
himself&#x200a;—&#x200a;An audience is granted to ask the King’s
permission to present the woven Silk Engraving of Jacquard to Her
Majesty&#x200a;—&#x200a;Singular but Comic Scene&#x200a;—&#x200a;The
final Capture of the Butterflies&#x200a;—&#x200a;Visit to
Raconigi&#x200a;—&#x200a;The Vintage.</div>

<p class="pfirst"><span class="smcap">A<b>BOUT</b></span> a quarter of
a century ago the Court of Turin had the reputation of being the most
formal and punctilious of any in Europe. It was dull to the diplomatic
officials, who were doomed like planets to circulate around it, though
not without interest to the inquiring traveller, whose orbit, like that
of a comet, passed through its atmosphere only at distant intervals.</p>

<p>In 1840 I received a gratifying invitation to meet the <i>élite</i>
of the science of Italy at Turin. On my arrival I immediately
took measures to pay my respects in the usual manner
to the sovereign of the country. Having inquired of a
nobleman<a class="afnanc" href="#fn44" id="fnanc44">44</a>
high in the confidence of the King, when there
<span class="xxpn" id="p299">{299}</span>
would occur a levee, in order that I might have the honour
of being presented, I was informed that his Majesty was
aware of my arrival, and would receive me at a private
audience. Two days after I had a formal visit from Count
Alessandro Saluzzo to inform me that the King would receive
me the next day at two o’clock.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc44" id="fn44">44</a>
Conte D. Alessandro Saluzzo di Monesiglio, Grande di Corona, Presid.
della sexiare dell’ interno nel consiglio di stato, &amp;c.</p></div>

<div class="dsdnote">〈THE COURT OF TURIN IN 1840.〉</div>

<p>I then made inquiries as to the usual dress, and found that
a court dress was not considered essential on such occasions,
especially for a foreigner, and that I might with perfect propriety
go in plain clothes. I was glad to avail myself of this
permission; but in order to prevent any misapprehension, I
drove up to the palace about a quarter of an hour before the
appointed time, and called upon General Cesare de Salluce,<a class="afnanc" href="#fn45" id="fnanc45">45</a>
the governor of the two young princes, the present King of
Italy and the late Duke of Genoa, then respectively about
eighteen and seventeen years of age.</p>

<p>The General kindly offered to accompany me to the antechamber.
In the course of our conversation I took an opportunity
of mentioning that, having been informed I might
appear in plain clothes, I had thought it most respectful to
his sovereign to wear the same dress I had worn a few days
before I left England, when I had the honour of being invited
to the first party<a class="afnanc" href="#fn46" id="fnanc46">46</a>
given by a subject to my own sovereign.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc45" id="fn45">45</a>
Saluzzo di Monesiglio, Car. Cesare, Luogoten, Gen., Gran Mastro
d’Artiglieria et Governatore de Reali Principi, &amp;c.; the younger brother
of the Count Alexander.</p>

<p class="pfirst padtopc"><a class="afnlabel" href="#fnanc46" id="fn46">46</a>
The déjeûné at Wimbledon Park, the residence of the late Duke of
Somerset.</p></div>

<p>I had already been informed that the King, Charles Albert,
took a great interest in the success of the meeting; that he
was a very good man, but remarkably shy; and that he probably
would not detain me more than perhaps five minutes.</p>

<p>I had myself experienced the misery of that affliction, and
<span class="xxpn" id="p300">{300}</span>
felt how much more painful it must inevitably become when
it fell to the lot of a person placed in the most exalted
rank.</p>

<div class="dsdnote">〈RECEPTION OF THE PHI­LOS­O­PHER.〉</div>

<p>On entering the ante-room I found a number of the most
distinguished people of the country waiting for audience,
the king at that time being occupied, as I was informed, with
one of his ministers. On his exit the master of the ceremonies
announced that his Majesty would receive me.</p>

<p>I then entered the royal reception-room, and was presented
to the King. He was a remarkably tall person, dressed
in military costume, having a very peculiar expression of
countenance, which I was at a loss how immediately to interpret.
The King invited me to sit down, and I followed his
Majesty to a large bay-window, where we immediately sat
down on two stools opposite to each other.</p>

<p>The King expressed his sat­is­fac­tion that I had come from
so considerable a distance to assist at the councils of the
men of science then assembling in his own capital. Of course
I replied by remarking that the advancement of the sciences
contributed to the material as well as to the in­tel­lec­tual progress
of every nation, and that when a sovereign, intimately
convinced of this truth, took measures for the extension and
diffusion of knowledge, it was the duty of all those engaged in
its cultivation respectfully to assist as far as their individual
circumstances permitted.</p>

<p>After a short pause, the King put some question which I
do not remember, except that it was one of the conventional
topics of society: perhaps it might have related to my
journey. I now felt that unless I could raise some question
of curiosity in his Majesty’s mind, to overcome his natural
reserve, the interview would soon terminate precisely in the
manner predicted. I therefore, in replying
to this question, <span class="xxpn" id="p301">{301}</span>
contrived to introduce a remarkable fact relative to the
electric telegraph. I soon perceived that it had taken hold
of the King’s imagination, and the next question confirmed
my view. “For what purposes,” said the King, “will the
electric telegraph become useful?”</p>

<p>I must here request the reader to go back in his memory
to the state of our knowledge in 1840, when electricity and
other subjects, now of every-day application, were just commencing
their then eccentric but now regulated course.</p>

<div class="dsdnote">〈THEORY OF STORMS—ELECTRIC TELEGRAPH.〉</div>

<p>The King put the very question I had wished. Carefully
observing his countenance, I felt that I was advancing in a
tract in which he was interested. At each pause the proper
question was suggested, and at last I pointed out the probability
that, by means of the electric telegraphs, his Majesty’s
fleet might receive warning of coming storms. This led to
the new theory of storms, about which the king was very
curious. By degrees I endeavoured to make it clear. I cited,
as an illustration, a storm which had occurred but a short
time before I left England. The damage done by it at
Liverpool was very great, and at Glasgow immense. On one
large property in the west coast of Scotland thirty thousand
timber-trees had been thrown down.</p>

<p>I then explained that by subsequent inquiries it had been
found that this storm arose from the overlapping of two circular
whirlwinds, one of them coming up from the Atlantic bodily
at the rate of twenty miles an hour, the other passing at the
rate of twelve miles an hour, in a north-westerly direction, to
Glasgow, where they coalesced, and destroyed property to the
value of above half a million sterling. I added that if there
had been electric communication between Genoa and a few
other places the people of Glasgow might have had information
of one of those storms twenty-four hours
previously to its <span class="xxpn" id="p302">{302}</span>
arrival, and could then have taken effective measures for the
security of much of their shipping.</p>

<div class="dsdnote">〈THE PHI­LOS­O­PHER TROUBLED WITH A CONSCIENCE.〉</div>

<p>During this conversation I had felt rather uneasy at occupying
the king’s time so long when several of his own ministers
were waiting in his ante-room for an audience, perhaps upon
important business. Urged by this truly conscientious motive,
I committed a <i>gaucherie</i> of the deepest water—I half rose
from my stool to take leave of his Majesty. The King, as
well he might, lifted up both his hands and then expressed
the greatest interest in the continuance of the subject.</p>

<p>After a conversation of about five-and-twenty minutes the
King rose, and, walking with me to the door, I made my bow.
The King then held out his hand.</p>

<p>Here might have arisen a puzzling question, what I ought
to have done; but previously to the interview I had taken
the precaution of inquiring of one of my Sardinian friends
what were the usual forms, and whether it was customary to
kiss hands on being presented to the sovereign. The answer
was in the negative. The ceremony of kissing hands, he
informed me, never took place except when a native subject
was appointed to some very high office.</p>

<p>I therefore immediately perceived that the King had done
me the honour of adopting the salutation of my own country.
Under these circumstances I shook hands as an Englishman
does, and then, bowing profoundly, retired.</p>

<p>In the course of the evening of that day, being at the
opera, I visited the box of one of my Italian acquaintances.
A great friend of mine, also an Italian, who had been dining
at the palace, came in soon after. He said to me, “What an
extraordinary person you are! You have perfectly fascinated
our King, who has done nothing but talk of you and the
things you have told him during the
whole of dinner-time.” <span class="xxpn" id="p303">{303}</span></p>

<p>I admit I felt great sat­is­fac­tion at this announcement of
the complete success of my daring experiment. It assured
me that my unusual deviation from the routine of a Court was
fully justified by the interest the matter communicated had
awakened in the King’s mind.</p>

<div class="dsdnote">〈EXHIBITS VARIOUS INSTRUMENTS.〉</div>

<p>I had brought with me to Turin several models and various
instruments connected with science and mechanical art, which
of course had been examined by many of my scientific and
personal friends. Unfortunately, on two occasions, when
General de Salluce, who was much my senior in years, called
upon me, I happened to be absent from the house. Knowing
how fully his time was occupied by his illustrious pupils, I
much regretted that I had not been at home when he called,
and during one of my visits at the palace I offered to bring
with me, on another occasion, some of the things I thought
might be most interesting.</p>

<p>The General could not think of giving me that trouble, and
at first very courteously declined the proposal. But after a
moment or two he said, “On second thoughts, I will accept
your kind offer, because I think it may be useful to my
young pupils.”</p>

<p>On the morning proposed I drove up to the palace with
some boxes containing the various apparatus, and was immediately
shown into a large room nearly at the top of the
palace. After opening the boxes and giving the General a
glance at the various articles, I remarked that several of
them were interesting to ladies, and that possibly the Queen,
if made acquainted with it, might like to accompany her
sons; in which case it would, perhaps, be more convenient for
her Majesty if they were placed in a lower room of the
palace.</p>

<div class="dsdnote">〈THE QUEEN UNABLE TO COME.〉</div>

<p>The idea appeared a happy one; the
General was much <span class="xxpn" id="p304">{304}</span>
pleased at it, and said he would go immediately and take her
Majesty’s pleasure on the subject. After considerable delay
General de Salluce returned, evidently much disappointed,
and said he was commanded by the Queen to thank me for
the attention, and to express her Majesty’s regret that she
was prevented by an engagement from accompanying the
young Princes.</p>

<p>When everything was arranged, and the hour appointed
had arrived, the young Princes, accompanied by, I presume,
various members of the royal household, and their Governor,
arrived. Altogether there might have been about a dozen or
fourteen persons of both sexes present.</p>

<p>I pointed out the use and structure of most of the instruments.
Some objects belonged to mechanical art, such as
patent locks and tools; a few were related to the Fine Arts.</p>

<p>The whole party seemed much pleased; the young Princes
par­tic­u­lar­ly took a great interest in them, whereat the General
was highly gratified. Before his young pupils retired, I took
the General aside and inquired whether it was consistent with
their customs that I should present to each of his two pupils
one of the various (but in a pecuniary sense trifling) articles
which they had examined. I was glad to find that I might
be permitted to leave behind me two little souvenirs of a
most agreeable day.</p>

<p>The whole party, with the exception of General de Salluce,
had now retired. We walked up and down the room together
for some time, conversing upon the success of the meeting.
My excellent friend was justly delighted with the intelligent
inquiries made by his pupils.</p>

<p>I thought I now perceived a favourable opportunity of
ascertaining the cause of the Queen’s absence.</p>

<p>After some kind expression towards me,
I suddenly stopped, <span class="xxpn" id="p305">{305}</span>
and, looking inquiringly into his countenance, said, “Now,
General, just before this very agreeable party met you went
to invite the Queen, and you returned and then told me the
<i>official</i>. Now pray do tell me the <i>real</i>.”</p>

<div class="dsdnote">〈THE REASON EXPLAINED.〉</div>

<p>The surprise of the General was certainly great, but, with a
most agreeable smile, he immediately consented.</p>

<p>It appears that its history was thus. The General went to
the Queen’s apartments and asked, through her lord-in-waiting,
to be permitted to see her Majesty. This request was
immediately granted. The General then informed the Queen
that amongst the things her sons were going to see were
several which might, perhaps, interest her Majesty. The
Queen said she would accompany her sons, and then directed
her own lord-in-waiting to go and ask the King’s permission.</p>

<p>Accordingly the Queen’s lord-in-waiting went to the King’s
apartments, and found that he was sitting in Council. He
proceeded to the ante-room of the Council-chamber, and there
found the King’s lord-in-waiting, to whom he communicated
his mission.</p>

<p>The King’s lord-in-waiting then informed the Queen’s lord-in-waiting
that important news<a class="afnanc" href="#fn47" id="fnanc47">47</a>
had just arrived, and that a
special council had been called; that of course he was ready
to convey the Queen’s message immediately, but he suggested
whether, under these circumstances, the Queen would wish it.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc47" id="fn47">47</a>
The Syrian question.</p></div>

<p>The Queen’s lord-in-waiting now returned to her Majesty
for further in­struc­tions.</p>

<p>Of course the Queen, like a good wife, at once gave up the
intention of accompanying her sons in their interview with
the phi­los­o­pher. I felt much regret at this disappointment.
The Queen of Sardinia was the sister of the Grand Duke of
Tuscany (Leopold II.), from whom I had, many years before,
<span class="xxpn" id="p306">{306}</span>
when under severe affliction from the loss of a large portion
of my family, received the most kind and gratifying attention.</p>

<div class="dsdnote">〈THE WOVEN PORTRAIT.〉</div>

<p>On my road to Turin I had passed a few days at Lyons, in
order to examine the silk man­u­fac­ture. I was specially
anxious to see the loom in which that admirable specimen of
fine art, the portrait of Jacquard, was woven. I passed many
hours in watching its progress.</p>

<p>I possessed one copy, which had been kindly given to
me by a friend; but as I had proposed to visit Florence after
the meeting at Turin, I wished to procure another copy to
present to the Grand Duke of Tuscany.</p>

<p>These beautiful productions were not made for sale; but,
as a favour, I was allowed to purchase one of them.</p>

<p>Whilst the General was giving me this illustration of Court
etiquette, it occurred to me that the silken engraving would
be an appropriate offering to a lady.</p>

<p>I therefore again asked my friend whether, consistently
with the usages of the country, I might be permitted to offer
the engraving to the Queen.</p>

<p>The sudden change of his countenance from gay to grave
was very remarkable. I feared I had proposed something of
the most unusual kind. The General then slowly replied, “I
will take the King’s pleasure on the subject.”</p>

<p>Two days after the General informed me that the King
would give me an audience the next day, in order that I
might ask permission to present the woven engraving to the
Queen.</p>

<p>Accordingly, at the appointed hour, I went to the palace
with the large cartoon-case containing the portrait of Jacquard.<a class="afnanc" href="#fn48" id="fnanc48">48</a>
On being admitted into the presence of the King,
I placed the case upon a sofa, and,
opening it carefully, <span class="xxpn" id="p307">{307}</span>
unfolded the woven portrait from a crowd of sheets of silver
paper of the most ethereal lightness. I then placed it in his
Majesty’s hands. The King examined it minutely on both
sides, inquired about its structure, and appeared much pleased
at the sight.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc48" id="fn48">48</a>
The dimensions were 2 ft. 8 in. by 2 ft. 2 in.</p></div>

<div class="dsdnote">〈A FLIGHT OF BUTTERFLIES.〉</div>

<p>I now went over to replace the engraving in its travelling-carriage.
The instant it approached its paper case a multitude
of sheets of silver paper were disturbed in their snug
repose, and forthwith flew up into the air. I made many ineffectual
efforts to catch these runaways. The King most
condescendingly came to my assistance, took the portrait out
of my hands, and endeavoured himself to replace it in its
nest, whilst I was attempting to catch the flying covey.</p>

<p>But these volatile papers had no proper respect even for
royalty. The quires of silver paper which had remained in the
case now came out in all directions, whether to do honour to
the King by rising to receive him, or to recall their flighty
sisters to their deserted couch I know not; but somehow or
other both the King and myself were on the floor upon our
knees, having secured some few of the fallen angels, whilst
a cloud of others, still on the wing, continually eluded our
grasp.</p>

<p>At last I gave up the idea of grabbing at the flying sheets,
and confined my attention to seizing on the fallen ones.
While still on my knees, I suddenly felt an obstacle presented
to my right foot. On looking round I perceived that
the heel of royalty had come into contact with the toe of
philosophy.</p>

<p>A comic yet kindly smile beamed upon the countenance of
the King, whilst an irrepressible but not irreverent one,
lightened up my own.</p>

<p>The whole army of butterflies being at
last captured, and <span class="xxpn" id="p308">{308}</span>
the engraving replaced, the King entered into a conversation
with me upon various subjects.</p>

<div class="dsdnote">〈THE VINTAGE AT RACONIGI.〉</div>

<p>The processes of wine-making then became the subject of
conversation. I believe I may have observed incidentally in
reply to some question, that my information was only derived
from books, as I had not had an opportunity of seeing any of its
processes. About a week after this, one of the officers of the
household called upon me, and told me that the vintage of
Raconigi, one of the King’s beautiful domains, at about a dozen
miles from Turin, would commence in the following week;
that he was commanded by his Majesty, in case I should wish
to examine the processes, to inform me of the circumstance,
and to accompany me for the purpose of explaining them—a
mission, he was so kind as to add, which would personally be
highly gratifying to himself.</p>

<p>I willingly accepted this most agreeable proposition, and
the day was fixed upon. At an early hour my friend was at
my door in one of the royal carriages. The weather was
magnificent, and we drove through a beautiful country.</p>

<p>On arriving at the vineyard we found several of the processes
in full operation. Each in succession was explained;
and after spending a most instructive morning, we found an
excellent dinner prepared for us at the palace, where I had
the pleasure of meeting General ——, who presided, and
who had spent several years in England.</p>

<p>On our return in the evening I observed a dragoon apparently
accompanying the carriage. At first I took it for
granted that his road happened to be the same as ours; but
after a mile or two had been passed over, seeing him still
close to us, I inquired of my companion if he knew whither
the soldier was going. It then appeared that he had been
sent by the General as
a complimentary escort. <span class="xxpn" id="p309">{309}</span></p>

<p>However gratified I felt by this attention, I still was quite
uncomfortable at the idea of having a man galloping after
our carriage for ten miles. I therefore appealed to my
friend to suspend this unnecessary loss of <i>vis viva</i>. With
some reluctance the dragoon was exempted from further
attendance upon the phi­los­o­pher.</p>

<p>Shortly before I left Turin, one of my Italian friends remarked,
with evident feelings of pride and sat­is­fac­tion, upon
the attentions I had received from his sovereign. “The King,
he observed, has done three things for you, which are very
<span class="nowrap">unusual—</span></p>

<p>“He has shaken hands with you.</p>

<p>“He has asked you to sit down at an audience.</p>

<p>“He has permitted you to make a present to the Queen.
This last,” he added, “is the rarest of all.”</p>

<hr class="hrblk" />

<div class="dsdnote">〈AUDIENCE TO TAKE LEAVE.〉</div>

<p>Two days before my departure from Turin, I had an
audience, to take leave of his Majesty. The King inquired in
what direction I intended to travel homeward. I mentioned
my intention of taking the mail to Geneva, because it traversed
a most remarkable suspension-bridge over a deep ravine.
The span of this bridge, which is named, after the king, Pont
Charles Albert, is six hundred French feet, and the depth of
the chasm over which it is suspended is also six hundred
French feet. The King immediately opened a drawer, and,
taking out a small bronze medal, struck to celebrate the
opening of the bridge, presented it to me.</p>

<p>I now took the opportunity of expressing to the King my
gratitude for the many and kind attentions I had received from
his subjects, and more especially for the honour he had himself
recently done me by sending one of his ministers officially to
convey to me his Majesty’s high approbation
of my conduct. <span class="xxpn" id="p310">{310}</span>
The King then entered upon another course of inquiry,
more immediately connected with his government. I had on
several occasions, when a favourable opportunity presented
itself, drawn the King’s attention to the doctrine of free trade—a
subject on which he evidently felt a great desire to be
informed. The questions put to me, though necessary for
assisting the King to arrive at right conclusions, were of such
a nature that I considered them confidential, and therefore
forbear to relate them.</p>

<p>Two days after I started by the mail for Geneva. I shared
the Coupé of the Malle Poste with the courier, a very
intelligent officer. On mentioning my wish to see the celebrated
bridge, he informed me that he was already aware of
my wishes, and that he had received orders to detain the mail
a quarter of an hour, that I might have a good opportunity
of seeing it.</p>

<div class="dsdnote">〈THE PONT CHARLES ALBERT.〉</div>

<p>The scene which presented itself on my approach to the
Pont Charles Albert was singularly grand. We had been
driving for some time along a road skirting the edge of an
immense chasm, six hundred and forty English feet in depth.
The opposite side was hid from our view by a mist which
hung over it. At the next bend in the road a portion of the
bridge suddenly became visible to us. It appeared to spring
from a massive pier on which the chains on our side of the
ravine rested. The bridge itself was nearly level, and was
visible for about three-quarters only of its length as it traversed
the valley far beneath it. The termination of the
ascending portion of the chains on the further pier, and that
part of the bridge itself, were completely concealed by the
mist. It really seemed like a bridge springing from a lofty
cliff spanning the sea beneath and suspended on the distant
clouds. When we had descended from the
mail at the <span class="xxpn" id="p311">{311}</span>
commencement, we had directed the postilions to drive slowly
across the bridge, then about a third of a mile distant
from us.</p>

<div class="dsdnote">〈ITS MYSTIC SCENERY.〉</div>

<p>We were singularly favoured by circumstances. We saw
the carriage which had just left us apparently crossing the
bridge, then penetrating into the clouds, and finally becoming
entirely lost to our view. At the same time the dissolving
mist in our own immediate neighbourhood began to
allow us to perceive the depth of the valley beneath, and at
last even the little wandering brook, which looked like a
thread of silver at its bottom.</p>

<p>The sun now burst out from behind a range of clouds,
which had obscured it. Its warm rays speedily dissipated the
mist, illuminated the dark gulf at our own side, and discovered
to us the mail on terra firma on the opposite side of the chasm
waiting to convey us to our destination.</p>

<p>On our arrival at Annecy, my thoughtful companion informed
me that the mail would wait five-and-forty minutes.
He suggested, as I was not in good health, that I should immediately
on my arrival get into bed, whilst he would order tea,
or supper, or any refreshment I might prefer, and that he
would be answerable for calling me at the proper time to
enable me to get comfortably whatever I might require, and
be ready to start again with the mail.</p>

<hr class="hrblk" />

<p>I have frequently attempted to assign in my own mind the
reasons of the singularly favourable reception I met with from
the King of Sardinia. The reputation arising from the Analytical
Engine could scarcely have produced that effect. The
position of a sovereign is a very exceptional one. He is
surrounded by persons each of whom has always one or more
objects to gain. It is scarcely within the
limits of possibility <span class="xxpn" id="p312">{312}</span>
that he can have a real friend, or if he have that rarest
commodity, that he can know the fact.</p>

<div class="dsdnote">〈ELEMENTS OF MY SUCCESS AT TURIN.〉</div>

<p>A certain amount of distrust must therefore almost always
exist in his mind. But this habitual distrust applies less to
foreigners than to his own subjects. The comet which passes
through the thick atmosphere of a Court may be temporarily
disturbed in its path though it may never revisit it again.</p>

<p>Perhaps the first element of my success was, that having
been the victim of shyness in early life, I could sympathise
with those who still suffered under that painful complaint.</p>

<p>Another reason may have been, that I never stated more
than I really knew. This is, I believe, a very unusual practice
in Courts of <i>every</i> kind; and when it happens to be obviously
sincere, it commands great influence.</p>

<p>There might be yet another reason:—it was well known
that I had nothing to ask for—to
expect—or to desire.</p></div><!--section-->

<div class="section" id="p313">
<h2 class="h2herein">CHAPTER XXV.
<span class="hsmall">RAILWAYS.</span></h2>

<div class="dsynopsis">
Opening of Manchester and Liverpool Railway&#x200a;—&#x200a;Death
of Mr. Huskisson&#x200a;—&#x200a;Plate-glass
Manufactory&#x200a;—&#x200a;Mode of separating Engine from
Train&#x200a;—&#x200a;Broad-gauge Question&#x200a;—&#x200a;Experimental
Carriage&#x200a;—&#x200a;Measure the Force of Traction, the
Vertical, Lateral, and End Shake of Carriage, also its Velocity by
Chronometer&#x200a;—&#x200a;Fortunate Escape from meeting on the
same Line Brunel on another Engine&#x200a;—&#x200a;Sailed across the
Hanwell Viaduct in a Waggon without Steam&#x200a;—&#x200a;Meeting
of British Association at Newcastle&#x200a;—&#x200a;George
Stephenson&#x200a;—&#x200a;Dr. Lardner&#x200a;—&#x200a;Suggestions for
greater Safety on Railroads&#x200a;—&#x200a;George Stephenson’s Opinion
of the Gauges&#x200a;—&#x200a;Railways at National Exhibitions.</div>

<p class="pfirst"><span class="smcap">A<b>T</b></span>
the commencement of the railway system I naturally
took a great interest in the subject, from its bearings upon
mechanism as well as upon political economy.</p>

<p>I accompanied Mr. Woolryche Whitmore, the member
for Bridgenorth, to Liverpool, at the opening of the Manchester
and Liverpool Railway. The morning previous to
the opening, we met Mr. Huskisson at the Exchange, and my
friend introduced me to him. The next day the numerous
trains started with their heavy load of travellers. All went
on pleasantly until we reached Parkside, near Newton.
During the time the engines which drew us were taking in
their water and their fuel, many of the passengers got out and
recognized their friends in other trains.</p>

<p>At a certain signal all resumed their seats;
but we had <span class="xxpn" id="p314">{314}</span>
not proceeded a mile before the whole of our trains came to a
stand-still without any ostensible cause. After some time
spent in various conjectures, a single engine almost flew past
us on the other line of rail, drawing with it the ornamental
car which the Duke of Wellington and other officials had so
recently occupied. Instead of its former numerous company
it appeared to convey only two, or at most three, persons; but
the rapidity of its flight prevented any close ob­ser­va­tion of
the passengers.</p>

<div class="dsdnote">〈FATAL ACCIDENT TO MR. HUSKISSON.〉</div>

<p>A certain amount of alarm now began to pervade the
trains, and various conjectures were afloat of some serious
accident. After a while Mr. Whitmore and myself got out
of our carriage and hastened back towards the halting place.
At a little distance before us, in the middle of the railway,
stood the Duke of Wellington, Sir Robert Peel, and the
Boroughreeve of Manchester, discussing the course to be
pursued in consequence of the dreadful accident which had
befallen Mr. Huskisson, whom I had seen but a few minutes
before standing at the door of the carriage conversing with
the Duke of Wellington. The Duke was anxious that the
whole party should return to Liverpool; but the chief officer
of Manchester pressed upon them the necessity of continuing
the journey, stating that if it were given up he could not be
answerable for the safety of the town.</p>

<p>It was at last mournfully resolved to continue our course
to Manchester, where a luncheon had been prepared for us;
but to give up all the ceremonial, and to return as soon as we
could to Liverpool.</p>

<p>For several miles before we reached our destination the
sides of the railroad were crowded by a highly-excited populace
shouting and yelling. I feared each moment that some
still greater sacrifice of life might occur
from the people <span class="xxpn" id="p315">{315}</span>
madly attempting to stop by their feeble arms the momentum
of our enormous trains.</p>

<div class="dsdnote">〈GREAT DELAY—RUMOURS OF DISASTER.〉</div>

<p>Having rapidly taken what refreshment was necessary,
we waited with anxiety for our trains; but hour after hour
passed away before they were able to start. The cause of
this delay arose thus. The Duke of Wellington was the
guest of the Earl of Wilton, the nearest station to whose
residence was almost half way between Manchester and
Liverpool. A train therefore was ordered to convey the
party to Heaton House. Unfortunately, our engines had
necessarily gone a considerable distance upon that line to get
their supply of water, and were thus cut off by the train conveying
the Duke, from returning direct to Manchester.</p>

<p>There were not yet at this early period of railway history
any sidings to allow of a passage, or any crossing to enable
the engines to get upon the other line of rails. Under these
circumstances the drivers took the shortest course open to
them. Having taken in their water, they pushed on as fast
as they could to a crossing at a short distance from Liverpool.
They backed into the other line of rail, and thus returned to
Manchester to pick up their trains.</p>

<p>In the meantime the vague rumour of some great disaster
had reached Liverpool. Thousands of persons, many of
whom had friends and relatives in the excursion trains,
were congregated on the bridges and at the railway station,
anxious to learn news of their friends and relatives.</p>

<p>About five o’clock in the evening they perceived at a
distance half-a-dozen engines without any carriages, rushing
furiously towards them—suddenly checking their speed—then
backing into the other line of rail—again flying away towards
Manchester, without giving any signs or explanation of the
mystery in which many of them were
so deeply interested. <span class="xxpn" id="p316">{316}</span></p>

<p>It is difficult to estimate the amount of anxiety and misery
which was thus unwillingly but inevitably caused amongst
all those who had friends, connections, or relatives in the
missing trains.</p>

<p>When these engines returned to Manchester, our trains
were unfortunately connected together, and three engines
were attached to the front of each group of three trains.</p>

<p>This arrangement considerably diminished their joint
power of traction. But another source of delay arose: the
couplings which were strong enough when connecting an
engine and its train were not sufficiently strong when three
engines were coupled together. The consequence was that
there were frequent fractures of our couplings and thus great
delays arose.</p>

<p>About half-past eight in the evening I reached the great
building in which we were to have dined. Its tables were
half filled with separate groups of three or four people each,
who being strangers in Liverpool, had no other resource than
to use it as a kind of coffee-room in which to get a hasty
meal, and retire.</p>

<div class="dsdnote">〈PLATE-GLASS MANUFACTORY.〉</div>

<p>The next morning I went over to see the plate-glass
manufactory at about ten miles from Liverpool.</p>

<p>On my arrival I found, to my great disappointment, that
there were orders that nobody should be admitted on that
day, as the Duke of Wellington and a large party were
coming over from Lord Wilton’s. This was the only day at
my disposal, and it wanted nearly an hour to the time appointed:
so I asked to be permitted to see the works, promising
to retire as soon as the Earl of Wilton’s party arrived.
I added incidentally that I was not entirely unknown to the
Duke of Wellington.</p>

<p>On the arrival of the party I quietly
made my retreat <span class="xxpn" id="p317">{317}</span>
unobserved, and had just entered the carriage which had conveyed
me from Liverpool, when a messenger arrived with the Duke’s
compliments, hoping that I would join his party. I willingly
accepted the invitation; the Duke presented me to each of
his friends, and I had the advantage of having another survey
of the works. This was my first acquaintance with the
late Lady Wilton, who afterwards called on me with the
Duke of Wellington, and put that sagacious question relative
to the Difference Engine which I have mentioned in another
part of this volume. Amongst the party were Mr. and Mrs.
Arbuthnot, with the former of whom I afterwards had several
interesting discussions relative to subjects connected with
the ninth “Bridgewater Treatise.”</p>

<p>A few days after, I met at dinner a large party at the
house of one of the great Liverpool merchants. Amongst
them were several officers of the new railway, and almost all
the party were more or less interested in its success.</p>

<p>In these circumstances the conversation very naturally
turned upon the new mode of locomotion. Its various difficulties
and dangers were suggested and discussed. Amongst
others, it was observed that obstacles might be placed upon
the rail, either accidentally or by design, which might produce
expensive and fatal effects.</p>

<div class="dsdnote">〈ON PREVENTING RAILWAY ACCIDENTS.〉</div>

<p>To prevent the occurrence of these evils, I suggested two
remedies.</p>

<p>1st. That every engine should have just in advance of each
of its front wheels a powerful framing, supporting a strong
piece of plate-iron, descending within an inch or two of the
upper face of the rail. These iron plates should be fixed at
an angle of 45° with the line of rail, and also at the same
angle with respect to the horizon. Their shape would be
something like that of ploughshares, and
their effect would <span class="xxpn" id="p318">{318}</span>
be to pitch any obstacle obliquely off the rail unless its
heavier portion were between the rails.</p>

<p>Some time after, a strong vertical bar of iron was placed in
front of the wheels of every engine. The objection to this is,
that it has a tendency to throw the obstacle straight forward
upon another part of the rail.</p>

<p>2nd. The second suggestion I made, was to place in front of
each engine a strong leather apron attached to a powerful
iron bar, projecting five or six feet in front of the engine and
about a foot above the ballast. The effect of this would be,
that any animal straying over the railway would be pitched
into this apron, probably having its legs broken, but forming
no impediment to the progress of the train.</p>

<div class="dsdnote">〈VARIOUS PLANS PROPOSED.〉</div>

<p>I have been informed that this contrivance has been
adopted in America, where the railroads, being unenclosed,
are subject to frequent obstruction from cattle. If used on
enclosed roads, it still might oc­ca­sion­al­ly save the lives of
incautious persons, although possibly at the expense of broken
limbs.</p>

<p>Another question discussed at this party was, whether, if
an engine went off the rail, it would be possible to separate it
from the train before it had dragged the latter after it. I
took out my pencil and sketched upon a card a simple method
of accomplishing that object. It passed round the table, and
one of the party suggested that I should communicate the
plan to the Directors of the railway.</p>

<p>My answer was, that having a great wish to diminish the
dangers of this new mode of travelling, I declined making
any such communication to them; for, I added, unless these
Directors are quite unlike all of whom I have had any experience,
I can foresee the inevitable result of
such a communication. <span class="xxpn" id="p319">{319}</span></p>

<p>It might take me some time and trouble to consider the best
way of carrying out the principle and to make the necessary
drawings. Some time after I have placed these in the hands
of the Company, I shall receive a very pretty letter from the
secretary, thanking me in the most flattering terms for the
highly ingenious plan I have placed in their hands, but regretting
that their engineer finds certain practical difficulties
in the way.</p>

<p>Now, if the same Company had taken the advice of some
eminent engineer, to whom they would have to pay a large
fee, no practical difficulties would ever be found to prevent
its trial.</p>

<p>It was evident from the remarks of several of the party
that I had pointed out the most probable result of any such
communication.</p>

<p>It is possible that some report of this plan sub­se­quent­ly
reached the Directors; for about six months after, I received
from an officer of the railway Company a letter, asking my
assistance upon this identical point. I sent them my sketch
and all the information I had sub­se­quent­ly acquired on the
subject. I received the stereotype reply I had anticipated,
couched in the most courteous language; in short, quite a
model letter for a young secretary to study.</p>

<div class="dsdnote">〈REASONS WHY REJECTED.〉</div>

<p>Several better contrivances than mine were sub­se­quent­ly
proposed; but experience seems to show that the whole train
ought to be connected together as firmly as possible.</p>

<p>Not long after my return from Liverpool I found myself
seated at dinner next to an elderly gentleman, an eminent
London banker. The new system of railroads, of course, was
the ordinary topic of conversation. Much had been said in
its favour, but my neighbour did not appear to concur with
the majority. At last I had an opportunity
of asking his <span class="xxpn" id="p320">{320}</span>
opinion. “Ah,” said the banker, “I don’t approve of this
new mode of travelling. It will enable our clerks to plunder
us, and then be off to Liverpool on their way to America at
the rate of <i>twenty</i> miles an hour.” I suggested that science
might perhaps remedy this evil, and that possibly we might
send lightning to outstrip the culprit’s arrival at Liverpool,
and thus render the railroad a sure means of arresting the
thief. I had at the time I uttered those words no idea how
soon they would be realized.</p>

<div class="dsdnote">〈THE AUTHOR’S EXPERIMENTS ON THE GREAT WESTERN RAILWAY.〉</div>

<p>In 1838 and 1839 a discussion of considerable public
importance had arisen respecting the Great Western Railway.
Having an interest in that undertaking, it was the
wish of Mr. Brunel and the Directors that I should state my
own opinion upon the question. I felt that I could not speak
with confidence without making certain experiments. The
Directors therefore lent me steam-power, and a second-class
carriage to fit up with machinery of my own contrivance, and
appointed one of their officers to accompany me, through
whom I might give such directions as I deemed necessary
during my experiments.</p>

<p>I removed the whole of the internal parts of the carriage.
Through its bottom firm supports, fixed upon the framework
below, passed up into the body of the carriage, and supported
a long table entirely independent of its motions.</p>

<p>On this table slowly rolled sheets of paper, each a thousand
feet long. Several inking pens traced curves on this paper,
which expressed the following <span class="nowrap">measures:—</span></p>

<ul>
<li>1. Force of traction.</li>

<li>2. Vertical shake of carriage at its middle.</li>

<li>3. Lateral ditto.</li>

<li>4. End ditto.</li>

<li>5, 6, and 7. The same shakes at the end
of the carriage. <span class="xxpn" id="p321">{321}</span></li>

<li>8. The curve described upon the earth by the centre of
the frame of the carriage.</li>

<li>9. A chronometer marked half seconds on the paper.</li></ul>

<p>Above two miles of paper were thus covered. These experiments
cost me about 300&#x200a;<i>l.</i>, and took up my own time,
and that of all the people I was then employing, during five
months.</p>

<p>I had previously travelled over most of the railways then
existing in this country, in order to make notes of such facts
as I could observe during my journeys.</p>

<p>The result of my experiments convinced me that the broad
gauge was most convenient and safest for the public. It also
enabled me fearlessly to assert that an immense array of
experiments which were exhibited round the walls of the
meeting-room by those who opposed the Directors were made
with an instrument which could not possibly measure the
quantities proposed, and that the whole of them were worthless
for the present argument. The production of the work
of such an instrument could not fail to damage even a good
cause.</p>

<p>On the discussion at the general meeting at the London
Tavern, I made a statement of my own views, which was
admitted at the time to have had considerable influence on
the decision of the proprietors. Many years after I met
a gentleman who told me he and a few other proprietors
holding several thousand proxies came up from Liverpool
intending to vote according to the weight of the arguments
adduced. He informed me that he and all his friends decided
their votes on hearing my statement. He then added, “But
for that speech, the broad gauge would not now exist in
England.”</p>

<div class="dsdnote">〈THE PHI­LOS­O­PHER’S ADVENTURES AND ESCAPES BY RAIL.〉</div>

<p>These experiments were not
unaccompanied with danger. <span class="xxpn" id="p322">{322}</span>
I sometimes attached my carriage to a public train to convey
me to the point where my experiments commenced, and I
had frequently to interrupt their course, in order to run on to
a siding to avoid a coming train.</p>

<p>I then asked to be allowed to make such experiments
during the night when there were no trains; but Brunel told
me it was too dangerous to be permitted, and that ballast-waggons,
and others, carrying machinery and materials for
the construction and completion of the railroad itself, were
continually traversing various parts of the line at uncertain
hours.</p>

<p>The soundness of this advice became evident a very short
time after it was given. On arriving one morning at the
terminus, the engine which had been promised for my experimental
train was not ready, but another was provided
instead. On further inquiry, I found that the “North Star,”
the finest engine the Company then possessed, had been
placed at the end of the great polygonal building devoted to
engines, in order that it might be ready for my service in the
morning; but that, during the night, a train of twenty-five
empty ballast-waggons, each containing two men, driven by
an engine, both the driver and stoker of which were asleep,
had passed right through the engine-house and damaged the
“North Star.”</p>

<p>Most fortunately, no accident happened to the men beyond
a severe shaking. It ought, however, in extenuation of such
neglect, to be observed that engine-drivers were at that
period so few, and so thoroughly overworked, that such an
occurrence was not surprising.</p>

<p>It then occurred to me, that being engaged on a work
which was anything but profitable to myself, but which contributed
to the safety of all travellers,
I might, without <span class="xxpn" id="p323">{323}</span>
impropriety, avail myself of the repose of Sunday for advancing
my measures. I therefore desired Brunel to ask for the
Directors’ permission. The next time I saw Brunel, he told
me the Directors did not like to give an official permission,
but it was remarked that having put one of their own officers
under my orders, I had already the power of travelling on
whatever day I preferred.</p>

<p>I accordingly availed myself of the day on which, at that
time, scarcely a single train or engine would be in motion
upon it.</p>

<p>Upon one of these Sundays, which were, in fact, the only
really safe days, I had proposed to investigate the effect of
considerable additional weight. With this object, I had
ordered three waggons laden with thirty tons of iron to be
attached to my experimental carriage.</p>

<p>On my arrival at the terminus a few minutes before the
time appointed, my aide-de-camp informed me that we were
to travel on the north line. As this was an invasion of the
usual regulations, I inquired very minutely into the authority
on which it rested. Being satisfied on this point, I desired
him to order my train out immediately. He returned shortly
with the news that the fireman had neglected his duty, but that
the engine would be ready in less than a quarter of an hour.</p>

<p>A messenger arrived soon after to inform me that the obstructions
had been removed, and that I could now pass upon
the south, which was the proper line.</p>

<p>I was looking at the departure of the only Sunday train,
and conversing with the officer, who took much pains to
assure me that there was no danger on whichever line we
might travel; because, he observed, when that train had departed,
there can be no engine except our own on either line
until five o’clock
in the evening. <span class="xxpn" id="p324">{324}</span></p>

<p>Whilst we were conversing together, my ear, which had become peculiarly
sensitive to the distant sound of an engine, told me that one was
approaching. I mentioned it to my railway official: he did not hear
it, and said, “Sir, it is impossible.”—“Whether it is possible or
impossible,” I said, “an engine <i>is</i> coming, and in a few minutes we
shall see its steam.” The sound soon became evident to both, and our
eyes were anxiously directed to the expected quarter. The white cloud
of steam now faintly appeared in the distance; I soon perceived the
line it occupied, and then turned to watch my companion’s countenance.
In a few moments more I saw it slightly change, and he said, “It <i>is</i>,
indeed, on the north line.”</p>

<p>Knowing that it would stop at the engine-house, I ran as
fast I could to that spot. I found a single engine, from
which Brunel, covered with smoke and blacks, had just descended.
We shook hands, and I inquired what brought my
friend here in such a plight. Brunel told me that he had
posted from Bristol, to meet the only train at the furthest
point of the rail then open, but had missed it. Fortunately,
he said, “I found this engine with its fire up, so I ordered it
out, and have driven it the whole way up at the rate of fifty
miles an hour.”</p>

<div class="dsdnote">〈ESCAPES MEETING BRUNEL.〉</div>

<p>I then told him that but for the merest accident I should
have met him on the <i>same</i> line at the rate of forty miles, and
that I had attached to my engine my experimental carriage,
and three waggons with thirty tons of iron. I then inquired
what course he would have pursued if he had perceived
another engine meeting him upon his own line.</p>

<p>Brunel said, in such a case he should have put on all the
steam he could command, with a view of driving off the opposite
engine by the superior velocity
of his own. <span class="xxpn" id="p325">{325}</span></p>

<p>If the concussion had occurred, the probability is, that
Brunel’s engine would have been knocked off the rail by the
superior momentum of my train, and that my experimental
carriage would have been buried under the iron contained in
the waggons behind.</p>

<p>These rates of travelling were then unusual, but have now
become common. The greatest speed which I have personally
witnessed, occurred on the return of a train from
Bristol, on the occasion of the floating of the “Great Britain.”
I was in a compartment, in conversation with three eminent
engineers, when one of them remarked the unusual speed of
the train: my neighbour on my left took out his watch, and
noted the time of passage of the distance posts, whence it
appeared that we were then travelling at the rate of seventy-eight
miles an hour. The train was evidently on an incline,
and we did not long sustain that dangerous velocity.</p>

<p>One very cold day I found Dr. Lardner making experiments
on the Great Western Railway. He was drawing a
series of trucks with an engine travelling at known velocities.
At certain intervals, a truck was detached from his train.
The time occupied by this truck before it came to rest was
the object to be noted. As Dr. Lardner was short of assistants,
I and my son offered to get into one of his trucks and
note for him the time of coming to rest.</p>

<div class="dsdnote">〈SAILS ACROSS HANWELL VIADUCT.〉</div>

<p>Our truck having been detached, it came to rest, and I had
noted the time. After waiting a few minutes, I thought I
perceived a slight motion, which continued, though slowly. It
then occurred to me that this must arise from the effect of
the wind, which was blowing strongly. On my way to the
station, feeling very cold, I had purchased three yards of coarse
blue woollen cloth, which I wound round my person. This I
now unwound; we held it up as a sail,
and gradually acquiring <span class="xxpn" id="p326">{326}</span>
greater velocity, finally reached and sailed across the whole
of the Hanwell viaduct at a very fair pace.</p>

<div class="dsdnote">〈THE BATTLE OF THE GAUGES.〉</div>

<p>The question of the best gauge for a system of railways is
yet undecided. The present gauge of 4·8½ was the result of
the accident that certain tram-roads adjacent to mines were
of that width. When the wide gauge of the Great Western
was suggested and carried out, there arose violent party
movements for and against it. At the meeting of the British
Association at Newcastle, in 1838, there were two sources of
anxiety to the Council—the discussion of the question of
Steam Navigation to America, and what was called “The
battles of the Gauges.” Both these questions bore very
strongly upon pecuniary interests, and were expected to be
fiercely contested.</p>

<p>On the Council of the British Association, of course, the
duty of nominating the Presidents and Vice-Presidents of its
various sections devolves. During the period in which I
took an active part in that body, it was always a principle, of
which I was ever the warm advocate, that we should select
those officers from amongst the persons most distinguished
for their eminence in their respective subjects, who were
born in or connected with the district we visited.</p>

<p>In pursuance of this principle, I was deputed by the
Council to invite Mr. George Stephenson to become the President
of the Mechanical Section. In case he should decline
it, I was then empowered to offer it to Mr. Buddle, the eminent
coal-viewer; and in case of these both declining, I was
to propose it to the late Mr. Bryan Donkin, of London, a
native of that district, and connected with it by family ties.</p>

<div class="dsdnote">〈BRITISH ASSOCIATION AT NEWCASTLE.〉</div>

<p>On my arrival at Newcastle, I immediately called on
George Stephenson, and represented to him the unanimous
wish of the Council of the British Association.
To my great <span class="xxpn" id="p327">{327}</span>
surprise, and to my still greater regret, I found that he at
once declined the offer. All my powers of persuasion were
exercised in vain. Knowing that the two great controverted
questions to be discussed most probably formed the real
obstacle, I mentioned them, and added that, as I should be
one of his Vice-Presidents, I would, if he wished it, take the
Chair upon either or upon both the discussions of the Gauges
and of the Atlantic Steam Voyage, or upon any other occasion
that might be agreeable or convenient to himself: I found
him immoveable in his decision. I made another attempt the
next day, and renewed the expression of my own strong
feeling, that we should pay respect and honour to the most
distinguished men of the district we visited. I then told him
the course I was instructed by the Council to pursue.</p>

<p>My next step was to apply to Mr. Buddle. I need not
repeat the arguments I employed: I was equally unsuccessful
with each of the eminent men the Council had wished to
honour. I therefore now went back to George Stephenson,
told him of the failure of my efforts, and asked him, if he
still persisted in declining the Chair, would he do me
the favour to be one of the Vice-Presidents, as the Council
had now no resource but to place me in the Chair, which I
had hoped would have been occupied by a more competent
person.</p>

<p>To this latter application he kindly acceded; and I felt
that, with the assistance of George Stephenson’s and Mr.
Donkin’s pro­fes­sion­al knowledge, and their presence by my
side, I should be able to keep order in these dreaded discussions.</p>

<p>The day before the great discussion upon Atlantic Steam
Navigation, I had a short conversation with Dr. Lardner: I
told him that in my opinion some of his
views were hasty; <span class="xxpn" id="p328">{328}</span>
but that much stronger opinions had been assigned to him
than those he had really expressed, and I recommended him
to admit as much as he fairly could.</p>

<div class="dsdnote">〈RAILWAY DISCUSSION.〉</div>

<p>At the appointed hour the room was filled with an expectant
and rather angry audience. Dr. Lardner’s beautiful
apparatus for illustrating his views was before them, and the
Doctor commenced his statement. He was listened to with
the greatest attention, and was really most judicious as well as
very instructive. At the very moment which seemed to me
the most favourable for it, he turned to the explanation of the
instruments he proposed to employ, and having concluded his
statement, it became my duty to invite discussion upon the
question.</p>

<p>I did so in very few words, merely observing that several
opinions had been attributed to Dr. Lardner which he had
never maintained, and that additional information had induced
him candidly to admit that some of those doctrines which he
had supported were erroneous. I added, that nothing was
more injurious to the progress of truth than to reproach any
man who honestly admitted that he had been in error.</p>

<p>The discussion then commenced: it was continued with considerable
energy, but with great temper; and after a long and instructive
debate the assembled multitude separated. Some few who attended in
expectation of a scene were sorely disappointed. As I was passing
out, one of my acquaintance remarked, “You have saved that <span
class="nowrap">——</span> <span class="nowrap">——</span> Lardner:”
to which I replied, “I have saved the British Association from a
scandal.”</p>

<p>Before I terminate this Chapter on Railways, it will perhaps
be expected by some of my readers that I should point out
such measures as occur to me for rendering this universal
system more safe. Since the long series
of experiments I <span class="xxpn" id="p329">{329}</span>
made in 1839, I have had no experience either official or
pro­fes­sion­al upon the subject. My opinions, therefore, must
be taken only at what they are worth, and will probably be
regarded as the dreams of an amateur. I have indeed formed
very decided opinions upon certain measures relative to railroads;
but my hesitation to make them public arises from
the circumstance, that by publishing them I may possibly
delay their adoption. It may happen, as is now happening
to my system of distinguishing lighthouses from each other,
and of night telegraphic communication between ships at sea—that
although officially communicated to all the great maritime
governments, and even publicly exhibited for months
during the Exhibition of 1851, it will be allowed to go to
sleep for years, until some official person, casually hearing of
it, or perhaps re-inventing it, shall have <i>interest</i> with the
higher powers to get it quietly adopted as his own invention.
I have given, in a former page, a list of the self-registering
apparatus I employed in my own experiments.</p>

<div class="dsdnote">〈MEANS OF SAFETY FOR TRAINS.〉</div>

<p>In studying the evidence given upon the inquiries into the
various lamentable accidents which have occurred upon railways,
I have been much struck by the discordance of that
evidence as to the speed with which the engines were travelling
when they took place.</p>

<p>Even the best and most unbiassed judgment ought not to
be trusted when mechanical evidence can be produced. The
first rule I propose is, <span class="nowrap">that—</span></p>

<p><i>Every engine should have mechanical self-registering means
of recording its own velocity at every instant during the whole
course of its journey.</i></p>

<div class="dsdnote">〈SELF-RECORDING MEANS.〉</div>

<p>In my own experiments this was the first point I attended
to. I took a powerful spring clock, with a chronometer movement,
which every half second lifted a peculiar
pen, and left <span class="xxpn" id="p330">{330}</span>
a small dot of ink upon the paper, which was moving over a
table with the velocity given to it by the wheels of the carriage.</p>

<p>Thus the comparative frequency of these dots indicated the
rate of travelling at the time. But the instrument was susceptible
of giving different scales of measurement. Thus it
might be that only three inches of paper passed under the
pen in every mile, or any greater length of paper, up to sixty
feet per mile, might be ordered to pass under the paper
during an equal space. Again, the number of dots per
second could, if required, be altered.</p>

<p>The clock was broken four or five times during the earliest
experiments. This arose from its being fixed upon the platform
carrying the axles of the wheels. I then contrived a
kind of parallel motion, by which I was enabled to support
the clock upon the carriage-springs, and yet allow it to impress
its dots upon the paper, which did not require that
advantage. After this, the clock was never injured.</p>

<p>The power of regulating the length of paper for each mile
was of great importance; it enabled me to examine, almost
microscopically, the junctions of the rails. When a large
scale of paper was allowed, every joining was marked upon
the paper.</p>

<p>I find, on referring to my paper records, that on the
3rd March, 1839, the “Atlas” engine drew my experimental
carriage, with two other carriages attached behind it, from
Maidenhead to Drayton, with its paper travelling only eleven
feet for each mile of journey; whilst from Drayton to Slough,
forty-four feet of paper passed under the pen during each
mile of progress.</p>

<p>The inking pens at first gave me some trouble, but after
successively discovering their various
defects, and remedying <span class="xxpn" id="p331">{331}</span>
them at an expense of nearly £20, they performed their
work satisfactorily. The information they gave might be
fully relied upon.</p>

<div class="dsdnote">〈THEIR REMARKABLE EFFECT.〉</div>

<p>We had an excellent illustration of this on one occasion
when we were returning, late in the evening, from Maidenhead,
after a hard day’s work. The pitchy darkness of the
night, which prevented us from seeing any objects external to
our carriage, was strongly contrasted with the bright light of
four argand lamps within it. I was accompanied by my
eldest son, Mr. Herschel Babbage, and three assistants. A
roll of paper a thousand feet in length was slowly unwinding
itself upon the long table extended before us, and winding
itself up on a corresponding roller at its other extremity.
About a dozen pens connected with a bridge crossing the
middle of the table were each marking its own independent
curve gradually or by jumps, as the circumstances attending
our railway course was dictating. The self-feeding pens, which
the self-acting roller of blotting-paper continually followed, but
never overtook, were quietly marking their inevitable courses.
All had gone on well for a considerable time amidst perfect
silence, if the steady pace of thirty miles an hour, the dogged
automatic action of the material, and the muteness of the
living machinery, admitted of such a term. Being myself
entirely ignorant of our position upon the rail, I disturbed
this busy repose by inquiring whether any one knew where
we were? To this question there was no reply. Each continued
to watch in silence for the duties which his own department
might at any moment require, but no such demands
were made.</p>

<p>After some minutes, as I was watching the lengthening
curves, I perceived a slight indication of our position on the
railroad. I instantly looked at my son, and saw,
by a faint <span class="xxpn" id="p332">{332}</span>
smile on his countenance, that he also perceived our situation
on the line. I had scarcely glanced back at the growing
curves upon the paper, to confirm my interpretation, when
each of my three assistants at the same instant called out
“Thames Junction.”</p>

<p>At the period I speak of the double line of a small railway,
called the Thames Junction, crossed the Great Western line
on a level at between two and three miles from its terminus.
The in­ter­rup­tion caused certain jerks in several of our curves,
which, having once noticed, it was impossible to mistake.</p>

<p>I would suggest that every engine should carry a spring
clock, marking small equal intervals of time by means of a
needle-point impinging upon paper, the speed of whose
transit should be regulated by the speed of the engine. It
might, perhaps, be desirable to have a differently-formed
mark to indicate each five minutes. Also, two or more studs
on the driving-wheel should mark upon the same paper the
number of its revolutions. Besides this, it might be imperative
on the engine-driver to mark upon the paper a dot
upon passing each of certain prescribed points upon the railway.
This latter is not absolutely necessary, but may oc­ca­sion­al­ly
supply very valuable information.</p>

<div class="dsdnote">〈TRACTIVE POWER REGISTERED.〉</div>

<p>The second point which I consider of importance is, <span class="nowrap">that—</span></p>

<p><i>Between every engine and its train there should be interposed
a dynamometer, that is, a powerful spring to measure the force
exerted by the engine.</i></p>

<p>It may, perhaps, be objected that this would require a
certain amount of movement between the engine and its
train. A very small quantity would be sufficient, say half
an inch, or less. The forces in action are so very large, that
even a still smaller amount of motion than this might be
sufficiently magnified. Its indications should
be marked by <span class="xxpn" id="p333">{333}</span>
self-acting machinery governing points impinging upon the
paper on which the velocity is marked.</p>

<p>Whenever any unusual resistance has opposed the progress
of the train, it will thus be marked upon the paper. It will
indicate in some measure the state of the road, and it will
assuredly furnish valuable information in case an accident
happens, and the train or the engine gets off the rails.</p>

<div class="dsdnote">〈CURVE OF PROGRESS REGISTERED.〉</div>

<p>The third recommendation I have to make <span
class="nowrap">is—</span></p>

<p><i>That the curve described by the centre of the engine itself upon
the plane of the railway should be laid down upon the paper.</i></p>

<p>Finding this a very important element, I caused a plate of
hardened steel to be pressed by a strong spring against the inner
edge of the rail. It was supported by a hinge upon a strong
piece of timber descending from the platform supporting the
carriage itself. The motion of this piece of steel, arising from
the varying position of the wheels themselves upon the rail,
was conveyed to a pen which transferred to the paper the
curve traversed by the centre of the carriage referred to the
plane of the rail itself.</p>

<p>The contrivance and management of this portion of my
apparatus was certainly the most difficult part of my task,
and probably the most dangerous. I had several friendly
cautions, but I knew the danger, and having examined its
various causes, adopted means of counteracting its effect.</p>

<p>After a few trials we found out how to manage it, and
although it often broke four or five times in the course of
the day’s work, the fracture inevitably occurred at the place
intended for it, and my first notice of the fact often arose
from the blow the fragment made when suddenly drawn
by a strong rope up to the under side of the floor of our
experimental carriage.</p>

<p>I have a very strong opinion that the
adoption of such <span class="xxpn" id="p334">{334}</span>
mechanical registrations would add greatly to the security of
railway travelling, because they would become the unerring
record of facts, the incorruptible witnesses of the immediate
antecedents of any catastrophe.</p>

<p>I have, however, little expectation of their adoption, unless
Directors can be convinced that the knowledge derived from
them would, by pointing out incipient defects, and by acting
as a check upon the vigilance of all their officers, considerably
diminish the repairs and working expenses both of the
engine and of the rail. Nor should I be much surprised even
if they were pronounced impracticable, although they existed
very nearly a quarter of a century ago.</p>

<p>The question of the gauges has long been settled. A small
portion of broad gauge exists, but it is probable that it will
ultimately be changed. The vast expense of converting the
engines and the rolling stock for use on the narrower gauge
presents the greatest obstacle.</p>

<div class="dsdnote">〈GEORGE STEPHENSON’S REAL OPINION ON THE QUESTION
OF THE GAUGES.〉</div>

<p>It may, however, be interesting to learn the opinion of
the father of railways at an early period of their progress.
I have already mentioned the circumstances under which
my acquaintance with George Stephenson began. They
were favourable to that mutual confidence which immediately
arose. I was naturally anxious to ascertain the effect of the
existing experience upon his own mind, but I waited patiently
until a favourable opportunity presented itself.</p>

<p>At a large public dinner, during the meeting of the British
Association at Newcastle, I sat next to George Stephenson.
It occurred to me that the desired opportunity had now
arrived. I said little about railways until after the first glass
of champagne. I mentioned several that I had travelled
upon, and the conclusions I had drawn relative to the
mechanical department. I then referred to
the economy of <span class="xxpn" id="p335">{335}</span>
management, and pointed out one railway in which the
accounts were so well arranged, that I had been able to
arrive at a testing point of an opinion I had formed from
my own ob­ser­va­tions.</p>

<p>One great evil of the narrow gauge was, that when some
trifling derangement in the engine occurred, which might be
repaired at the expense of two or three shillings, it frequently
became necessary to remove uninjured portions of
the machine, in order to get at the fault; that the re-making
the joints and replacing these parts thus temporarily removed,
frequently led to an expense of several pounds.</p>

<p>The second glass of champagne now interrupted a conversation
which was, I hope, equally agreeable to both, and was
certainly very instructive for me. I felt that the fairest
opportunity I could desire of ascertaining my friend’s real
opinion of the gauge had now arrived. Availing myself of
the momentary pause after George Stephenson’s glass was
empty, I <span class="nowrap">said—</span></p>

<p>“Now, Mr. Stephenson, will you allow me to ask you to
suppose for an instant that no railways whatever existed, and
yet that you were in full possession of all that large amount
of knowledge which you have derived from your own experience.
Under such circumstances, if you were consulted
respecting the gauge of a system of railways about to be
inaugurated, would you advise the gauge of 4 feet 8½ inches?”</p>

<p>“Not exactly that gauge,” replied the creator of railroads;
“I would take a few inches more, but a very few.”</p>

<p>I was quite satisfied with this admission, though I confess
it reminded me of the frail fair one who, when reproached by
her immaculate friend with having had a child—an ecclesiastical
licence not being first obtained—urged, as an
extenuating circumstance, that it was a
very small one. <span class="xxpn" id="p336">{336}</span></p>

<div class="dsdnote">〈RAILWAYS OF THE FUTURE.〉</div>

<p>In this age of invention, it is difficult to predict the railroads
of the future. Already it has been suggested to give up
wheels and put carriages upon sledges. This would lower the
centre of gravity considerably, and save the expense of wheels.
On the other hand, every carriage must have an apparatus to
clean and grease the rails, and the wear and tear of these
latter might overbalance the economy arising from abolishing
wheels.</p>

<p>Again, short and much-frequented railways might be
formed of a broad, continuous strap, always rolling on. At
each station means must exist for taking up and putting down
the passengers without stopping the rolling strap.</p>

<p>The exhaustion of air in a continuous tunnel was proposed
many years ago for the purpose of sucking the trains along.
This has recently been applied with success to the transmission
of parcels and letters.</p>

<p>Possibly in the next International Exhibition a light railway
might be employed within the building.<a class="afnanc" href="#fn49"
id="fnanc49">49</a></p>

<ul>
<li>1st. A quick train to enable visitors to get rapidly from
end to end, avoiding the crowd and saving time, say at the
expense of a penny.</li>

<li>2nd. A very slow train passing along the most attractive
line, and oc­ca­sion­al­ly stopping, to enable persons not capable
of bearing the fatigue of pushing on foot through crowds.</li></ul>

<p>If such railways were considered in the original design of
the building, they might be made to interfere but little with
the general public, and would bring in a considerable revenue
to the concern.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc49" id="fn49">49</a>
A gallery, elevated about seven feet, in the centre of
each division of the new National Gallery, might be used either for a
light railway, or for additional means of seeing the pictures on the
walls.</p></div></div><!--section-->

<div class="section" id="p337">
<h2 class="h2herein">CHAPTER XXVI.
<span class="hsmall">STREET NUISANCES.</span></h2>

<div class="dsynopsis">
Various Classes injured&#x200a;—&#x200a;Instruments of
Torture&#x200a;—&#x200a;Encouragers; Servants, Beer-shops, Children,
Ladies of elastic virtue&#x200a;—&#x200a;Effects on the Musical
Profession&#x200a;—&#x200a;Retaliation&#x200a;—&#x200a;Police
themselves disturbed&#x200a;—&#x200a;Invalids
distracted&#x200a;—&#x200a;Horses run away&#x200a;—&#x200a;Children
run over&#x200a;—&#x200a;A Cab-stand placed in the
Author’s street attracts Organs&#x200a;—&#x200a;Mobs
shouting out his Name&#x200a;—&#x200a;Threats to Burn his
House&#x200a;—&#x200a;Disturbed in the middle of the night when
very ill&#x200a;—&#x200a;An average number of Persons are always
ill&#x200a;—&#x200a;Hence always disturbed&#x200a;—&#x200a;Abusive
Placards&#x200a;—&#x200a;Great Difficulty of getting
Convictions&#x200a;—&#x200a;Got a Case for the Queen’s
Bench&#x200a;—&#x200a;Found it useless&#x200a;—&#x200a;A Dead
Sell&#x200a;—&#x200a;Another Illustration&#x200a;—&#x200a;Musicians
give False Name and Address&#x200a;—&#x200a;Get Warrant
for Apprehension&#x200a;—&#x200a;They keep out of the
way&#x200a;—&#x200a;Offenders not yet found and arrested by the
Police&#x200a;—&#x200a;Legitimate Use of Highways&#x200a;—&#x200a;An
Old Lawyer’s Letter to <i>The Times</i>&#x200a;—&#x200a;Proposed Remedies;
Forbid entirely&#x200a;—&#x200a;Authorize Police to seize the
Instrument and take it to the Station&#x200a;—&#x200a;An Association
for Prevention of Street Music proposed.</div>

<p class="pfirst"><span class="smcap">D<b>URING</b></span>
the last ten years, the amount of street music has
so greatly increased that it has now become a positive
nuisance to a very considerable portion of the inhabitants of
London. It robs the industrious man of his time; it annoys
the musical man by its intolerable badness; it irritates the
invalid; deprives the patient, who at great inconvenience
has visited London for the best medical advice, of that repose
which, under such circumstances, is essential for his recovery,
and it destroys the time and the energies of all the in­tel­lec­tual
classes of society by its continual in­ter­rup­tions of their
pursuits. <span class="xxpn" id="p338">{338}</span></p>

<ul class="ulp338a">
<li><div><i>Instruments of torture permitted by the Government to be in
daily and nightly use in the streets of London.</i></div>
<ul>
<li>Organs.</li>

<li>Brass bands.</li>

<li>Fiddles.</li>

<li>Harps.</li>

<li>Harpsichords.</li>

<li>Hurdy-gurdies.</li>

<li>Flageolets.</li>

<li>Drums.</li>

<li>Bagpipes.</li>

<li>Accordions.</li>

<li>Halfpenny whistles.</li>

<li>Tom-toms.</li>

<li>Trumpets.</li>

<li>The human voice in various forms.
<ul id="ulp338b"><li>Shouting out objects for sale.</li>
<li>Religious canting.</li>
<li>Psalm-singing.</li>
</ul></li></ul></li></ul>

<p>I have very frequently been disturbed by such music after
eleven and even after twelve o’clock at night. Upon one
occasion a brass band played, with but few and short intermissions,
for five hours.</p>

<ul class="ulp338a"><li><div><i>Encouragers of Street Music.</i></div>
<ul><li>Tavern-keepers.</li>

<li>Public-houses.</li>

<li>Gin-shops.</li>

<li>Beer-shops.</li>

<li>Coffee-shops.</li>

<li>Servants.</li>

<li>Children.</li>

<li>Visitors from the country.</li>

<li>Ladies of doubtful virtue.</li>

<li>Oc­ca­sion­al­ly titled ladies; but these are almost invariably of recent
elevation, and deficient in that taste which their sex usually possess.
</li></ul></li></ul>

<p>The habit of frequenting public-houses, and the amount of
intoxication, is much augmented by these means. It therefore
finds support from the whole body of licensed victuallers,
and from all those who are interested, as the proprietors of
public-houses.</p>

<p>The great encouragers of street music belong chiefly to the
lower classes of society. Of these, the frequenters of public-houses
and beer-shops patronize the worst
and the most <span class="xxpn" id="p339">{339}</span>
noisy kinds of music. The proprietors of such establishments
find it a very successful means of attracting customers.
Music is kept up for a longer time, and at later hours, before
the public-house, than under any other circumstances. It
not unfrequently gives rise to a dance by little ragged
urchins, and sometimes by half-intoxicated men, who oc­ca­sion­al­ly
accompany the noise with their own discordant voices.</p>

<p>Servants and children are great admirers of street music;
also people from the country, who, coming up to town for a
short time, often encourage it.</p>

<p>Another class who are great supporters of street music,
consists of ladies of elastic virtue and cosmopolitan tendencies,
to whom it affords a decent excuse for displaying their
fascinations at their own open windows. Most ladies resident
in London are aware of this peculiarity, but oc­ca­sion­al­ly
some few to whom it is not known have found very unpleasant
inferences drawn, in consequence of thus gratifying their
musical taste.</p>

<div class="dtablebox">
<table summary="">
<caption><span class="smcap">M<b>USICAL</b></span>
<span class="smcap">P<b>ERFORMERS.</b></span></caption>
<tr>
 <th scope="col"><i>Musicians.</i></th>
 <th scope="col"><i>Instruments.</i></th></tr>
<tr>
 <td class="tdleft">Italians</td>
 <td class="tdleft">Organs.</td></tr>
<tr>
 <td class="tdleft">Germans</td>
 <td class="tdleft">Brass bands.</td></tr>
<tr>
 <td class="tdleft">Natives of India</td>
 <td class="tdleft">Tom-toms.</td></tr>
<tr>
 <td class="tdleft">English</td>
 <td class="tdleft">Brass bands, fiddles, &amp;c.</td></tr>
<tr>
 <td class="tdleft">The lowest class of clubs</td>
 <td class="tdleft">Bands with double drum.</td></tr>
</table></div>

<p>The most numerous of these classes, the organ-grinders, are
natives of Italy, chiefly from the mountainous district,
whose language is a rude <i>patois</i>, and who are entirely unacquainted
with any other. It is said that there are above
a thousand of these foreigners usually in London employed
in tormenting the natives. They
mostly reside in <span class="xxpn" id="p340">{340}</span>
the neighbourhood of Saffron Hill, and are, of course, from
their ignorance of any other language than their own, entirely
in the hands of their padrones. One of these, a most persevering
intruder with his organ, gave me a false address.
Having ascertained the real address, he was sought for by
the police for above a fortnight, but not discovered. His
<i>padrone</i> becoming aware of his being “<i>wanted</i>,” sent him on a
country circuit. I once met, within a few miles of the Land’s
End, one of these fellows whom I had frequently sent away
from my own street.</p>

<p>The amount of in­ter­rup­tion from street music, and from other
occasional noises, varies with the nature and the habits of its
victims. Those whose minds are entirely unoccupied receive
it with sat­is­fac­tion, as filling up the vacuum of time. Those
whose thoughts are chiefly occupied with frivolous pursuits or
with any other pursuits requiring but little attention from the
reasoning or the reflective powers, readily attend to occasional
street music. Those who possess an impaired bodily frame,
and whose misery might be alleviated by <i>good</i> music at proper
intervals, are absolutely driven to distraction by the vile and
discordant music of the streets waking them, at all hours, in
the midst of that temporary repose so necessary for confirmed
invalids.</p>

<p>By pro­fes­sion­al musicians its effects are most severely
felt. It interrupts them in their own studies, and entirely
destroys the value of the in­struc­tions they are giving their
domestic pupils. When they leave their own house to give
lessons to their employers, the “<i>infernal</i>” organ still pursues
them. Their Belgravian employer is obliged, at every
lesson, to bribe the itinerant miscreant to desist—his charge
for this act of mercy being from a shilling to half-a-crown
for each lesson. <span class="xxpn" id="p341">{341}</span></p>

<p>It is, however, right to hint to the members of the
musical profession, that their immediate neighbours do not
quite so much enjoy even the most exquisite pro­fes­sion­al music
when filtered through brick walls, or trans­mit­ted circuitously
and partially through open windows into the houses of their
neighbours. I know of no remedy to propose for the benefit
of the latter class, but I think that a proper self-respect should
induce the pro­fes­sion­al musician himself to close his windows,
and even to suffer the inconvenience of heat, rather than
permanently annoy his neighbours.</p>

<p>The law of retaliation, which is only justified when other
arguments fail, was curiously put in force in a case which was
brought under my notice a few years ago. An artist of considerable
eminence, who resided in the west end of London,
had for many a year pursued his own undisturbed and undisturbing
studies, when one fine morning his pro­fes­sion­al
studies were interrupted by the continuous sound of music
trans­mit­ted through the wall from his neighbour’s house.</p>

<p>Finding the noise continuous and his in­ter­rup­tion complete,
he rang for his servant, and putting his maul into the man’s
hand desired him to continue knocking against the wall from
whence the disturbance proceeded until he returned from a
walk in the Park. He added that he should probably be
absent for an hour, and that if any person called and wished
to see him, he should be at home at the end of that time.</p>

<p>On his return he was informed that the new tenant of the
adjacent house had called during his absence, and that on being
informed of the hour of his master’s return, he had expressed
his intention of calling again. A short time after this the new
tenant of the adjacent house was introduced. He apologized
for this visit to a stranger, but said that during the last
hour he had been annoyed by a
most extraordinary knocking <span class="xxpn" id="p342">{342}</span>
against the wall, which entirely interrupted his pro­fes­sion­al
pursuits.</p>

<p>To this the artist replied in almost precisely the same words,
that during the previous hour he had been annoyed by a most
extraordinary and unusual sound which entirely interrupted
<i>his</i> pro­fes­sion­al pursuits. After some discussion it was settled
that the piano should be removed to the opposite wall,
and that it should be covered with a stratum of blankets.</p>

<p>This arrangement went on for a few months; but the
pupils and their relatives disapproving of a dumb piano
gradually left the professor, who found it desirable to give up
the house and retire to a more music-tolerating neighbourhood.
In this case the evil was equal on both sides, and it was
reasonable that the new comer should retire.</p>

<p>In my own case it has often been suggested to me to retaliate;
and as many of my in­ter­rup­tions have been <i>intentional</i>, that
course might be justifiable. But as they have been confined
to one or two of the lowest persons in the neighbourhood, I
thought it not right to disturb my more respectable neighbours.
The means at my command for producing the most
hideously discordant noises are ample, having a considerable
collection of shrill organ pipes, with appropriate bellows, and
an indefatigable steam engine ever ready to work them whilst
I might be “taking a walk in the Park.” I hope by the
timely amendment of the law no person may be driven to
practise what it refuses to prevent, and thus test the laws of
the country by the <i>reductio ad absurdum</i>.</p>

<p>It is difficult to estimate the misery inflicted upon thousands
of persons, and the absolute pecuniary penalty imposed upon
multitudes of in­tel­lec­tual workers by the loss of their time,
destroyed by organ-grinders and other similar nuisances.</p>

<p>I have witnessed much and
suffered more; many <span class="xxpn" id="p343">{343}</span>
communications on the subject have reached me, and I fear that I
may appear to have neglected several of them. I hope,
however, that the great sacrifice of my own time, which has
been forced upon me in order to secure the remainder, may
be accepted as my excuse. I will now mention some few of
the results.</p>

<p>Even policemen have frequently told me that organs are a
great nuisance to them personally. A large number of the
police are constantly on night duty, and of course these can
only get their sleep during the day. On such occasions their
rest is constantly broken by the nuisance of street music.</p>

<p>A lady, the wife of an officer on half-pay, writes to me,
stating her own sad case. Her husband, suffering under a
painfully nervous affection, is brought up to London for the
benefit of medical advice. Under these circumstances a
sensible improvement takes place, but it requires time and
constant attention to advance the cure. In order to profit by
the eminent skill which London supplies, the lady and her
husband, at considerable sacrifice, take a very small house in a
very quiet little square. Unfortunately, the organ-grinders
had possession of it, and no entreaties would banish them.
The irritation produced on the invalid was frightful, and I
feel it some relief not to have known its almost inevitable
termination.</p>

<p>Various accidents occur as the consequence of street music.
It oc­ca­sion­al­ly happens that horses are frightened, and perhaps
their riders thrown; that carriages are run away with, and
their occupiers dreadfully alarmed and possibly even bruised.</p>

<p>The following casualties were reported, about three years
ago, in most of the daily <span class="nowrap">newspapers:—</span></p>

<div class="dblockquote">
<p>“<span class="smcap">S<b>HOCKING</b></span>
<span class="smcap">O<b>CCURRENCE</b>.</span>—<span class="smcap">S<b>IX</b></span>
<span class="smcap">C<b>HILDREN</b></span>
<span class="smcap">R<b>UN</b></span>
<span class="smcap">O<b>VER</b></span>
<span class="smmaj">AND</span>
<span class="smcap">M<b>UTILATED.</b></span>—Yesterday
afternoon, shortly after four o’clock, a
German band, whilst <span class="xxpn" id="p344">{344}</span>
performing in the Old St. Pancras Road, was the cause of a most dreadful
accident. At the time mentioned, the band referred to was playing at the
corner of Aldenham Terrace, when a man named Charles Field was driving
one of Atcherley’s (the horse-slaughterer’s) carts down Aldenham Street.
At the end of Aldenham Street there is a great declivity into the St. Pancras
Road, and just as the cart was turning it, laden with a dead horse, the big
drum was beaten with extraordinary violence. A cart was standing on the
opposite side of the road, to avoid which a short turn on the part of the
driver of Atcherley’s cart was necessary. The sudden beating of the drum
caused the horse to take fright, and the driver being pitched head foremost
from his seat, caused him to lose control over the animal he was driving,
which dashed in amongst the children and others who were standing in the
road listening to the music, knocking them down right and left. When
the consternation created by the occurrence had subsided, no less than six
poor children were found lying on the ground in a helpless condition, the
vehicle having passed over some part of their persons. They were conveyed
as fast as possible into the adjacent surgery of Dr. Sutherin, of 28, Aldenham
Terrace, who, with his assistant, promptly attended upon them.</p>

<p>“William Hill, aged nine years, of 34, Stanmore Street, who had sustained
fractured ribs and other injuries; and</p>

<p>“Charles Harwood, aged eleven years, of 4, Clarendon Square, with fracture
of the left arm and groin, as well as right leg, caused by the vehicle
passing over them, were removed, by direction of Dr. Sutherin, to University
College Hospital.</p>

<p>“The other sufferers are Robert Thwaites, of 2, St. Pancras Square, aged
seven years, injury to leg and one of his feet;</p>

<p>“James Gunn, 34, Stanmore Street, crushed toes;</p>

<p>“William Young, 8, Percy Terrace, aged six years, contusion to head and
face; and</p>

<p>“A child, name unknown, considerably injured.</p>

<p>“The persons who witnessed the occurrence do not attribute any blame
to the driver; but as soon as it took place the German band were off with
as little delay as possible.”—<i>Daily Telegraph, Oct. 3, 1861.</i></p></div>

<p>If this sad accident had fortunately happened in Belgravia,
there can be little doubt that the law would have been
altered, in order to prevent the recurrence of such frightful
misery.</p>

<p>No attempt, however, has yet been made to remove the
cause; and I have myself more recently seen a German brass
band playing in a very narrow, crowded street,
close to the <span class="xxpn" id="p345">{345}</span>
Bank of England, at three o’clock in the afternoon, making
it difficult to pass, as well as dangerous to one’s pocket.</p>

<p>On another occasion, at two o’clock, a German band was
playing in Piccadilly, at that crowded part, the Circus. In
both instances the police were looking on, and seemed to enjoy
the music they were not directed to stop.</p>

<p>I have obtained, in my <i>own</i> country, an unenviable celebrity,
not by anything I have done, but simply by a determined
resistance to the tyranny of the lowest mob, whose
love, not of music, but of the most discordant noises, is so
great that it insists upon enjoying it at all hours and in every
street. It may therefore be expected that I should in this
volume state at least the outline of my own case.</p>

<p>I claim no merit for this resistance; although I am quite
aware that I am fighting the battle of every one of my
countrymen who gains his subsistence by his in­tel­lec­tual
labour. The simple reason for the course I have taken is,
that however disagreeable it has been, it would have been
still more painful to have given up a great and cherished
object, already fully within my reach. I have been compelled
individually to resist this tyranny of the lowest mob,
because the Government itself is notoriously afraid to face it.</p>

<p>On a careful retrospect of the last dozen years of my life,
I have arrived at the conclusion that I speak within limit
when I state that one-fourth part of my working power has
been destroyed by the nuisance against which I have protested.
Twenty-five per cent. is rather too large an additional
income-tax upon the brain of the in­tel­lec­tual workers of this
country, to be levied by permission of the Government, and
squandered upon its most worthless classes.</p>

<p>The effect of a <i>uniform</i> and <i>continuous</i> sound, in distracting
the attention or in disturbing in­tel­lec­tual
pursuits, is almost <span class="xxpn" id="p346">{346}</span>
insensible. Those who reside near a waterfall—even Niagara—have
their organs soon seasoned and adapted to its monotony.
It is the <i>change</i> from quietness to noise, or from one
kind of noise to another, which instantly distracts the attention.
It would be equally distracted by the reverse—by the
sudden change from the hum of the busy world to the stillness
of the desert.</p>

<p>The injurious effect of noisy in­ter­rup­tions upon our attention
also varies with the nature of the investigations upon
which we are engaged. If they are of a kind requiring but a
very small amount of in­tel­lec­tual effort, as, for instance, the
routine of a public office, they will be little felt. If, on the
other hand, those subjects are of such a character as to require
the highest efforts of the thinker, then their examination is
interrupted by the slightest change in the surrounding circumstances.</p>

<p>When the work to be done is proportioned to the powers
of the mind engaged upon it, the painful effect of in­ter­rup­tion
is felt as deeply by the least in­tel­lec­tual as by the most highly
gifted. The condition which determines the maximum of
in­ter­rup­tion is,—that the mind disturbed, however moderate
its powers, shall be working up to its full stretch.</p>

<p>Finding, many years ago, the increasing in­ter­rup­tion of my
pursuits from street music, as it is now tolerated, I determined
to endeavour to get rid of it by putting in force our
imperfect law, as far it goes. I soon found how very imperfect
it is.</p>

<p>The first step is to require the performer to desist, and to
assign illness or other sufficient reason for the request. If
a female servant is sent on this mission it is quite useless.
The organ-player is scarcely ever acquainted with more than
four or five words of our language: but these
always the most <span class="xxpn" id="p347">{347}</span>
vulgar, the most offensive, and the most insulting. If a manservant
is sent, the Italians are often very insolent, and constantly
refuse to depart. But there are multitudes of sufferers
who are ill and are in lodgings, and have no servant to send.
Besides, the servants must oc­ca­sion­al­ly be absent, being sent
by their employers on their various duties.</p>

<p>The principle on which I proposed to act is, whenever it
can be fully carried out, usually very effective. It was simply
this—to make it more unprofitable to the offender to do the
wrong than the right.</p>

<p>Whenever, therefore, an itinerant musician disturbed me,
I immediately sent out, or went out myself, to warn him away.
At first this was not successful; but after summoning and
convicting a few, they found out that their precious time was
wasted, and most of them deserted the immediate neighbourhood.
This would have succeeded had the offenders been
few in number; but their name is legion: upwards of a thousand
being constantly in London, besides those on their circuit
in the provinces.</p>

<p>It was not, however, the interest of those who deserted my
station to inform their countrymen of its barrenness; consequently,
the freshly-imported had each to gain his own experience
at the expense of his own and of my time. Perhaps
I might have succeeded at last in banishing the Italian nuisance
from the neighbourhood of my residence; but various
other native professors of the art of tormenting with discords
increased as the licence of these Italian itinerants was encouraged.
Another event, however, occurred, which added
much more seriously to my difficulty.</p>

<p>Many years before I had purchased a house in a very quiet
locality, with an extensive plot of ground, on part of which
I had erected workshops and offices, in which
I might carry <span class="xxpn" id="p348">{348}</span>
on the experiments and make the drawings necessary for the
construction of the Analytical Engine. Several years ago the
quiet street in which I resided was invaded by a hackney-coach
stand. I, in common with most of the inhabitants, remonstrated
and protested against this invasion of our comfort
and this destruction of the value of our property. Our
remonstrance was ineffectual: the hackney-coach stand was
established.</p>

<p>The immediate consequence was obvious. The most respectable
tradesmen, with some of whom I had dealt for
five-and-twenty years, saw the ruin which was approaching,
and, wisely making a first sacrifice, at once left their deteriorated
property as soon as they could find for it a purchaser.
The neighbourhood became changed: coffee-shops, beer-shops,
and lodging-houses filled the adjacent small streets. The
character of the new population may be inferred from the
taste they exhibit for the noisiest and most discordant music.</p>

<p>I have looked in vain for any public advantage to justify
this heavy injury to private property. It will scarcely be
believed that another hackney-coach stand actually exists
within two hundred yards,<a class="afnanc" href="#fn50" id="fnanc50">50</a>
namely, that in Paddington
Street, which has a very large space unoccupied by any
houses on either side of the street, and which had frequently
cabs on it plying for hire during the whole night.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc50" id="fn50">50</a>
The distance of the most eastern cab on the stand in Dorset Street
from the spot in Paddington Street, on which cabs might stand without being
opposite any houses, is in reality less than 140 yards. I am not aware of
any two cab-stands placed so near each other as those in question.</p></div>

<p>In endeavouring to put in force the existing law, imperfect
as it is, I have met with sundry small inconveniences which
a Cabinet Minister might perhaps think trivial, but which, in
a slight degree, try the temper even of a phi­los­o­pher. <span class="xxpn" id="p349">{349}</span></p>

<p>Some of my neighbours have derived great pleasure from
inviting musicians, of various tastes and countries, to play
before my windows, probably with the pacific view of ascertaining
whether there are not some kinds of instruments
which we might both approve. This has repeatedly failed,
even with the accompaniment of the human voice divine,
from the lips of little shoeless children, urged on by their
ragged parents to join in a chorus rather disrespectful to their
philosophic neighbour.</p>

<p>The enthusiasm of the performer, excited by such applause,
has oc­ca­sion­al­ly permitted him to dwell too long upon the
already forbidden notes, and I have been obliged to find a
policeman to ascertain the residence of the offender. In the
meantime the crowd of young children, urged on by their
parents, and backed at a judicious distance by a set of vagabonds,
forms quite a noisy mob, following me as I pass along,
and shouting out rather uncomplimentary epithets. When I
turn round and survey my illustrious tail, it stops; if I move
towards it, it recedes: the elder branches are then quiet—sometimes
they even retire, wishing perhaps to avoid my
future recognition. The instant I turn, the shouting and the
abuse are resumed, and the mob again follow at a respectful
distance. The usual result is that the deluded musicians find
themselves left in the lurch at the police-court by their enthusiastic
encouragers, and have to pay a heavier fine for
having contributed to collect this unruly and ungenerous
mob.</p>

<p>Such occurrences have unfortunately been by no means
rare. In one case there were certainly above a hundred
persons, consisting of men, women, and boys, with multitudes
of young children, who followed me through the streets before
I could find a policeman. To such an
extent has this <span class="xxpn" id="p350">{350}</span>
annoyance of shouting out my name, without or with insulting
epithets, been carried, that I can truly affirm, unless I am
detained at home by illness, no week ever passes without
many instances of it.</p>

<p>The police tell me that the children, “who are put up to
the trick by their parents,” belong chiefly to several ragged-schools
in my neighbourhood. I have myself repeatedly
traced numbers of them into the Portman Chapel School,
in East Street. In one instance I went into that school and
made a formal complaint to the teacher, who expressed great
regret for it, and requested me, if I could see any of the
offenders, to point them out; but amongst the number of
children then present I was unable to identify the offenders.</p>

<p>The insults arising from boys, set on by their parents, and
from other older, and therefore less pardonable offenders,
shouting out my name under my windows, or as I pass along
the streets, and even in the middle of the night, are of almost
constant occurrence. Of course, I always appear to take
no notice of such circumstances. Only a few days ago, whilst
I was engaged upon the present chapter, I had occasion to
pass down Manchester Street: when I was about half way
down, I heard from that end of the street I had left, loud and
repeated cries of “Stop thief.” I naturally turned round,
when I saw two young fellows at the corner, who repeated
the cry twice, as loudly as they could, and then ran, as hard
as they were able, round the corner out of my sight. There
could be no mistake that this was intended to annoy me,
because it happened at a time when there was no person
except myself in the upper part of the street.</p>

<p>Another source of annoyance, fortunately only of a very
limited amount, arises from a perverse disposition of some of
my neighbours, who, in two or three instances,
have gone to <span class="xxpn" id="p351">{351}</span>
the expense of purchasing worn-out or damaged wind instruments,
which they are incapable of playing, but on which
they produced a discordant noise for the purpose of annoying
me. One of these appearing at the police-court as a witness
for an organ-grinder, was questioned by the magistrate, and
informed that he would render himself liable to an indictment
by the continuance of such conduct. Another foolish young
fellow purchased a wind instrument with a hole in it, with
which he made discordant noises purposely to annoy me.
Travelling in a third-class carriage to Deptford, he described,
with great zest to the person sitting opposite to him, the
instrument, its price, and the use he made of it. The listener
to this confidence was one of the best of my own draughtsmen,
who was quite as much disturbed by the street music
as myself. The police were made acquainted with the fact,
and I believe still have, from time to time, their eyes upon the
young vagabond.</p>

<p>Another wilful disturber of my quiet, was a workman
inhabiting an attic in a street which overlooked my garden.
When he returned daily to his dinner, this fellow, possessing
a penny tin whistle, opened his window, and leaning out of it,
blew his shrill instrument in the direction of my garden for
about half-an-hour. I simply noted the fact in a memorandum
book, and then employed the time he thought he was
destroying, in taking my daily exercise, or in any other outdoor
mission my pursuits required. After a perseverance in
this course during many months, he discontinued the annoyance,
but for what reason I never knew.</p>

<p>At an early period when I was putting the law in force, as
far as I could, for the prevention of this destruction of my
time, I received constantly anonymous letters, advising,
and even threatening me with all sorts of
evils, such as <span class="xxpn" id="p352">{352}</span>
destruction of my property, burning my house, injury to myself.
I was very often addressed in the streets with similar
threats. On one occasion, when I was returning home from
an affair with a mob whom the police had just dispersed, I
met, close to my own door, a man, who, addressing me, said,
“You deserve to have your house burnt, and yourself in it,
and I will do it for you, you old villain.” I asked him if he
had any objection to give me his address. Of course he
refused. I then followed him at a short distance, looking out
for a policeman. Whenever he saw one at a distance he turned
rapidly up the next street; this chase continued above half-an-hour;
he was then joined by a companion, an ill-looking
fellow. They still continued to turn off into another street
whenever a constable became visible in the distance. At last
we saw a great crowd, into which they both rushed, and
further pursuit became impossible.</p>

<p>I will not describe the smaller evils of dead cats, and other
offensive materials, thrown down my area; of windows from
time to time purposely broken, or from occasional blows from
stones projected by unseen hands.</p>

<p>The last annoyance I shall mention, occurred in the month
of December of the past year. I had been suffering considerably
from ill-health, and it became necessary that I should
undergo a painful surgical operation. Late in the night of
that day, I got into a refreshing sleep, when at one o’clock in
the morning I was suddenly awakened by the crash of a brass
band, which continued playing whilst I was unable to move,
and was compelled passively to submit to the tormentors.</p>

<p>By a most singular accident, many weeks after, I became
possessed of evidence, that the musicians held a consultation
in Manchester Square about going to the top of the street to
wake me up. I am glad, however, to add, for
the credit of <span class="xxpn" id="p353">{353}</span>
human nature, that <i>one</i> of the party advised them not to do
it, and that he himself immediately left them.</p>

<p>It has been found, upon undoubted authority, by returns
from benefit societies, that in London, about 4·72 persons per
cent. are constantly ill. This approximation may be fairly
assumed as the nearest yet attained for the population of
London. It follows, therefore, that about forty-seven out of
every thousand inhabitants are always ill. The number of
persons per house varies in different parts. In my own district
it averages ten to each house; in a neighbouring district
the average is thirteen per house.</p>

<p>In Manchester Street, which faces my own residence, there
are fifty-six houses. This, allowing the above average of ill-health,
will show that about twenty-six persons are usually
ill in that street. Now the annoyance from street music is
by no means confined to the performers in the street in which
a house is situated. In my own case, there are portions of five
other streets in which street music constantly interrupts me
in my pursuits. If the portions of these five streets are considered
to be only equal in population to that of Manchester
Street, it will appear that upwards of fifty people who are ill,
are constantly disturbed by the same noises which so frequently
interrupt my own pursuits.</p>

<p>The misery inflicted upon those who are really ill is far
greater than that which arises from the mere destruction of
time, however valuable. A friend of mine, himself an excellent
magistrate, suffering under a severe and fatal complaint,
was almost driven to distraction during the last six months of
his painful existence, by the constant occurrence of the organ
nuisance, which he was entirely unable to stop.</p>

<p>I have at times made attempts to register the number of
such in­ter­rup­tions in my pursuits; but these
have been very <span class="xxpn" id="p354">{354}</span>
partial and imperfect. I find by some notes, that during about
eighty days, I registered one hundred and sixty-five instances,
the greater part of which I went out myself to put a stop to
the nuisance. In several of these cases my whole day’s work
was destroyed, for they frequently occurred at times when I
was giving in­struc­tion to my workmen relative to some of the
most difficult parts of the Analytical Engine.</p>

<p>At one period after I had succeeded in getting two or
three convictions, some of my neighbours put themselves to
the expense of having large placards printed, in which they
abused me for having put the law in force against the destroyers
of my time. These placards they stuck up in the
windows of their little shops, at intervals from Edgware Road
to Tottenham Court Road. Some of them attempted verse
and thought it poetry; though the only part really imaginative
was their prose statements.</p>

<p>Unfortunately for my comfort, a few years ago, Mr. <span
class="nowrap">X——,</span> one of the magistrates of Marylebone Office,
was succeeded by Mr. <span class="nowrap">Y——.</span> Now the taste of
the new magistrate, like that of his predecessor, was favourable to the
Italian organ: his predecessor might, however, have been excused, as he
was deaf. Possibly Mr. <span class="nowrap">Y——</span> thinks that all
Italian music is high art, and therefore ought to be encouraged.</p>

<p>I soon discovered that it was useless to bring any musical offender
before him, and I had for some time to endure the most intolerable
in­ter­rup­tion of my pursuits.</p>

<p>Upon one occasion, when I had summoned an organ-grinder before him,
his decision was, in my opinion, so unsat­is­fac­tory, that I determined
to address to the Home Secretary a remonstrance against it.</p>

<p>The case was heard by Mr. <span class="nowrap">Y——</span> about the
middle of July. My letter to Sir George Grey, accompanied by a series
<span class="xxpn" id="p355">{355}</span> of the placards, was sent to
the Home Office about the middle of August. I waited patiently for a
reply, but, receiving none, I took it for granted that my letter could
not have reached the Home Secretary. At last, on the 17th of December,
I wrote to his private secretary, in order to ascertain the fact: the
reply to my note was—the simple admission that <i>the letter had been
received</i>. I confess that this event baffled all my calculations. I
had observed that high officials, distinguished by their in­tel­lec­tual
powers, were oc­ca­sion­al­ly oblivious upon minor points; but that high
officials distinguished only by the office they held were usually most
rigidly courteous and exact.</p>

<p>After this I abstained for a long time from bringing any
case before Mr. <span class="nowrap">Y——.</span>
At last a case occurred, which it
appeared to me could not be resisted. I brought it before
that magistrate; it was heard, and the charge was dismissed.
Believing the decision to be erroneous in law, I consulted a
solicitor who had much experience in the Metropolitan Police
Courts, with the view of getting the opinion of the Court of
Queen’s Bench upon the subject.</p>

<p>My legal adviser had no doubt that the decision would be
favourable, but urged upon me the great expense, and
advised me not to proceed. On inquiry as to the probable
amount, he suggested that it might reach fifty pounds. I
immediately replied that it would be good economy to purchase
my own time at that expense, and I desired him to take
the necessary steps.</p>

<p>The first was to get some housekeeper to enter with me
into a bond for twenty pounds to pay the magistrate’s costs,
in case I failed. Having wasted some time upon this, the
magistrate granted a case for the Queen’s Bench, a copy of
which my solicitor
immediately sent me. <span class="xxpn" id="p356">{356}</span></p>

<p>The grounds of Mr. <span class="nowrap">Y——’s</span>
decision, <span class="nowrap">were—</span></p>

<ul>
<li>1st. That the man was not <i>legally</i> in custody.</li>

<li>2nd. That he was not within reasonable distance of my
house.</li>

<li>3rd. That he did not understand the English language.</li></ul>

<p>On receiving this, I felt quite relieved, and thought that a
clear decision upon these three points would be very cheaply
purchased by an expenditure of fifty pounds.</p>

<p>However, on mentioning the subject to several of my personal
friends, who were themselves high in the profession of
the law, I was destined to be grievously disappointed. I was
informed that the Court of Queen’s Bench would not decide
upon any one of the questions, but would decide generally
that the magistrate’s decision was right or was wrong, without
giving me the least intimation on which of the grounds it rested.</p>

<p>I now perceived the <i>dodge</i> that had been practised upon me,
and I felt compelled to admit that Mr. <span class="nowrap">Y——</span> was a <i>clever
fellow</i>. A regard for truth, however, forbids me to extend
the application of this ob­ser­va­tion to anybody else concerned
in this matter.</p>

<p>I have spared neither expense nor personal trouble in endeavouring
to put a stop to this nuisance. During one twelvemonth
those expenses amounted, within a few shillings, to
one hundred and four pounds. I was not, however, the only
sufferer; that amount would otherwise have been expended
in giving a year’s employment to a skilled workman, whose
wages are about two pounds a week.</p>

<p>I shall now give one illustration from my own experience
of the utterly imperfect state of the law for suppressing the
nuisance of street <span class="nowrap">music:—</span></p>

<p>On Monday, the 29th of February, in the present year, at
3
<span class="smmaj">P.M.</span>, in the midst of a thick fog, a brass
band struck up <span class="xxpn" id="p357">{357}</span>
close under my windows. I was in ill-health, and engaged in
a subject requiring much attention. I knocked at the window;
but the band continued their performance. Then I
opened the window and desired them to desist; they still continued,
and I then sent my servant to desire them to go away.
Having finished their tune, they removed about five doors
from my residence, and commenced another performance.
My patience being exhausted, I then went out myself to
desire my tormentors to depart. My servant went on to the
station before he could get a constable. In the meantime
the band had removed about six doors further, and began
another tune. At last my servant arrived with a policeman,
who took down the names and addresses of the nine musicians
constituting the band.</p>

<p>The next day I paid twenty-seven shillings for summonses.
The day after, the police informed me that all the addresses
given, which were either in Richmond or Brentford, were false.
I applied to the police, who watched at certain haunts; but
they only succeeded in identifying two of them. I then
obtained warrants to apprehend those two, and came up
from the country expressly to attend at the police-court; but
the men were not to be found. I am still waiting in the hope
that our police is not quite so inefficient as to allow them to
escape. I have already been put to the charge of employing
a solicitor and to other expenses. But the band itself is, I
believe, still going about in London and playing every day.</p>

<p>Now, if it had been legal for the police to have taken
possession of the instruments of those disturbers of the public
peace, a false address would have been useless, for it would
have been cheaper to have paid the penalties than to have
lost their instruments.</p>

<p>It is, I presume, admitted that streets and high
roads are not <span class="xxpn" id="p358">{358}</span>
the property of those who use them. They are the Queen’s
highways, and were devoted to the public for certain uses only.</p>

<p>The public have an undoubted right to traverse them, and
convey over them persons, goods, materials, &amp;c. The adjacent
householders must bear any amount of noise which is
fairly required for the legitimate use of roads; but no individual
has any right to use them for other purposes, as for
<span class="nowrap">instance—</span></p>

<ul>
<li>Theatrical rep­re­sen­ta­tions—as Punch, Gymnastics.</li>
<li>Playground and games.</li>
<li>Religious services.</li>
<li>Music—as Organs and Brass Bands.</li>
</ul>

<p class="pcontinue">These not merely interfere with their proper use, but disturb
the householders and are in most cases a positive nuisance.</p>

<p>The following letter, from an “Old Lawyer,” recently
appeared in <i>The Times</i>. It states the law briefly, and with
<span class="nowrap">authority:—</span></p>

<div class="dblockquote">
<div>STREET MUSIC.</div>

<div><i>To the Editor of The Times.</i></div>

<p>“<span class="smcap">S<b>IR</b>,</span>—Whether street music in London ought to be put
down or not, I, living in the country, am not concerned to
answer. I suppose it is a question, like smoking, on which the
public will always be divided; but as the law on the subject is
so clear and simple, I am surprised how legislators and justices
can be puzzled about it.</p>

<p>“Every public road or street belongs to the Sovereign, as
embodying the nation, and is accordingly called the King’s or
Queen’s highway. The interest of each individual is limited
to a right of passing and repassing over such highway, and he
is no more entitled to use it for business or amusement than
he is to build upon it or dig for ore
beneath its surface. <span class="xxpn" id="p359">{359}</span>
Hence the keeping of stalls for sale is illegal, and, though
often winked at, is sometimes denounced and punished.
Hence, the police are justified in desiring you to ‘move on,’
if you loiter, in looking at a shop window or conversing with
a friend, so as to bar the progress of passengers. <i>A fortiori</i>, a
band of musicians has no <i>locus standi</i> on the ground.</p>

<p>“There is, in my neighbourhood, a right of way over a
gentleman’s park. But I have only the privilege of passage,
and none of remaining on the path for the purpose of reading,
sketching, or playing the violin.</p>

<p class="pcompclose">“I am, Sir, your obedient Servant,</p>

<p class="psignature">“<span class="smcap">A<b>N</b></span>
<span class="smcap">O<b>LD</b></span>
<span class="smcap">L<b>AWYER</b>.</span>”</p></div>

<p>At most, the tolerance of noisy occupants of the streets,
such as organ-grinders, German bands, <i>et hoc genus omne</i>, is
on sufferance only, and neither the municipal law nor common
sense justifies the invasion or curtailment of a man’s liberty
to use his brain, and exert his mental energies as the occasion
may require; and that, too, even within the very recesses of
the “Englishman’s castle.”</p>

<p>With respect to the remedies against street music, I am not
at all sanguine. The only one which is certain is, positively
to forbid it in all cases, and with it also that varied multitude
of vocal noises made by persons parading the streets singing,
relating tales, praying, offering trifling articles for sale,
&amp;c., all of them with the transparent object of begging.</p>

<p>In all these cases which admit of it, the police ought to be
directed to take possession of the offensive instrument and
convey it to the police-court, there to await the decision of
the magistrate.</p>

<p>Certain street nuisances re-appear periodically every few
years: thus the game called
‘tip-cat’ again prevails. <span class="xxpn" id="p360">{360}</span></p>

<p>After a certain number of eyes have been knocked out, the
police will probably have orders to stop the nuisance. It will
then be put down in a few weeks, and, perhaps, after a year
or two it may break out afresh, and be again as easily put
down.</p>

<p>A similar cycle occurs with children’s hoops: they are
trundled about until they get under horses’ legs. Now if, as
it frequently happens, they are made of iron, not only is the
rider thrown as well as the horse, but the poor animal is
almost sure to have his leg broken.</p>

<p>In these and other similar cases, the offending instrument
should invariably be detained by the police and taken to the
station to be destroyed, or only to be returned on payment of
a small fine by the offending party within three days after the
seizure.</p>

<p>If this were the case, a multitude of daily street nuisances
would very soon disappear. Boys with accordions and other
noisy instruments, small children with shrill tin whistles would
then be obliged to ask their parents to go to the police-office
and pay a fine for the recovery of toys, and the parents themselves
would prevent their children from destroying the time
of other persons as soon as they were made to feel that it
incurred an equal penalty on their own.</p>

<p>Every kind of noisy instrument, whether organ or harp, or
trumpet or penny whistle, if sounded, should be seized by the
police and taken to the station, also all hoops and instruments
for playing games. The effect of this would ultimately
be to diminish the labours of the police. At first they would
have some additional trouble; but a few months would make
the disturbers feel that it was a very unprofitable practice;
and after that, if the police did their duty, they would
only oc­ca­sion­al­ly have to seize a stray
instrument or two. <span class="xxpn" id="p361">{361}</span></p>

<p>Proper warning of this intention to enforce the law ought to
be given. The multitude of music-halls now established in
all parts of London is such that those who enjoy street music
may have a much larger quantity of it, and of a better kind,
at a cheaper rate than that which in their own street disturbs
all their neighbours.</p>

<p>If street music is to be at all tolerated by law, against
which I protest in the strongest manner, then every performer
ought to carry on his back or upon his instrument his
name and address, or an authorized number, by which the
public might be saved from wasting their time by false addresses,
now so frequently given.</p>

<p>I have received several suggestions about organizing a
society, to endeavour to put a stop to these street nuisances.
My reply has been that such a combination well managed
would probably have a very considerable effect, but that it
would be impossible for me to give up to it any of my own
time. I would willingly subscribe to it, and offer it any
suggestions that might assist its operations. Its most important
duty would be to ascertain whether the present law
is sufficient to put down the nuisance. In case it is not, then
it would become necessary to get it amended, and for that
purpose to consult with influential Members about the introduction
of a Bill for that purpose.</p>

<p>Amongst the legal difficulties are the following:—The
magistrates in different districts interpret the law differently.
Might it not be expedient that police magistrates should
meet from time to time and discuss such differences of
opinion, and agree to act upon that of the majority? Or
ought they not to apply to the Home Secretary for his
authority how to interpret it?</p>

<p>If I am right in the opinion which is
confirmed in the <span class="xxpn" id="p362">{362}</span>
letter of the “Old Lawyer,” that the Queen’s highways can only
be legally used by her subjects for the passage of themselves
and the transport of their property, then it is desirable to
ascertain how that principle of the common law can be
enforced. Hitherto all proceedings have been under certain
clauses of the Metropolitan Police Act.</p>

<p>In case any Association should be formed to endeavour to
procure an Act of Parliament to put an end to the music
nuisance, it would be desirable to apply distinctly to each of
the Members for the Metropolitan Boroughs, in order that it
might be known on which side of the question they intended
to vote.</p>

<p>As upon all other subjects, men differ upon street nuisances.
An ancient phi­los­o­pher divided all mankind into <i>two</i>
sections, namely, fools and phi­los­o­phers; and, unhappily for
the race, the one cannot enjoy his whistle except at the
expense of the other. I was once asked by an astute and
sarcastic magistrate whether I seriously believed that a man’s
brain would be injured by listening to an organ; my reply
was, “<i>Certainly not</i>;” for the obvious reason that no man
having brain ever listened to street musicians.</p>

<div class="dpoemctr"><div class="dstanzactr">
<div class="dquoteverse"><span class="spquotebox">“</span>The
 opera, like the pillory, may be said</div>
<div class="dpp00">To nail the ears down, but expose the head.”</div>
</div></div>

<p>I believe that the greater part of the householders of London would
gladly assist in putting a stop to street-music. The proportion of
cases prosecuted compared with the number of in­ter­rup­tions, is, in
my own case, less than one in a thousand. If the annoyance is not
absolutely prohibited by law, the number of the police must be at least
double, to give quiet working people any repose.</p></div><!--section-->

<div class="section" id="p363">
<h2 class="h2herein">CHAPTER XXVII.
<span class="hsmall">WIT.</span></h2>

<div class="dsynopsis">
Poor Dogs&#x200a;—&#x200a;Puns Double and
Triple&#x200a;—&#x200a;History of the Silver
Lady&#x200a;—&#x200a;Disappointed by the Milliner&#x200a;—&#x200a;The
Phi­los­o­pher performs her functions&#x200a;—&#x200a;Lady Morgan’s
Criticism&#x200a;—&#x200a;Allsop’s Beer&#x200a;—&#x200a;Sydney
Smith&#x200a;—&#x200a;Toss up a Bishop&#x200a;—&#x200a;Lady
M&nbsp;.&nbsp;.&nbsp;. and the Gipsy in Spain&#x200a;—&#x200a;Epigram
on the Planet Neptune&#x200a;—&#x200a;Epigram on Henry Drummond’s
attack upon Catholics in the House of Commons&#x200a;—&#x200a;On
Catholic Miracles.</div>

<p class="pfirst"><span class="smcap">I<b>T</b></span>
has often struck me that an analysis of the causes of
wit would be a very interesting subject of inquiry. With that
view I collected many jest-books, but fortunately in this one
instance I had resolution to abstain from distracting my attention
from more important inquiries.</p>

<p>I may, however, note some illustrations of it which occur
to my memory. The late Sir Harris Nicolas used to practice
rather strongly upon some of his friends. I was not an unwilling
victim. The pleasure derived from the wit far
exceeded any pain it inflicted. Indeed, Sir Harris himself
one day expressed his disappointment at my insensibility, by
saying that he had never in his whole life been able really to
hit me.</p>

<p>The late Lord S&nbsp;.&nbsp;.&nbsp;.&nbsp;. was sitting with him one morning
listening to a very astute but rather dry explanation of some
matter about which his Lordship had inquired. At last he
threw himself back in his arm-chair and said, “My dear
Nicolas, I am very stupid this morning: my
brains are all <span class="xxpn" id="p364">{364}</span>
gone to the dogs.” On which Sir Harris pathetically exclaimed,—“Poor
dogs!”</p>

<p>It is evident in this case, that the wit of the reply arose
from sympathy expressed on the wrong side. The peer expected
sympathy from the knight: but the knight gave it to
the dogs.</p>

<p>Another remarkable feature of jokes formed upon this principle
is, that they generally depend upon the intimate meaning
of the words employed, and not either upon their sound
or their arrangement; consequently, they possess the rare
quality of being translatable into all languages.</p>

<p>One of the principles of discovery in many subjects is,
to generalize from the individual case up to the species, and
thence to descend to other individual instances.</p>

<div class="dsdnote">〈A TRIPLE PUN.〉</div>

<p>Puns are detestable. The greater number of them depend
on the double meaning of the same word, or on the similar
pronunciation of words differently spelt. The following may
serve as an example of a triple <span class="nowrap">pun:—</span></p>

<p>A gentleman calling one morning at the house of a lady
whose sister was remarkably beautiful, found her at the
writing-table. Putting his hand upon the little bell used for
calling the attendant, he inquired of the lady of the house
what relationship existed between his walking-stick, her sister,
and the instrument under his finger.</p>

<div class="fsz6">His walking-stick was
<span class="sppunlist"><span class="spblk">{cane,</span><span
 class="spblk">&#x2008;Cain}</span></span>
the brother of <span class="sppunlist">
<span class="spblk">{a bell,</span>
<span class="spblk">&#x2008;a belle,</span>
<span class="spblk">&#x2008;Abel}.</span></span></div>

<p>I mentioned, in an early chapter, my boyish admiration of
an automaton in the shape of a silver lady, who attitudinized
in the most graceful manner. Her fate was singular: at the
death of her maker she was sold with the rest
of his collection <span class="xxpn" id="p365">{365}</span>
of mechanical toys, and was purchased by Weekes, who had a
mechanical exhibition in Cockspur Street. No attempt appears
to have been made to finish the automaton; and it
seems to have been placed out of the way in an attic uncovered
and utterly neglected.</p>

<div class="dsdnote">〈THE SILVER LADY.〉</div>

<p>On the sale by auction of Weeke’s Museum, I met again
the object of my early admiration. Having purchased the
silver figure, I proceeded to take to pieces the whole of the
mechanism, and found a multitude of small holes which had
been stopped up as not having fulfilled their intended object.
In fact, it appeared tolerably certain that scarcely any
drawings could have been prepared for the automaton, but
that the beautiful result arose from a system of continual
trials.</p>

<p>I myself repaired and restored all the mechanism of the
Silver Lady, by which title she was afterwards known to my
friends. I placed her under a glass case on a pedestal in my
drawing-room, where she received, in her own silent but graceful
manner, those valued friends who so frequently honoured
me with their society on certain Saturday evenings.</p>

<p>This piece of mechanism formed a striking contrast with the
unfinished portion of the Difference Engine, No. 1, which
was placed in the adjacent room: the whole of the latter
mechanism existed in drawings upon paper before any portion
of it was put together.</p>

<p>The external surface of the figure, which was beautiful in
form, was made of silver. It was, therefore, necessary to
supply her with robes suitable to her station. This would
have been rather difficult for a phi­los­o­pher, but it was made
easy by the aid of one or two of my fair friends who kindly
intervened. These generously assisted with their own peculiar
skill and taste at the <i>toilette</i> of
their rival Syren. <span class="xxpn" id="p366">{366}</span></p>

<p>Sketches were made and modists of the purest water were
employed. The result was, upon the whole, highly sat­is­fac­tory.
One evening, however, the arrival of the new dress
was postponed to so late a period, that I feared it had entirely
escaped the recollection of the executive department. The
hour at which my friends usually arrived was rapidly approaching.</p>

<p>In this difficulty it occurred to me that there were a few
remnants of beautiful Chinese crape in the silver lady’s wardrobe.
Having selected two strips, one of pink and the other
of light green, I hastily wound a platted band of bright auburn
hair round the block on which her head-dresses were usually
constructed, and then pinned on the folds of coloured crape.
This formed a very tolerable turban, and was not much unlike
a kind of head-dress called a toke, which prevailed at
that period. Another larger piece of the same pink Chinese
crape I wound round her person, which I thought showed
it off to considerable advantage. Fortunately, I found in
her wardrobe a pair of small pink satin slippers, on each of
which I fixed a single silver spangle: then placing a small
silver crescent in the front of her turban, I felt I had accomplished
all that time and circumstances permitted.</p>

<div class="dsdnote">〈LADY MORGAN’S CRITICISM.〉</div>

<p>The criticisms on the costume of the Silver Lady were
various. In the course of the evening, Lady Morgan communicated
to me confidentially her own opinion of the dress.</p>

<p>Holding up her fan, she whispered, “My dear Mr. Babbage,
I think your Silver Lady is rather slightly clad to-night; shall
I lend her a petticoat?” to which I replied, “My dear Lady
Morgan, I am much indebted for your very considerate offer,
but I fear you have not got <i>one</i> to spare.”</p>

<p>This retort was not a pun, but merely a “double-entendre.”
It might mean either that her Ladyship had
on invisibles, but <span class="xxpn" id="p367">{367}</span>
not enough to be able to spare one: or it might imply that,
having no garment of that kind, she was unable to lend one
to a friend.</p>

<p>About the time of the attempt to assassinate the Emperor
of the French by Orsini, an Englishman named Alsop was
arrested in London, and afterwards tried and acquitted of a
connection with the assassins.</p>

<div class="dsdnote">〈ALLSOP’S BEER.〉</div>

<p>At a distinguished dinner-party, amongst whom was the
Attorney-General of that day, there arose a question as to
who Mr. Alsop was. One of the company asked, “Whether it
was Allsop’s beer?” meaning, whether the prisoner was the
concoctor of that delightful beverage. The gentleman to
whom the question was addressed, immediately replied, “It
is not at present Allsop’s <i>beer</i>, but,” said he, turning to the
Attorney-General, “if your prosecution succeeds, it is very
likely to become Alsop’s <i>bier</i>.”</p>

<p>Sydney Smith oc­ca­sion­al­ly called upon me in the morning,
and was ever a most welcome visitor. The conversation
usually commenced upon grave subjects, and I was always
desirous of profiting by the light his powerful mind threw upon
the most difficult questions.</p>

<p>When railways first came into existence much reasonable
alarm arose from the rapidity of the trains and the immense
masses of matter in motion. One morning my friend called
and asked my opinion on the subject. I pointed out what
then appeared to me the chief sources of danger, and entered
upon some of the precautions to be attended to, and of remedies
to be applied.</p>

<p>Sydney Smith then asked me why I did not go and inform
the Government of the danger and of the means of remedying
it. My answer was, that such a mission would be a pure
waste of time, that nothing whatever would
be done until <span class="xxpn" id="p368">{368}</span>
some great man, a prime minister for instance, were smashed.
I then continued, “Perhaps a bishop or two would do; for
you know,” said I, looking slyly at my friend, “they are so
much better prepared for the change than we are.”</p>

<p>I have heard this view of the subject assigned to Sydney
Smith. It is very probable that it should have occurred to
him, although I scarcely imagine he would have given the
reason I did for the preference. His celebrated suggestion to
the person who asked him how a man could find which way the
wind blew when there was no weathercock in sight,<a class="afnanc" href="#fn51" id="fnanc51">51</a>
adds to
the probability of Sydney Smith’s originality. On the other
hand, I may support my own pretensions to independent invention
by referring to a parallel remark I made many years
<span class="nowrap">before:—</span></p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc51" id="fn51">51</a>
Toss up a bishop.</p></div>

<div class="dsdnote">〈OPINION ON DUELLING.〉</div>

<p>At a large dinner party the subject of duelling was discussed.
Various opinions were propounded as to its absolute
necessity. I had made no remark upon the question, but
during a slight pause somebody on the opposite side of the
table asked my opinion on the subject. My reply was,
I always wished that the injured man should fall. On
being asked my reason for that wish, I answered, “Because
he is so much better prepared for the change than the wrong-doer.”
I afterwards learned, with great sat­is­fac­tion, that
when the ladies retired to the drawing-room, the discussion
was much criticized and my reply highly applauded.</p>

<p>The late Lady M.........., having a great desire to see
Mr. Borrow, asked me to invite him to one of my Saturday
evening parties. I expressed my regret that, not having
the pleasure of his acquaintance, I was unable to ask him to
my house, as I never made “lions” of my guests.</p>

<p>A short time after, a friend who was coming to me on the
<span class="xxpn" id="p369">{369}</span>
following Saturday, called to ask me to allow him to
bring Mr. Borrow who dined with him on that day, to my
party in the evening. Of course, I willingly gave the invitation,
and then wrote a note to inform Lady M..........
of the occurrence of the opportunity she wished for.</p>

<p>On the following Saturday evening Lady M.......... was
announced, and immediately asked me whether Mr. Borrow
had arrived. I said that he had, and that he was in the
further room. I then added, that in the course of a few
moments I should have great pleasure in presenting to her
Mr. Borrow.</p>

<p>Lady M.........., who had several other engagements that
evening, said, “Only tell me what sort of a person he is,
and I will go and find him out myself.”</p>

<p>I observed that he was a remarkably tall, straggling person,
with a very intelligent countenance. With these in­struc­tions
her ladyship left me, and finding, as she imagined, exactly
the man I had described, immediately accosted him. The
conversation was highly interesting, and included a great
variety of widely different subjects. It concluded by Lady
M.......... expressing her delight with her new acquaintance,
from whom she parted with this remark, “What a
delightful gipsying life you must have led!”</p>

<div class="dsdnote">〈A SLIGHT MISTAKE.〉</div>

<p>A slight mistake had, however, occurred, which was not
discovered until long after: the person thus addressed
was not Mr. Borrow, but Dr. Whately, the Archbishop of
Dublin.</p>

<p>In this chapter may be placed one or two epigrams which,
though upon subjects of transitory interest, may amuse those
who are acquainted with the attending circumstances.</p>

<p>It will be remembered that great discussion arose about
the conflicting claims of Adams and Le
Verrier to the <span class="xxpn" id="p370">{370}</span>
discovery of the planet Neptune. A great controversy resulted,
which was at last summed up in the following <span class="nowrap">couplet:—</span></p>

<div class="dpoemctr"><div class="dstanzactr">
<div class="dquoteverse"><span class="spquotebox">“</span>When
 Airy was told, he wouldn’t believe it;</div>
<div class="dpp00">When Challis saw, he couldn’t perceive it.”</div>
</div></div>

<div class="dsdnote">〈WINKING STATUES.〉</div>

<p>The clever and eccentric member for East Surrey, the late
Henry Drummond, who founded a professorship of Political
Economy at Oxford, made in the House of Commons a most
amusing, though rather strong speech against the modern
miracles of the Roman Catholic Church, in which he spoke
of “their bleeding pictures, their winking statues, and the
Virgin’s milk.” On this some profane wag wrote the following
<span class="nowrap">couplet:—</span></p>

<div class="dpoemctr"><div class="dstanzactr">
<div class="dquoteverse"><span class="spquotebox">“</span>Sagacious
 Drummond, explain, with your divinity:</div>
<div class="dpp00">Why reject the milk, yet swallow the virginity?”</div>
</div></div>

<p>Probably some clever fellow of that faith was at the bottom
of this mischief; for I have observed that the cleverest fellows
seem to think that the merit of adhering to a cause entitles
them to the right of quizzing it.</p>

<p>I was par­tic­u­lar­ly struck with this idea when I saw, for the first
time, at Cologne, the celebrated picture of St. Ursula and her eleven
thousand virgins. The artist has quietly made every one of them more or
less matronly.</p></div><!--section-->

<div class="section" id="p371">
<h2 class="h2herein">CHAPTER XXVIII.
<span class="hsmall">HINTS FOR TRAVELLERS.</span></h2>

<div class="dsynopsis">
New Inventions&#x200a;—&#x200a;Stomach Pump&#x200a;—&#x200a;Built
a Carriage&#x200a;—&#x200a;Description of Thames
Tunnel&#x200a;—&#x200a;Barton’s Iridescent
Buttons&#x200a;—&#x200a;Chinese Orders of
Nobility&#x200a;—&#x200a;Manufactory of Gold Chains at
Venice&#x200a;—&#x200a;Pulsations and Respirations of
Animals&#x200a;—&#x200a;Punching a Hole in Glass without
cracking it&#x200a;—&#x200a;Specimen of an Enormous
Smash&#x200a;—&#x200a;Proteus Anguineus&#x200a;—&#x200a;Travellers’
Hotel at Sheffield&#x200a;—&#x200a;Wentworth House.</div>

<p class="pfirst"><span class="smcap">I<b>N</b></span>
this chapter I propose to throw together a few suggestions,
which may assist in rendering a tour successful for its
objects and agreeable in its reminiscences.</p>

<p>Money is the fuel of travelling. I can give the traveller
a few hints how to get money, although I never had any skill
in making it myself.</p>

<p>In one tour, extending over more than a twelvemonth, I
took with me two letters of credit, each for half the sum I
should probably require. My reasons for this were, that in
case one was lost the other might still be available. One of
these was generally kept about my person, the other concealed
in my writing-case. Another reason was, that if I were unluckily
carried off and detained for a ransom, it might thus
be mitigated.</p>

<div class="dsdnote">〈TRAVELLING CARRIAGE.〉</div>

<p>It is of great advantage to a traveller to have some acquaintance
with the use of tools. It is often valuable for his
own comfort, and sometimes renders him able to assist a
friend. I met at Frankfort the eldest son
of the coachmaker <span class="xxpn" id="p372">{372}</span>
of the Emperor of Russia. He had been travelling over the
western part of Europe, and showed me drawings he had made
of all the most remarkable carriages he had met with. Some
of these were selected for their elegance, others for the reverse;
take, as an example, the Lord Mayor’s.</p>

<p>We travelled together to Munich, and I took that opportunity
of discussing, seriatim, with my very intelligent young
friend, every part of the structure of a carriage.</p>

<p>I made notes of certain portions in case I should find
occasion to have a carriage built for my own use.</p>

<p>The young Russian was on his way to Moscow, and was
very anxious to prevail on me to accompany him thither, for
which purpose he offered to wait my own time at Munich.
As, however, I wished to reach Italy as soon as possible, I
declined his proposition with much regret.</p>

<p>However, in the following year, I profited by the information
I then gained. I had built for me at Vienna, from my
own design, a strong light four-wheeled calèche in which I
could sleep at full length. Amongst its conveniences were a
lamp by which I oc­ca­sion­al­ly boiled an egg or cooked my
breakfast. A large shallow drawer in which might be placed,
without folding, plans, drawings, and dress-coats. Small
pockets for the various kinds of money, a larger one for
travelling books and telescopes, and many other conveniences.
It cost somewhat about sixty pounds. After carrying me
during six months, at the expense of only five francs for repair,
I sold it at the Hague for thirty pounds.</p>

<p>It is always advantageous for a traveller to carry with him
anything of use in science or in art if it is of a portable
nature, and still more so if it has also the advantage of
novelty. At the time I started on a lengthened tour the
stomach-pump had just been invented. It
appeared to give <span class="xxpn" id="p373">{373}</span>
promise of great utility. I therefore arranged in a small box
the parts of an instrument which could be employed either
as a syringe, a stomach-pump, or for cupping. As a stomach-pump,
it was in great request from its novelty and utility.
I had many applications for permission to make drawings of
it, to which I always most willingly acceded. At Munich,
Dr. Weisbrod, the king’s physician, was greatly interested
with it, and at his wish I lent it to the chief surgical instrument-maker
who produced for him an exact copy of the
whole apparatus.</p>

<div class="dsdnote">〈DESCRIPTION OF THAMES TUNNEL.〉</div>

<p>Having visited the Thames Tunnel a day or two before I
started for the Continent, I purchased a dozen copies of the
very lucid account of that most interesting work. Six of
the copies were in French and the other six in the German
language. I frequently lent a copy, and upon some occasions
I gave one away; but if I had had twice that number I
should have found that I might have distributed them with
advantage as acknowledgments of the many attentions I
received.</p>

<p>Another most valuable piece of travelling merchandise
consisted of a dozen large and a dozen small gold buttons
stamped by Barton’s steel dies. These buttons displayed the
most beautiful iridescence, especially in the light of the sun.
They were formed by ruling the steel die in parallel lines
in various forms. The lines were from the four to the ten
thousandth of an inch apart.</p>

<p>I possessed a die which Mr. Barton had kindly given me.
This I kept in my writing-case; but I had had a small piece
of steel ruled in the same way, though not with quite the
same perfection, which I always kept in my waistcoat pocket;
it was also accompanied by a small gold button in a sandalwood
case. These were frequently of
great service. The <span class="xxpn" id="p374">{374}</span>
mere sight of them procured me many little attentions in
diligences and steamboats.</p>

<div class="dsdnote">〈IRIDESCENT BUTTONS.〉</div>

<p>Of course I never appeared to be the possessor of more
than one of these treasured buttons; so that if any one had
saved my life, its gift would have been thought a handsome
acknowledgment. If I had travelled in the East, as I had
originally intended until the battle of Navarino prevented
me, my buttons might have given me unlimited success in
the celestial empire.</p>

<p>The Chinese, like ourselves, have five orders of nobility.
They are indicated by spherical buttons. The Chinese
nobles, however, wear them on the top of their caps, whilst
our nobility wear their pearls and strawberry-leaves in their
armorial bearings.</p>

<p>It is a curious circumstance that the most anciently
civilized nation should have invented an order of knighthood
almost exactly similar to our own—the order of the Peacock’s
Feather—which, like our own Garter, is confined to certain
classes of nobility of the highest rank. Of the two the
decoration of the Chinese noble is certainly the more graceful.</p>

<p>One out of many illustrations may show the use I made of
a button. During my first visit to Venice I wished to see a
manufactory of gold chains for which that city is justly celebrated.
I readily got permission, and the proprietor was so
good as to accompany me round his factory. I had inquired
the price of various chains, and had expressed my wish to
purchase a few inches of each kind; but I was informed that
they never sold less than a braccia of any one chain. This
amount would have made my purchase more costly than I
proposed, so I gave it up.</p>

<div class="dsdnote">〈THE VALUE OF A BUTTON.〉</div>

<p>In the meantime we proceeded through several rooms in
which various processes were going
on. Observing some <span class="xxpn" id="p375">{375}</span>
tools in one of the shops, I took up a file and asked whence
it was procured. This led to a conversation on the subject,
in which the proprietor gave me some account of files from
various countries, but concluded by observing that the
Lancashire files, when they could be got, were by far the
best. I took this opportunity of asking him whether he had
seen any of our latest productions in steel: then pulling
out of my waistcoat-pocket the piece of hardened steel, ruled
by a diamond, I put it into his hands. The sun was shining
brightly, and he was very much interested with it. I remarked
that in a darkened room, and with a single lamp, it
would be seen with still greater advantage. A room was soon
darkened, and a single lamp produced, and the effect was
still more perfect. My conductor then observed that his managing
man was a very skilful workman, and if I could afford
the time, he should much wish to show him this beautiful
sight. I said it always gave me pleasure to see and converse
with a skilful workman, and that I considered it as time
well spent. The master sent for his superintendent, who,
being of a judicious turn of mind, was lavish in admiring
what his master approved. The master himself, gratified by
this happy confirmation, turning to me, said that he would let
me have pieces of any or all of his gold chains of any length,
however short I might wish them to be.</p>

<p>I thanked him for thus enabling me to make my countrymen
appreciate the excellence of Venetian workmanship, and
purchased small samples of every kind of chain then man­u­fac­tured.
These, on my return to London, I weighed and
measured, and referred to them in the economy of man­u­fac­tures
as illustrations of the different proportions in which
skilled labour and price of raw material occur in the same
class
of man­u­fac­tured articles. <span class="xxpn" id="p376">{376}</span></p>

<p>A friend of mine, then at Venice, again visited that city about
five years afterwards. He sub­se­quent­ly informed me that
he had purchased, at the manufactory I visited, samples of
gold chains about an inch or two long, fixed on black velvet,
and that it formed a regular article of trade in some demand.</p>

<hr class="hrblk" />

<div class="dsdnote">〈PULSATIONS AND INSPIRATIONS.〉</div>

<p>A man may, without being a proficient in any science, and
indeed with only the most limited knowledge of a small
portion of it, yet make himself useful to those who are most
instructed. However limited the path he may himself pursue,
he will insensibly acquire other information in return for
that which he can communicate. I will illustrate this by one
of my own pursuits. I possess the slightest possible acquaintance
with the vast fields of animal life, but at an early period
I was struck by the numerical regularity of the pulsation
and of the breathings. It appeared to me that there must
exist some relation between these two functions. Accordingly,
I took every opportunity of counting the numbers of
the pulsations and of the breathings of various animals. The
pig fair at Pavia and the book fair at Leipsic equally placed
before me menageries in which I could collect such facts.
Every zoological collection of living animals which I visited
thus gained an additional interest, and oc­ca­sion­al­ly excited
the attention of those in charge of it to making a collection
of facts relating to that subject. This led me at another
period to generalize the subject of inquiry, and to print a
skeleton form for the constants of the class mammalia. It
was reprinted by the British Association at Cambridge in
1833, and also at Brussels in the ‘Travaux du Congress
Général de Statistique,’ Brussels, 1853.</p>

<hr class="hrblk" />

<p>I have so frequently been mortified
by having the <span class="xxpn" id="p377">{377}</span>
utterly-undeserved reputation of knowing everything that I was led
to inquire into the probable grounds of the egregious fallacy.
The most frequent symptom was an address of this kind:—“Now
Mr. Babbage, will you, who know everything, kindly
explain to me — — <span class="nowrap">—.”</span> Perhaps the thing whose explanation
was required might be the metre of some ancient
Chinese poem: or whether there were any large rivers in the
planet Mercury.</p>

<div class="dsdnote">〈HOW TO PUNCH A HOLE IN GLASS.〉</div>

<p>One of the most useful accomplishments for a philosophical
traveller with which I am acquainted, I learned from a workman,
who taught me how to punch a hole in a sheet of glass
without making a crack in it.</p>

<p>The process is very simple. Two centre-punches, a hammer,
an ordinary bench-vice, and an old file, are all the
tools required. These may be found in any blacksmith’s shop.
Having decided upon the part of the glass in which you
wish to make the hole, scratch a cross
<span class="nowrap">(<img class="iglyph-a" src="images/capxnonserif.png"
width="40" height="79" alt="X" />)</span>
upon the desired
spot with the point of the old file; then turn the bit of glass
over, and scratch on the other side a similar mark exactly
opposite to the former.</p>

<p>Fix one of the small centre-punches with its point upwards
in the vice. Let an assistant gently hold the bit of glass
with its scratched point exactly resting upon the point of the
centre-punch.</p>

<p>Take the other centre-punch in your own left hand and
place its point in the centre of the upper scratch, which is of
course nearly, if not exactly, above the fixed centre-punch.
Now hit the upper centre-punch a <i>very</i> slight blow with
the hammer: a mere touch is almost sufficient. This must
be carefully repeated two or three times. The result of these
blows will be to cause the centre of the cross to be, as it were,
gently pounded. <span class="xxpn" id="p378">{378}</span></p>

<p>Turn the glass over and let the slight cavity thus formed
rest upon the fixed centre-punch. Repeat the light blows
upon this side of the glass, and after turning it two or three
times, a very small hole will be made through the glass. It
not unfrequently happens that a small crack occurs in the
glass; but with a little skill this can be cut out with the
pane of the hammer.</p>

<p>The next process is to enlarge the hole and cut it into the
required shape with the pane of the hammer. This is accomplished
by supporting the glass upon the point of the fixed
centre-punch, very close to the edge required to be cut. A
light blow must then be struck with the pane of the hammer
upon the edge to be broken. This must be repeated until
the required shape is obtained.</p>

<p>The principles on which it depends are, that glass is a
material breaking in every direction with a conchoidal fracture,
and that the vibrations which would have caused cracking
or fracture are checked by the support of the fixed centre-punch
in close contiguity with the part to be broken off.</p>

<p>When by hastily performing this operation I have caused
the glass to crack, I have frequently, by using more care,
cut an opening all round the cracked part, and so let it drop
out without spreading.</p>

<div class="dsdnote">〈CUTTING A HOLE IN GLASS.〉</div>

<p>This process is rendered still more valuable by the use of
the diamond. I usually carried in my travels a diamond
mounted on a small circle of wood, so that I could easily cut
out circles of glass with small holes in the centre. The description
of this process is sufficient to explain it to an
experienced workman; but if the reader should wish to
employ it, his readiest plan would be to ask such a person to
show him how to do it.</p>

<p>The above technical description will
doubtless be rather <span class="xxpn" id="p379">{379}</span>
dry and obscure to the general reader; so I hope to make
him amends by one or two of the consequences which have
resulted to me from having instructed others in the art.</p>

<div class="dsdnote">〈THE GRATEFUL GLAZIER.〉</div>

<p>In the year 1825, during a visit to Devonport, I had apartments
in the house of a glazier, of whom one day I inquired
whether he was acquainted with the art of punching a hole
in glass, to which he answered in the negative, and expressed
great curiosity to see it done. Finding that at a short distance
there was a blacksmith whom he sometimes employed,
we went together to pay him a visit, and having selected
from his rough tools the centre-punches and the hammer, I
proceeded to explain and execute the whole process, with
which my landlord was highly delighted.</p>

<p>On the eve of my departure I asked for the landlord’s account,
which was duly sent up and quite correct, except the
omission of the charge for the apartments which I had agreed
for at two guineas a week. I added the four weeks for my
lodgings, and the next morning, having placed the total
amount upon the bill, I sent for my host in order to pay him,
remarking that he had omitted the principal article of his
account, which I had inserted.</p>

<p>He replied that he had intentionally omitted the lodgings,
as he could not think of taking payment for them from a
gentleman who had done him so great a service. Quite unconscious
of having rendered him any service, I asked him to
explain how I had done him any good. He replied that he
had the contract for the supply and repair of the whole of
the lamps of Devonport, and that the art in which I had instructed
him would save him more than twenty pounds a
year. I found some difficulty in prevailing on my grateful
landlord to accept what was justly his due.</p>

<div class="dsdnote">〈MODESTY REWARDED.〉</div>

<p>The second instance I shall mention of the use
to which I <span class="xxpn" id="p380">{380}</span>
turned this art of punching a hole in glass occurred in Italy,
at Bologna.</p>

<p>I spent some weeks very agreeably in that celebrated university,
which is still proud of having had the discoverer of
the circulation of the blood amongst its students. One
morning an Italian friend accompanied me round the town,
to point out the more remarkable shops and manufactories.
Passing through a small street, he remarked that there was a
very well-informed man who kept a little shop for the sale of
needles and tape and a few other such articles, but who also
made barometers and thermometers, and had a very respectable
knowledge of such subjects. I proposed that we should
look in upon him as we were passing through the street. On
entering his small shop, I was introduced to its tenant, who
conversed very modestly and very sensibly upon various math­e­mat­i­cal
instruments.</p>

<p>I had invited several of my friends and professors to spend
the evening with me at my hotel, for the purpose of examining
various instruments I had brought with me. I knew that
the sight of them would be quite a treat to the occupier
of this little shop, so I mentioned the idea to my friend, and
inquired whether my expected guests in the evening would
think I had taken a liberty with them in inviting the humble
constructor of instruments at the same time.</p>

<p>My friend and conductor immediately replied that he was
well known to most of the professors, and much respected by
them, and that they would think it very kind of me to give
him that opportunity of seeing the instruments I possessed.
I therefore took the opportunity of asking him to join the
very agreeable party which assembled in my apartments in
the evening.</p>

<div class="dsdnote">〈PRETENSION REPRESSED.〉</div>

<p>We now made a tour of the city, and
reached the factory <span class="xxpn" id="p381">{381}</span>
of the chief philosophical instrument-maker of Bologna.
He took great pleasure in showing me the various instruments
he man­u­fac­tured; but still there was a certain air
of presumption about him, which seemed to indicate a
less amount of knowledge than I should otherwise have
assigned to him. I had on the preceding day mentioned to
my Italian friend, who now accompanied me, that there
existed a very simple method of punching a hole in a piece
of glass, which, as he was much interested about it, I promised
to show him on the earliest opportunity.</p>

<p>Finding myself in the workshop of the first instrument
maker in Bologna, and observing the few tools I wanted, I
thought it a good opportunity to explain the process to my
friend; but I could only do this by applying to the master
for the loan of some tools. I also thought it possible that the
method was known to him, and that, having more practice,
he would do the work better than myself.</p>

<p>I therefore mentioned the circumstance of my promise,
and asked the master whether he was acquainted with the
process. His reply was, “Yes; we do it every day.” I then
handed over to him the punch and the piece of glass, declaring
that a mere amateur, who only oc­ca­sion­al­ly practised
it could not venture to operate before the first instrument-maker
in Bologna, and in his own workshop.</p>

<p>I had observed a certain shade of surprise glance across the
face of one of the workmen who heard the assertion of this
daily practice of his master’s, and, as I had my doubts of it, I
contrived to put him in such a position that he must either
retract his statement or else attempt to do the trick.</p>

<div class="dsdnote">〈AWFUL SMASH.〉</div>

<p>He then called for a flat piece of iron with a small hole in
it. Placing the piece of glass upon the top of this bit of
iron, and holding the punch upon it
directly above the <span class="xxpn" id="p382">{382}</span>
aperture, he gave a strong blow of the hammer, and smashed the
glass into a hundred pieces.</p>

<p>I immediately began to console him, remarking that I did
not myself always succeed, and that unaccountable circumstances
sometimes defeated the skill even of the most accomplished
workman. I then advised him to try a larger<a class="afnanc" href="#fn52" id="fnanc52">52</a>
piece
of glass. Just after the crash I had put my hand upon a
heavier hammer, which I immediately withdrew on his perceiving
it. Thus encouraged, he called for a larger piece of
glass, and a bit of iron with a smaller hole in it. In the
meantime all the men in the shop rested from their work to
witness this feat of every-day occurrence. Their master now
seized the heavier hammer, which I had previously just
touched. Finding him preparing for a strong and decided
blow, I turned aside my head, in order to avoid seeing him
blush—and also to save my own face from the coming cloud
of splinters.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc52" id="fn52">52</a>
The larger the piece of glass to be punched the more
certainly the process succeeds.</p></div>

<p>I just saw the last triumphant flourish of the heavy hammer
waving over his head, and then heard, on its thundering fall,
the crash made by the thousand fragments of glass which it
scattered over the workshop.</p>

<p>I still, however, felt it my duty to administer what consolation
I could to a fellow-creature in distress; so I repeated to
him (which was the truth) that I, too, oc­ca­sion­al­ly failed. Then
looking at my watch, and observing to my companion that
these tools were not adapted to my mode of work, I reminded
him that we had a pressing engagement. I then took leave
of this celebrated instrument-maker, with many thanks for all
he had shown me.</p>

<p>After such a misadventure, I thought it would be cruel to
<span class="xxpn" id="p383">{383}</span>
invite him to meet the learned professors who would be assembled
at my evening party, especially as I knew that I
should be asked to show my friends a process with which he
had assured me he was so familiar. The unpretending maker
of thermometers and barometers did however join the party;
and the kind and considerate manner in which my guests of
the university and of the city treated him raised both parties
in my estimation.</p>

<p>I will here mention another mode of treating glass, which
may oc­ca­sion­al­ly be found worth communicating.</p>

<p>Ground glass is frequently employed for trans­mit­ting light
into an apartment, whilst it effectually prevents persons on
the outside from seeing into the room. Rough plate-glass is
now in very common use for the same purpose. In both
these circumstances there is a reciprocity, for those who are
within such rooms cannot see external forms.</p>

<div class="dsdnote">〈ROUGH GLASS MADE TRANSPARENT.〉</div>

<p>It may in some cases be desirable partially to remedy this
difficulty. In my own case, I cut with my diamond a small
disc of window-glass, about two inches in diameter, and cemented
it with Canada balsam to the rough side of my rough
plate-glass. I then suspended a circular piece of card by a
thread, so as to cover the circular disc. When the Canada
balsam is dry, it fills up all the little inequalities of the rough
glass with a transparent substance, of nearly the same refracting
power; consequently, on drawing aside the suspended
card, the forms of external objects become tolerably well
defined.</p>

<p>The smooth surface of the rough plate-glass, not being
perfectly flat, produces a slight distortion, which might, if it
were worth while, be cured by cementing another disc of
glass upon that side. In case the ground glass itself happens
to be plate-glass, the image of external
objects is perfect. <span class="xxpn" id="p384">{384}</span></p>

<p>Oc­ca­sion­al­ly I met, in the course of my travels, with
various things which, though not connected with my own
pursuits, might yet be highly interesting to others. If the
cost suited my purse, and the subject was easily carried, or the
specimen of importance, I have in many instances purchased
them. Such was the case with respect to that curious creature
the <i>proteus anguineus</i>, a creature living only in the waters of
dark caverns, which has eyes, but the eyelids cannot open.</p>

<div class="dsdnote">〈THE CAVES OF ADELSBURG.〉</div>

<p>When I visited the caves of Adelsburg, in Styria, I inquired
whether any of these singular creatures could be
procured. I purchased all I could get, being six in number.
I conveyed them in large bottles full of river water, which I
changed every night. During the greater part of their journey
the bottles were placed in large leathern bags lashed to the
barouche seat of my calash.</p>

<p>The first of these pets died at Vienna, and another at
Prague. After three months, two only survived, and reached
Berlin, where they also died—I fear from my servant having
supplied them with water from a well instead of from a river.</p>

<p>At night they were usually placed in a large wash-hand
basin of water, covered over with a napkin.</p>

<p>They were very excitable under the action of light. On
several occasions when I have visited them at night with a
candle, one or more have jumped out of their watery home.</p>

<p>These rare animals were matters of great interest to many
naturalists whom I visited in my rambles, and procured for
me several very agreeable acquaintances. When their gloomy
lives terminated I preserved them in spirits, and sent the specimens
to the collections of our own universities, to India, and
some of our colonies.</p>

<hr class="hrblk" />

<p>When I was preparing materials for
the ‘Economy of <span class="xxpn" id="p385">{385}</span>
Man­u­fac­tures,’ I had oc­casion to trav­el fre­quent­ly through our
man­u­fac­tur­ing and min­ing dis­tricts. On these oc­ca­sions I
found the travellers’ inn or the travellers’ room was usually
the best adapted to my purpose, both in regard to economy
and to information. As my inquiries had a wide range, I
found ample assistance in carrying them on. Nobody doubted
that I was one of the craft; but opinions were widely different
as to the department in which I practised my vocation.</p>

<p>In one of my tours I passed a very agreeable week at the
Commercial Hotel at Sheffield. The society of the travellers’
room is very fluctuating. Many of its frequenters arrive at
night, have supper, breakfast early the next morning, and
are off soon after: others make rather a longer stay. One
evening we sat up after supper much later than is usual, discussing
a variety of commercial subjects.</p>

<div class="dsdnote">〈GUESSES AT MY VOCATION.〉</div>

<p>When I came down rather late to breakfast, I found only
one of my acquaintance of the previous evening remaining.
He remarked that we had had a very agreeable party last
night, in which I cordially concurred. He referred to the
intelligent remarks of some of the party in our discussion,
and then added, that when I left them they began to talk
about me. I merely observed that I felt myself quite safe in
their hands, but should be glad to profit by their remarks.
It appeared, when I retired for the night, they debated about
what trade I travelled for. “The tall gentleman in the
corner,” said my informant, “maintained that you were in
the hardware line; whilst the fat gentleman who sat next to
you at supper was quite sure that you were in the spirit
trade.” Another of the party declared that they were both
mistaken: he said he had met you before, and that you were
travelling for a great iron-master. “Well,” said I, “you, I
presume, knew my vocation better
than our friends.”—“Yes,” <span class="xxpn" id="p386">{386}</span>
said my informant, “I knew perfectly well that you were in
the Nottingham lace trade.” The waiter now appeared with
his bill, and announced that my friend’s trap was at the door.</p>

<div class="dsdnote">〈THE PHI­LOS­O­PHER FOUND OUT.〉</div>

<p>I had passed nearly a week at the Commercial Inn without
having broken the eleventh commandment; but the next day
I was doomed to be found out. A groom, in the gay livery
of the Fitzwilliams, having fruitlessly searched for me at all
the great hotels, at last in despair thought of inquiring for
me at the Commercial Hotel. The landlady was sure I was
not staying in her house; but, in deference to the groom’s
urgent request, went to make inquiries amongst her guests.
I was the first person she questioned, and was, of course,
obliged to admit the impeachment. The groom brought a
very kind note from the late Lord Fitzwilliam, who had
heard of my being in Sheffield, to invite me to spend a week
at Wentworth.</p>

<p>I gladly availed myself of this invitation, and passed it very
agreeably. During the few first days the party in the house
consisted of the family only. Then followed three days of
open house, when their friends came from great distances,
even as far as sixty or eighty miles, and that at a period
when railroads were unknown.</p>

<p>On the great day upwards of a hundred persons sat down to dinner,
a large number of whom slept in the house. This was the first time
the ancient custom of open house had been kept up at Wentworth since
the death of the former Earl, the celebrated Whig Lord Lieutenant of
Yorkshire.</p></div><!--section-->

<div class="section" id="p387">
<h2 class="h2herein">CHAPTER XXIX.
<span class="hsmall">MIRACLES.</span></h2>

<div class="dsynopsis">
Difference Engine set so as to follow a given law for a
vast period&#x200a;—&#x200a;Thus to change to another
law of equally vast or of greater duration, and so
on&#x200a;—&#x200a;Parallel between the successive creations of
animal life&#x200a;—&#x200a;The Author visited Dublin at the
first Meeting of the British Association&#x200a;—&#x200a;Is
the Guest of Trinity College&#x200a;—&#x200a;Innocently
wears a Waistcoat of the wrong colour&#x200a;—&#x200a;Is
informed of the sad fact&#x200a;—&#x200a;Rushes to a
Tailor to rectify it&#x200a;—&#x200a;Finds nothing but
party-colours&#x200a;—&#x200a;Nearly loses his Breakfast,
and is thought to be an amazing Dandy&#x200a;—&#x200a;The
Dean thinks better of the Phi­los­o­pher, and accompanied him to
Killarney&#x200a;—&#x200a;The Phi­los­o­pher preaches a Sermon to the
Divine by the side of the Lake.</div>

<p class="pfirst"><span class="smcap">A<b>FTER</b></span>
that portion of the Difference Engine which was
completed had been for some months promoted from the workshop
to my drawing-room, I met two of my friends from Ireland—Dr.
Lloyd, the present Provost of Trinity College, and
Dr. Robinson, of Armagh. I invited them to breakfast, that
they might have a full opportunity of examining its structure.
I invited also another friend to meet them—the late Professor
Malthus.</p>

<p>After breakfast we adjourned to the drawing-room. I then
proceeded to explain the mechanism of the Engine, and to
cause it to calculate Tables. One of the party remarked
two axes in front of the machine which had not hitherto been
performing any work, and inquired for what purpose they
were so placed. I informed him that these axes had been so
placed in order to illustrate a series of
calculations of the <span class="xxpn" id="p388">{388}</span>
most complicated kind, to which they contributed. I observed
that the Tables thus formed were of so artificial and
abstract a nature, that I could not foresee the time when
they would be of any use.</p>

<p>This remark additionally excited their curiosity, and they
requested me to set the machine at work to compute such a
table.</p>

<p>Having taken a simple case of this kind, I set the Engine
to do its work, and then told <span class="nowrap">them—</span></p>

<p>That it was now prepared to count the natural numbers;
but that it would obey this law only as far as the millionth
term.</p>

<div class="dsdnote">〈LAWS CHANGING AT VERY DISTANT INTERVALS.〉</div>

<p>That after that term it would commence a series, following
a different, but known law, for a very long period.</p>

<p>That after this new law had been fulfilled for another long
period, it would then suddenly abandon it, and calculate the
terms of a series following another new law, and so on throughout
all time.</p>

<p>Of course it was impossible to verify these assertions by
making the machine actually go through the calculations;
but, after having made the Engine count the natural numbers
for some time, I proceeded to point out the fact, that it was
impossible, by its very structure, that the machine could
record any but the natural numbers before it reached the
number 999,990. This I made evident to my friends, by
showing them the actual structure of the Engine. Having
dem­on­strated this to their entire sat­is­fac­tion, I put the
machine on to the number 999,990, and continued to work
the Engine, when the result I had predicted soon arrived.
After the millionth term a new law <i>was</i> taken up, and my
friends were convinced that it must, from the very structure
of the machine, continue for a very long
time, and then <span class="xxpn" id="p389">{389}</span>
inevitably give place to another new law, and so on throughout
all time.</p>

<p>When they were quite satisfied about this fact, I observed
that, in a new engine which I was then contemplating, it
would be possible to set it so <span class="nowrap">that—</span></p>

<ul>
<li>1st. It should calculate a Table for any given length of
time, according to any given law.</li>

<li>2nd. That at the termination of that time it should cease
to compute a Table according to that law; but that it should
commence a new Table according to any other given law that
might be desired, and should then continue this computation
for any other given period.</li>

<li>3rd. That this succession of a new law, coming in and continuing
during any desired time, and then giving place to
other new laws, in endless but known succession, might be
continued indefinitely.</li></ul>

<p>I remarked that I did not conceive the time ever could
arrive when the results of such calculations would be of any
utility. I added, however, that they offered a striking parallel
with, although at an immeasurable distance from, the
successive creations of animal life, as developed by the vast
epochs of geological time. The flash of in­tel­lec­tual light
which illuminated the countenances of my three friends at
this unexpected juxtaposition was most gratifying.</p>

<p>Encouraged by the quick apprehension with which these
views had been accepted, I continued the subject, and pointed
out the application of the same reasoning to the nature of
miracles.</p>

<p>The same machine could be set in such a manner that
these laws might exist for any assigned number of times,
whether large or small; also, that it was not necessary that
these laws should be different, but the same
law might, when <span class="xxpn" id="p390">{390}</span>
the machine was set, be ordered to reappear, after any desired
interval.</p>

<p>Thus we might suppose an observer watching the machine,
to see a known law continually fulfilled, until after a lengthened
period, when a new law has been appointed to come in.
This new law might after a single instance cease, and the first
law might again be restored, and continue for another interval,
when the second new law might again govern the
machine as before for a single instance, and then give place
to the original law.</p>

<p>This property of a mere piece of mechanism may have a
parallel in the laws of human life. That all men die is the
result of a vast induction of instances. That one or more
men at given times shall be restored to life, may be as much
a consequence of the law of existence appointed for man at
his creation, as the appearance and reappearance of the isolated
cases of apparent exception in the arithmetical machine.</p>

<div class="dsdnote">〈MIRACLES AND PROPHECY.〉</div>

<p>But the workings of machinery run parallel to those of intellect.
The Analytical Engine might be so set, that at definite
periods, known only to its maker, a certain lever might
become moveable during the calculations then making. The
consequence of moving it might be to cause the then existing
law to be violated for one or more times, after which the original
law would resume its reign. Of course the maker of the Calculating
Engine might confide this fact to the person using it,
who would thus be gifted with the power of prophecy if he
foretold the event, or of working a miracle at the proper time,
if he withheld his knowledge from those around until the
moment of its taking place.</p>

<div class="dsdnote">〈SINGULAR POINTS OF CURVES.〉</div>

<p>Such is the analogy between the construction of machinery
to calculate and the occurrence of miracles. A further illustration
may be taken from geometry.
Curves are represented <span class="xxpn" id="p391">{391}</span>
by equations. In certain curves there are portions, such as
ovals, disconnected from the rest of the curve. By properly
assigning the values of the constants, these ovals may be
reduced to single points. These singular points may exist
upon a branch of a curve, or may be entirely isolated from it;
yet these points fulfil by then positions the law of the curve
as perfectly as any of those which, by their juxtaposition and
continuity, form any of its branches.</p>

<p>Miracles, therefore, are not the breach of established laws,
but they are the very circumstances that indicate the existence
of far higher laws, which at the appointed time produce
their pre-intended results.</p>

<p>In 1835, the British Association visited Dublin. I had
been anxious to promote this visit, from political as well
as scientific motives. I had several invitations to the
residences of my friends in that hospitable country; but I
thought I could be of more use by occupying apartments in
Trinity College, which had kindly been placed at my disposal
by the provost and fellows.</p>

<p>After I had enjoyed the college hospitality during three or
four days, I was walking with an intimate friend, who suggested
to me that I was giving great cause of offence to my
learned hosts. Not having the slightest idea how this could
have arisen, I anxiously inquired by what inadvertence I had
done so. He observed that it arose from my dress. I looked
at the various articles of my costume with a critical eye, and
could discover nothing exaggerated in any portion of it. I
then begged my friend to explain how I had unconsciously
offended in that respect. He replied, “Your waistcoat is of
a bright green.” I became still more puzzled, until he
remarked that I was wearing O’Connell’s colours in the midst
of the Protestant University, whose
guest I was. <span class="xxpn" id="p392">{392}</span></p>

<div class="dsdnote">〈DIFFICULTY OF CHOOSING A DECENT WAISTCOAT.〉</div>

<p>I thanked my friend sincerely, and requested him to accompany
me to my rooms, that I might change the offending
waistcoat. My travelling wardrobe was not large, and, unfortunately,
we found in it no entirely unobjectionable waistcoat.
I therefore put on an under-waistcoat with a light-blue border,
and requested him to accompany me to a tailor’s, that I
might choose an inoffensive colour. As I was not to remain
long in Dublin, I wished to select a waistcoat which might do
double service, as not too gay for the morning, and not too
dull for the evening.</p>

<p>On arriving at the tailor’s, he placed before me a profusion
of beautiful silks, which I was assured contained all the
newest and most approved patterns. Out of these I selected
ten or a dozen, as best suiting my own taste. I then requested
him to remove from amongst them any which might be considered
as a party emblem. He took each of them rapidly
up, and tossing it to another part of the counter, pronounced
the whole batch to appertain to one party or the other.</p>

<p>Thus limited in my choice, I was compelled to adopt a
waistcoat of all work, of rather gayer colours than good taste
would willingly have selected for morning use. I explained
to the knight of the thimble my dilemma. He swore upon
the honour of his order that the finished waistcoat should be
at my rooms in the college punctually as the clock struck
eight the next morning.</p>

<p>During the rest of the day I buttoned up my coat, and the
broad light-blue border of my thin under-waistcoat was alone
visible. My modesty, however, was a little uneasy, lest it
should be thought that I was wearing the decoration of a
Guelphic knight.</p>

<p>I rose early the next morning: eight o’clock arrived, but
no waistcoat. The college breakfast in the
hall was punctual <span class="xxpn" id="p393">{393}</span>
at a quarter past eight; 8·20 had arrived, but still no waistcoat.
At last, at half-past eight, the squire of the faithless
knight of the thimble arrived with the vest.</p>

<p>Thus equipped, I rushed to the hall, and found that my
college friends had waited for my arrival. I explained to the
Dean<a class="afnanc" href="#fn53" id="fnanc53">53</a>
that I had been detained by an unpunctual tailor, who
had not brought home my waistcoat until half an hour after
the appointed time. We then commenced the serious business
which assembled us together. The breakfast was superb,
and the society delightful. I enjoyed them both, being fortunately
quite unconscious that every eye was examining
the artistic and æsthetic garment with which I had been so
recently invested. I thus acquired for a time the character
of a dandy of the first water. It has not unfrequently been
my fate in life to have gained a character for worth or worthlessness
upon grounds quite as absurd, which I have afterwards
seldom taken the trouble to explain.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc53" id="fn53">53</a>
The Rev. S. J. MacLean, Fellow Trin. Coll., Dublin.</p></div>

<p>The Dean, however, quickly saw through the outer covering,
and before the meeting was over I felt that a friendship
had commenced which time could only strengthen. One day,
whilst we were walking together, MacLean told me that he
had heard with great interest from one of his colleagues of
some views of mine relative to miracles, which he wished
much to hear from my own lips.</p>

<p>I remarked that the explanation of them would require
much more time than we could afford during the bustle of
the Association; but that I should afterwards, at any quiet
time, be delighted to discuss them with him.</p>

<p>After the meeting of the British Association terminated, I
made a short tour to visit some of my friends in the North of
Ireland. On my return to Dublin I again found MacLean,
<span class="xxpn" id="p394">{394}</span>
and had the good fortune to enjoy his society in a tour which
we took to Killarney.</p>

<div class="dsdnote">〈THE AUTHOR PREACHES A SERMON ON THE BANK OF KILLARNEY.〉</div>

<p>One fine morning, as we were walking together, it being
Sunday, MacLean, looking somewhat doubtfully at me, asked
whether I had any objection to go to church. I replied,
“None whatever,” and turned towards the church. Before
we reached it an idea occurred to my mind, and I said,
“MacLean, you asked me, in the midst of the bustle at
Dublin, about my views respecting miracles. Have you any
objection to take a walk with me by the side of the lake, and
I will give you a sermon upon that subject.”—“Not the least,”
replied my friend; and we turned immediately towards the
banks of that beautiful lake.</p>

<p>I then proceeded to explain that those views of the apparently
successive creations opened out to us by geology are
in reality the fulfilment of one far more comprehensive law.
I pointed out that a miracle, instead of being a violation of a
law, is in fact the most eminent fulfilment of a vast law—that
it bears the same relation to an apparent law that singular
points of a curve bear to the visible form of that curve. My
friend inquired whether I had published anything upon these
subjects. On my answering in the negative, he strongly
urged me to do so. I remarked upon the extreme difficulty
of making them intelligible to the public. Reverting again
to the singular points of curves, I observed that the illustration,
which in a few words I had placed before him, would be
quite unintelligible even to men of cultivated minds not
familiar with the doctrine of curves.</p>

<p>We had now arrived at a bench, on which we sat. MacLean,
wrapt up in the new views thus opened out to his mind,
remained silent for a long interval. At last, turning towards
me, he made these remarks: “How wonderful
it is! Here <span class="xxpn" id="p395">{395}</span>
am I, bound by the duties of my profession to inquire into
the attributes of the Creator; bound still more strongly by an
intense desire to do so; possessing, like yourself, the same
powerful science to aid my inquiries; and yet, within this
last short half hour, you have opened to me views of the
Creator surpassing all of which I have hitherto had any conception!”</p>

<p>These views had evidently made a very deep impression on
his mind. Amidst the beautiful scenery in the South of Ireland
he frequently reverted to the subject; and, having accompanied
me to Waterford, offered to cross the Channel
with me if I could spend one single day at Milford Haven.</p>

<p>Unfortunately, long previous arrangements prevented this
delay. I parted from my friend, who, though thus recently
acquired, seemed, from the coincidence of our thoughts and
feelings, to have been the friend of my youth. I little
thought, on parting, that one whom I so much admired, so
highly esteemed, would in a few short months be separated
for ever from the friends who loved him, and from the society
he adorned.</p></div><!--section-->

<div class="section" id="p396">
<h2 class="h2herein">CHAPTER XXX.
<span class="hsmall">RELIGION.</span></h2>

<hr class="hr20" />
<div class="dpoemctr fsz7"><div class="dstanzactr">
<div class="dquoteverse1"><span class="spquotebox">“</span>Before
 thy holy altar, sacred Truth,</div>
<div class="dpp01">I bow in manhood, as I knelt in youth;</div>
<div class="dpp00">There let me bend till this frail form decay,</div>
<div class="dpp01">And my last accents hail thine opening day.”</div>
</div></div><hr class="hr20" />

<div class="dsynopsis">
The <i>à priori</i> proof of the existence of a Deity&#x200a;—&#x200a;Proof
from Revelation&#x200a;—&#x200a;Dr. Johnson’s definition of
Inspiration&#x200a;—&#x200a;Various Meanings assigned to the
word ‘Revelation’&#x200a;—&#x200a;Illustration of trans­mit­ted
Testimony&#x200a;—&#x200a;The third source of proof of the
existence of a Deity&#x200a;—&#x200a;By an examination of His
Works&#x200a;—&#x200a;Effect of hearing the Athanasian Creed read for
the first time.</div>

<p class="pfirst"><span class="smcap">T<b>HERE</b></span>
are three sources from which it is stated that man can
arrive at the knowledge of the existence of a Deity.</p>

<ul>
<li>1. The <i>à priori</i> or metaphysical proof. Such is that of
Dr. Samuel Clarke.</li>

<li>2. From Revelation.</li>

<li>3. From the examination of the works of the Creator.</li></ul>

<p>1. The first of these, the <i>à priori</i> proof, is of such a nature
that it can only be apprehended in a high state of civilization,
and then only by the most in­tel­lec­tual. Even amongst that
very limited class it does not, as an argument, command
universal assent.</p>

<p>2. The argument deduced from revelation is advanced in
many countries and for several different
forms of faith. <span class="xxpn" id="p397">{397}</span>
When it is sincerely adopted it deserves the most respectful
examination. It must, however, on the other hand, be submitted
to the most scrutinizing inquiry. As long as the
believer in any form of revelation maintains it by evidence or
by argument, it is only by such means that it ought to be
questioned.</p>

<div class="dsdnote">〈WILFUL ABUSE OF LANGUAGE.〉</div>

<p>When, however, professed believers dare to throw doubt
upon the motives of those whose arguments they are unable
to refute, and still more, when, availing themselves of the
imperfections of language, they apply to their opponents
epithets which they can defend in one sense but know will
be interpreted in another—when they speak of an adversary
as a disbeliever, because, though he believes in the same
general revelation, he doubts the accuracy of certain texts,
or believes in a different interpretation of others—when they
apply the term infidel, meaning thereby a disbelief in their
<i>own</i> view of revelation, but knowing that it will be understood
as disbelief in a Deity,—then it is at least allowable to
remind them that they are richly paid for the support of their
own doctrines, whilst those they revile have no such motives
to influence or to mislead their judgment.</p>

<p>Before, however, we enter upon that great question it is
necessary to observe that belief is not a voluntary operation.
Belief is the result of the influence of a greater or less preponderance
of evidence acting upon the human mind.</p>

<p>It ought also to be remarked that the word revelation
assumes, as a fact, that a Being exists from whom it proceeds;
whilst, on the other hand, the existence of a Deity is
possible without any revelation.</p>

<div class="dsdnote">〈INSPIRATION.〉</div>

<p>The first question that arises is the meaning of the word
revelation. In its ordinary acceptation it is said to be a
direct communication from the Deity to
an individual human <span class="xxpn" id="p398">{398}</span>
being. Dr. Johnson remarks:—“Inspiration is when an
overpowering impression of any propositions is made upon
the mind by God himself, that gives a convincing and
indubitable evidence of the truth and divinity of it.” Be
it so; but then, as such, it is not revelation to any <i>other</i>
human being. All others receive it from the statement of
the person to whom the revelation was vouchsafed. To all
others its truth depends entirely on human testimony. Now
in a certain sense all our faculties being directly given to
us by the Supreme Being might be said to be revelations.
But this is clearly not the religious meaning of the word. In
the latter sense it is a direct special communication of knowledge
to one or more persons which is not given to the rest
of the race.</p>

<p>Before any person can admit the truth of a revelation
asserted by another, he must have clearly established in his
own mind what evidence he would require to believe in a
special revelation to himself.</p>

<p>But when he communicates this revelation to his fellow-creatures
that which may truly be a revelation to him is not
revelation to them. It is to them merely human testimony,
which they are bound to examine more strictly from its abnormal
nature.</p>

<p>Let us now suppose that this believer in his own special
revelation offers to work a miracle in proof of the truth of his
doctrine, and even, further, that he does perform a miracle.
Those who witness it have now before them far higher evidence
of inspiration than that of the prophet’s testimony.
They have the evidence of their own senses that an act contrary
to the ordinary laws of nature has been performed.</p>

<p>But even here the amount of conviction will be influenced
by the state of knowledge the spectator
of the miracle <span class="xxpn" id="p399">{399}</span>
himself possesses of the laws of nature which he <i>believes</i> he has
thus seen violated.<a class="afnanc" href="#fn54" id="fnanc54">54</a></p>

<div class="dsdnote">〈REVELATION.〉</div>

<p>Granting him, however, the most profound knowledge, the
evidence influencing his own mind will be inferior to that
which acts upon the mind of the inspired worker of the
miracle. If there are more witnesses than one thus qualified,
this will to a certain extent augment the evidence, although
a large number might not give it a proportional addition of
weight.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc54" id="fn54">54</a>
I have adopted in the text that view of the nature of
miracles which prevailed many years ago. In 1838, I published, in
the “Ninth Bridgewater Treatise,” my own views on those important
subjects—the nature of miracles and of prophecy. Those opinions have
been received and adopted by many of the most profound thinkers of very
different religious opinions.</p></div>

<p>It would be profane to compare evidence derived directly
from the Almighty, which must necessarily be irresistible,
with the testimony of man, which must always be carefully
weighed by taking into account the state of his knowledge,
his prejudices, his interests, and his truthfulness. On the
other hand, it would lead to endless confusion, and be destructive
to all reasoning on the subject, to apply the same word
‘Revelation’ to things so different in their nature <span class="nowrap">as—</span></p>

<ul>
<li>The immediate act of the Deity.</li>

<li>The impression produced by that act on the mind of
the person inspired.</li>

<li>The description of it given by him in the language of
the people he addressed.</li>

<li>The record made of his description by those who
heard it.</li>

<li>The transmission of this through various languages
and people to the present day.</li></ul>

<p>We have now arrived at the highest external evidence man
can have—the declaration of inspiration
by the prophet, <span class="xxpn" id="p400">{400}</span>
supported by an admitted miracle performed before competent
witnesses, to prove the truth of his inspiration.</p>

<div class="dsdnote">〈TRANSMITTED TESTIMONY.〉</div>

<p>But to all who were not present, the evidence of this is
entirely dependent on the truth and even upon the accuracy
of <i>human testimony</i>.</p>

<p>At every step of its transmission it undergoes some variation
in the words in which it is related; and without the
least want of good faith at any stage, the mere imperfection
of language will necessarily vary the terms by which it is
described. Even when written language has conveyed it to
paper as a MSS., there may be several different manuscripts
by different persons. Even in the extraordinary case of two
MSS. agreeing perfectly there remains a perpetual source of
doubt as to the exact interpretation arising from the continually
fluctuating meaning of the words themselves.</p>

<p>Few persons who have not reflected deeply, or had a very
wide experience, are at all aware of the errors arising from
this source.</p>

<div class="dsdnote">〈RUSSIAN SCANDAL.〉</div>

<p>There is a game oc­ca­sion­al­ly played in society which
eminently illustrates the value of testimony trans­mit­ted with
the most perfect good faith through a succession of truthful
persons. It is called Russian Scandal, and is thus <span class="nowrap">played:—</span></p>

<p>One of the party writes a short simple tale, perhaps a
single anecdote. The original composer of the tale, whom we
will call A, retires into another room with B, to whom he
communicates it. A then returns to the party, and sends in
C, who is told by B the tale he had just learnt. B then
returns to the party and sends in D, who is informed of the
anecdote by C, and so on until the story has been trans­mit­ted
through twelve educated and truthful witnesses.</p>

<p>The twelfth then relates to the whole party the story he has
just heard: after that the original written
document is read. <span class="xxpn" id="p401">{401}</span>
The wit or fun of the trans­mit­ted story is invariably gone,
and nothing but an unmeaning platitude generally remains.</p>

<p>One very interesting case occurred a few years ago in
which the wit of the original story had evidently been lost, but
had afterwards been revived in a different form in the latter
part of its transmission. The story at starting consisted of
the following <span class="nowrap">anecdote:—</span></p>

<p>The Duke of Rutland and Theodore Hook having dined
with the Lord Mayor, were looking for their hats previously
to their departure. The Duke, unable to find his own, said to
his friend: “Hook, I have lost my castor.” The Lord Chief
Baron, Sir Frederick Pollock, was at that moment passing
down the stairs. Hook perceiving him, replied instantly,
“Never mind, take Pollock’s” (Pollux).</p>

<p>The story told at the conclusion, after a dozen transmissions,
was <span class="nowrap">thus:—</span></p>

<p>Theodore Hook and the Duke of Rutland were dining with
the Bishop of Oxford. Both being equally incapable of finding
their respective hats, the Duke said to the wit, “Hook, you
have stolen my castor.” “No,” replied the prince of jokers,
“I haven’t stolen your castor, but I should have no objection
to take your beaver;” alluding to Belvoir Castle, the splendid
seat of the Duke of Rutland, which in the language of the
clay is pronounced precisely in the same way as the name of
that animal whom man robs of his great-coat in order to
make a covering for his own skull.</p>

<p>It requires considerable training to become an accurate
witness of facts. No two persons, however well trained, ever
express, in the same form of words, the series of facts they
have both observed.</p>

<hr class="hrblk" />

<div class="dsdnote">〈THE BELIEF IN THE CREATOR FROM HIS WORKS.〉</div>

<p>3. There remains a third source from which
we arrive at <span class="xxpn" id="p402">{402}</span>
the knowledge of the existence of a supreme Creator, namely,
from <i>an examination of his works</i>. Unlike trans­mit­ted testimony,
which is weakened at every stage, this evidence derives
confirmation from the progress of the individual as well as
from the advancement of the knowledge of the race.</p>

<p>Almost all thinking men who have studied the laws which
govern the animate and the inanimate world around us,
agree that the belief in the existence of one Supreme
Creator, possessed of infinite wisdom and power, is open to far
less difficulties than the supposition of the absence of <i>any</i>
cause, or of the existence of a <i>plurality</i> of causes.</p>

<p>In the <i>works</i> of the Creator ever open to our examination,
we possess a firm basis on which to raise the superstructure of
an enlightened creed. The more man inquires into the laws
which regulate the material universe, the more he is convinced
that all its varied forms arise from the action of a few
simple principles. These principles themselves converge, with
accelerating force, towards some still more comprehensive
law to which all matter seems to be submitted. Simple as
that law may possibly be, it must be remembered that it is
only one amongst an infinite number of simple laws: that
each of these laws has consequences at least as extensive as
the existing one, and therefore that the Creator who selected
the present law must have foreseen the consequences of all
other laws.</p>

<p>The <i>works</i> of the Creator, ever present to our senses, give a
living and perpetual testimony of his power and goodness far
surpassing any evidence trans­mit­ted through human testimony.
The testimony of man becomes fainter at every stage of transmission,
whilst each new inquiry into the works of the
Almighty gives to us more exalted views of his wisdom, his
goodness, and his power. <span class="xxpn" id="p403">{403}</span></p>

<div class="dsdnote">〈THE ATHANASIAN CREED.〉</div>

<p>When I was between sixteen and seventeen years of age, I
heard, or rather I attended, for the first time, to the words of
the Athanasian Creed. I felt the utmost disgust at the direct
contradiction in terms which its words implied; and during
several weeks I recurred, at intervals, to the Prayer-Book to
assure myself that I rightly remembered its singular and self-contradictory
assertions. On inquiry amongst my seniors, I
was assured that it was all true, and that it was part of the
Christian religion, and that it was most wicked to doubt a
single sentence of it. Whereupon I was much alarmed,
seeing that I found it absolutely impossible to believe it, and
consequently, if it were an essential dogma, I clearly did not
belong to that faith.</p>

<p>In the course of my inquiries, I met with the work upon the
Trinity, by Dr. Samuel Clarke. This I carefully examined,
and although very far from being satisfied, I ceased from
further inquiry. This change arose probably from my having
acquired the much more valuable work of the same author,
on the Being and Attributes of God. This I studied, and felt
that its doctrine was much more intelligible and sat­is­fac­tory
than that of the former work. I may now state, as the result
of a long life spent in studying the <i>works</i> of the Creator, that
I am satisfied they afford far more sat­is­fac­tory and more convincing
proofs of the existence of a supreme Being than any
evidence trans­mit­ted through human testimony can possibly
supply.</p>

<p>If I were to express my opinion of the Athanasian Creed
merely from my experience of the motives and actions of
mankind, I should say that it was written by a clever, but
most unscrupulous person, who did not believe one syllable of
the doctrine,—that he purposely asserted and reiterated propositions
which contradict each other in terms,
in order that <span class="xxpn" id="p404">{404}</span>
in after and more enlightened times, he should not be supposed
to have believed in the religion which he had, from
worldly motives, adopted.</p>

<p>The Athanasian Creed is a direct contradiction in terms:
if three things can be one thing, then the whole science of
arithmetic is at once annihilated, and those wonderful laws,
which, as astronomers have shown, govern the solar system, are
mere dreams. If, on the other hand, it is attempted to be
shown that there may be some mystic sense in which three
and one are the same thing, then all language through which
alone man can exert his reasoning faculty becomes useless,
because it contradicts itself and is untrue.<a class="afnanc" href="#fn55" id="fnanc55">55</a></p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc55" id="fn55">55</a>
See Appendix, Note B.</p></div>

<div class="dsdnote">〈THE BASIS OF VIRTUE IS TRUTH.〉</div>

<p>The great basis of virtue in man is <i>truth</i>—that is, the constant
application of the same word to the same thing.</p>

<p>The first element of accurate knowledge is <i>number</i>—the
foundation and the measure of all he knows of the material
world.</p>

<p>I believe these views of the Athanasian Creed are by no
means singular,—that they are indeed very generally held,
although very rarely asserted. If such is the case, it were wise
to take the opportunity which the new Commission for the
revision of the Liturgy presents, to remove from the Rubric
doctrines so thoroughly destructive of all true religion, and
about which the author, doubtless in mockery, so complacently
tells us, that whosoever does not believe them “without
doubt, he shall perish everlastingly.”</p>

<p>The true value of the Christian religion rests, not upon
speculative views of the Creator, which must <i>necessarily</i>
be different in each individual, according to the extent of the
knowledge of the finite being, who employs his own feeble
powers in contemplating the infinite: but it
rests upon those <span class="xxpn" id="p405">{405}</span>
doctrines of kindness and benevolence which that religion
claims and enforces, not merely in favour of man himself, but
of every creature susceptible of pain or of happiness.</p>

<div class="dsdnote">〈IDENTITY DEPENDS ON MEMORY.〉</div>

<p>A curious reflection presents itself when we meditate upon
a state of rewards and punishments in a future life. We
must possess the memory of what we did during our existence
upon this earth in order to give them those char­ac­ter­is­tics.</p>

<p>In fact, memory seems to be the only faculty which must
of necessity be preserved in order to render a future state
possible.</p>

<p>If memory be absolutely destroyed, our personal identity is
lost.</p>

<p>Further reflection suggests that in a future state we may, as
it were, awake to the recollection that, previously to this our
present life, we existed in some former state, possibly in many
former ones, and that the then state of existence may have
been the consequences of our conduct in those former stages.</p>

<p>It would be a very interesting research if naturalists could
devise any means of showing that the dragon-fly, in its three
stages of a grub beneath the soil—an animal living in the
water—and that of a flying insect—had in the last stage any
memory of its existence in its first.</p>

<p>Another question connected with this subject offers still
greater difficulty. Man possesses five sources of knowledge
through his senses. He proudly thinks himself the highest
work of the Almighty Architect; but it is quite <i>possible</i> that
he may be the very lowest. If other animals possess senses
of a different nature from ours, it can scarcely be possible
that we could ever be aware of the fact. Yet those animals,
having other sources of information and of pleasure, might,
though despised by us, yet enjoy a corporeal as well as an
in­tel­lec­tual existence far higher
than our own.</p></div><!--section-->

<div class="section" id="p406">
<h2 class="h2herein">CHAPTER XXXI.
<span class="hsmall">A VISION.</span></h2>

<p class="pfirst"><span class="smcap">H<b>OW</b>,</span>
when, and where this vision occurred it is unnecessary
for me at present to state. It did not arise under the action
of the laughing-gas or of chloroform, but by some much
more real and immediate spiritual action. I had no perception
of body or of matter, yet I felt that I was in the
presence of a reasoning being of a different order from man.
Language was not the means of our communication; yet it
became necessary, in order to be intelligible, when I wrote
down the facts immediately after that singular event—but
language itself is quite insufficient to give an adequate idea
of its immense apparent duration.</p>

<p>The first difficulty I felt in this communion with an unearthly
Spirit was the notion of space. Our views of it
differed widely. On many points, as, for instance, measure,
we apprehended each other perfectly, for each referred to
the height of an individual of his own race—of course about
six feet. At last I discovered that my idea of space, which
was founded upon vacuity, was exactly the reverse of that
of the Spirit, which was based upon solidity. I will now,
as far as I can, place before my reader the information I
received.</p>

<div class="dsdnote">〈THE CONSEQUENCES OF DOUBT.〉</div>

<p>The first desire I expressed to the Spirit was to learn, if
possible, his view of the origin of all things.
He stated that <span class="xxpn" id="p407">{407}</span>
the records of his race, which he declared was the highest in
creation, went back, with great certainty, for myriads of
years before all other created beings: that previously to this,
their history was somewhat obscure, but had recently been
placed upon a much surer footing by some of their most
prominent Spirits.</p>

<p>(<i>a.</i>) In the beginning all space was fluid—apparently one
universal whitish liquid extended in all directions through
what we should call space; so I thought at first that this might
have some relation to the “milky way.” Its temperature
was considerable; and in about every thousand years a torrent
of this fluid, of a still higher temperature, passed through
space with a kind of gushing rush. It was peopled by
myriads of happy spirits floating about in it.</p>

<p>After long ages of happiness a dispute arose between two
Spirits as to the possibility of the existence of matter under
any other form than that of a fluid. The Power which
controlled their destiny, justly angry at their presumption,
threw into the fluid a very small piece of what, as far as
I could understand, was like organic matter.</p>

<p>(<i>b.</i>) The effect was astounding: all the fluid in contact with
this intrusive piece of matter gradually lost its fluidity, and a
new state of matter or of space arose which had been unknown
in all past time. The change advanced slowly but
certainly, on every side of the intruded matter. In its new
form, as far as I could make out, space became elastic gelatinous
matter. The two quarrelsome Spirits were the first
to be surrounded in it. None in the immediate presence of
this new kind of space could move away, and absorption went
on rapidly imprisoning millions of beings.</p>

<p>A great controversy arose as to the state of those embedded
in the jelly. Some supposed that they
were miserably squeezed, <span class="xxpn" id="p408">{408}</span>
and maintained that they deserved to be thoroughly wretched.
Whilst others asserted, that being entirely relieved from
movement, theirs must be a state of perfect blessedness, their
whole faculties being absorbed in contemplation. In the
midst of these discussions the process of jellification was
advancing more and more rapidly, and in ten thousand years
the whole of infinite fluidity throughout all space, with all
its myriads of Beings embedded in it, was transformed into
this new form of space. From the description conveyed to
me by the Spirit, I should infer that the whole of what we
call infinite space had now become more nearly like <i>blancmange</i>
than any other sub-aërial substance.</p>

<div class="dsdnote">〈SPACE TOO LARGE FOR ITSELF.〉</div>

<p>(<i>c.</i>) After a state of repose of many hundred thousand years
a new catastrophe occurred. Space became too large even
for itself. It then suffered, for many hundred thousand
years, enormous compression. During this long period all
its embedded Spirits perished, and space itself, during six
hundred thousand years, became one vast and solid desert,
containing no living beings.</p>

<p>But the vast periods of the past were as nothing compared
with the long series of cycles which now succeeded—each
in itself comprising millions of years.</p>

<p>About this time recorded history began, and is believed, by
the Spirit with whom I was in conference, to be as authentic
as the nature of the circumstances admit.</p>

<p>One solitary survivor seems to have escaped the crash of
systems and the condensation of space. He proceeded to cut
himself into two parts, and to advise each part to follow out
the same course, directing them to transmit the command of
their first parent throughout all time. Alone, in the midst of
infinite solidity, the newly-severed beings, setting themselves
back to back, exerted force. Thus urged,
matter itself gave <span class="xxpn" id="p409">{409}</span>
way, and they occupied an elongated hollow space. Then
again bisecting themselves, they further lengthened the path.
After ten thousand years they began to exert their energies
in the transverse directions of that path, and thus widened it.
The race then began to form chambers, each for himself, into
which he might retire for abstruse calculations, the nature of
which seemed almost beyond the remotest reach of utility,
although not beyond the power of the Analytical Engine.
Thus vast cities, as it were, became formed, penetrating in
every direction through solid space.</p>

<p>(<i>d.</i>) After millions of years of industry quietness and calculations,
a most extraordinary catastrophe occurred. It was with
the greatest difficulty that I could discover its nature, or how
to explain it in ordinary language. The nearest approach I
can make towards its explanation is this:—It seemed, from
what my spiritual informant communicated, that the whole
universe was lifted up bodily, and then borne rapidly back
with a great shock, thus disarranging everything, and destroying
millions of their race.</p>

<div class="dsdnote">〈CONVERSION OF ATTICS INTO CELLARS.〉</div>

<p>But the most in­com­pre­hen­sible part of this historic narration
was, that on the survivors recovering their senses, they
found that everything which had formerly been on their right
hand was now on their left. They also observed, to their still
greater dismay, that every abode in the universe was turned
topsy-turvy, so that the surviving phi­los­o­phers, who had
retired to their attics to study, suddenly found themselves in
their cellars.</p>

<p>I have conveyed, as carefully as the nature of the subject
admits, the impressions this relation made upon me, sometimes
assisted in my slow apprehensions by another unembodied
Spirit, whom, to distinguish from the relator, I shall
call Mathesis. <span class="xxpn" id="p410">{410}</span></p>

<div class="dsdnote">〈THE TRUE USE OF FIGURES.〉</div>

<p>Whenever a man can get hold of numbers, they are invaluable:
if correct, they assist in informing his own mind,
but they are still more useful in deluding the minds of others.
Numbers are the masters of the weak, but the slaves of the
strong. I therefore earnestly pressed for more exact information
as to the possible number of years; but it appeared
beyond the Spirit’s power to estimate it, even within a few
millions. He mentioned incidentally that the last vast period
he had just described was merely one of many others of
similar extent: also, that though these periods were not
actually equal, the difference, which even in extreme cases
only reached a hundred thousand years, was not worth considering.</p>

<p>To gratify my longing desire for information on this most
important subject, the Spirit proceeded to inform me that
their histories recorded a large number of these successive
catastrophes, and that they were succeeded by a new and
more terrible one, which he was proceeding to explain, when
I interrupted him by asking for an approximate estimate of
their number. Aware of my anxious desire for numerical
accuracy, he said he could, in this one instance, gratify it
fully. “If there is,” said my informant, “any one point
better established than all others, it is that there had occurred
exactly one hundred and twenty-one of these avatars
of destruction.”</p>

<p>I now felt as if I had discovered one solitary fixed point in
the vast chaos of time. My guide described to me that, after
the termination of this system of one hundred and twenty-one
cycles, a new and more terrific system of events followed
each other.</p>

<p>First, however, he said he must mention an interregnum,
irregular in its progress, but still
of vast duration; <span class="xxpn" id="p411">{411}</span>
in fact, some of his race had been able to prove that it
occupied at least three times as long as any one of those just
described.</p>

<div class="dsdnote">〈VARIOUS SHAKES AND SMASHES.〉</div>

<p>(<i>e.</i>) It commenced by a motion very like that to which
space itself had been submitted at the end of each avatar,
finishing with a smash, and followed by a period of repose
of about ten thousand years. It however differed from those
avatars inasmuch as there was no inversion of the position of
cellar and attic.</p>

<p>(<i>f.</i>) A new form of shaking of universal solid space now
arose, much more frequent but less destructive than the
former. It occurred about once in two years, and was repeated
many hundred thousand times.</p>

<p>(<i>g.</i>) Again a period exactly similar to that recorded in
(<i>e</i>) occurred.</p>

<p>(<i>h.</i>) This was followed by a long series of movements of all
solidity, approaching, as far as I could understand it, to an
oscillating or wave motion. This continued without intermission
during exactly three of those cycles whose precise
number had been preserved.</p>

<p>(<i>i.</i>) During the whole of this period there was a great destruction
of the race. A universal sickness arose and continued
more or less, so that multitudes actually perished, and
those who escaped could scarcely carry on the ordinary calculations
necessary for their existence.</p>

<p>(<i>j.</i>) Another period followed, ending with a smash excessively
like (<i>e</i>).</p>

<p>(<i>k.</i>) Then followed a period of shaking like that in (<i>f</i>).</p>

<p>(<i>l.</i>) Then another smash like (<i>e</i>).</p>

<p>(<i>m.</i>) Period of long repose.</p>

<p>After this came a long state of absolute rest.</p>

<p>Such was the dawn of the most terrible, as
well as the <span class="xxpn" id="p412">{412}</span>
most recent, of these vast changes in the universe which had
been so well related by my ethereal guide.</p>

<div class="dsdnote">〈A COMMISSION SENT TO EXPLORE.〉</div>

<p>(<i>n.</i>) The temperature of the universe had been uniform
throughout many millions of years: it now began to change in
different isolated places. Increased cold in some parts drove
the inhabitants from their dwellings. This was followed by
torrents of invisible air, bringing infection and death to
millions of their race. Public opinion was roused, and their
academies of science and of arts were urged to devise
a remedy. An expedition was sent by their school of
Science and of Geology to endeavour to trace the origin of
this plague.</p>

<p>The Commission, after long investigation, reported that they
had penetrated solid space in their usual way, putting each
other back to back, and pressing the foremost forward. It
also stated that one of them had invented a method of
arrangement of the members in a kind of wedge form, which
they found much more effective for their object. The result
of this, however, was that the leader of the column got so
many squeezes, that all their best Spirits declined a position
for which coarser animals were better fitted. Consequently,
most of their Presidents of scientific bodies were selected from
what we should call the “<i>Demi-monde</i>” of science.</p>

<p>The first report of this Commission stated that, after penetrating
space (by pushing) through many thousand miles,
they had reached the cause of all the evil. They had ascertained
that it arose from the fact they had discovered,—that
space itself was discontinuous:—that they had reached a spot
where there was a kind of chasm in it, into which some of
them tumbled, and were with difficulty extricated:—in fact,
they reported that it was only necessary to send proper persons
to fill up this chasm in order to restore the
universe to health. <span class="xxpn" id="p413">{413}</span></p>

<div class="dsdnote">〈WELL FED AND WELL PAID ON RETURN.〉</div>

<p>Great rejoicings were made on the return of this Commission.
Public meetings were held, speeches were made,
papers were read, and medals were lavished. Those who
had interest used their services on this committee to justify
their promotion, each in his own different line. Those who
had no interest as well as those who had, were anointed
daily during twelve months with what I can but very imperfectly
describe by calling it <i>lip-salve</i>. All this while they
were fed at the public expense with <i>royal food</i>, which was
highly coveted; but as far as I could make out, its taste
must have been somewhat intermediate between rancid butter
and flummery. Whatever this may have been, they relished
it highly, and in truth it seems to have been well suited to
their organs of digestion.</p>

<p>Time, however, went on; the pestilence increased. Strange
reports arose: first, that space itself was decaying; then, that
there existed somewhere in decayed space an immense
dragon whose breath produced the pestilence, and who swallowed
up thousands of Spirits at each mouthful.</p>

<p>Another Commission was sent, with in­struc­tions to fill up
the hole in space. This was supposed to be a great step in
advance. Having penetrated a very short distance beyond
the celebrated chasm, they found another just like it, and on
the same level. They found the first chasm slightly curved,
which had indeed been remarked by an unpretending member
of the former Commission: but so simple a remark was not
thought worth reporting. The second chasm also was found
slightly curved, but its curvature was in an opposite direction,
presenting rudely the appearance of two parentheses, thus
(&nbsp;&nbsp;&nbsp;&nbsp;). Upon this discovery the Commission were inclined
to return and report that a series of chasms occurred in
advance of the first, and that it
would be useless—indeed, <span class="xxpn" id="p414">{414}</span>
that it would be highly dangerous—to open more chasms.
One of the most modest of the Com­mis­sion­ers, who had been
snubbed on the former occasion, suggested, however, that
these slightly-curved chasms might possibly be portions of
some vast circular crack: an idea which was ridiculed as a
wild hypothesis by the chairman, quizzed by the secretary,
and laughed at by all the rest. Fortunately they were persuaded
to excavate a few yards more on the second vertical
chasm or crack, when it became probable that the single
dissentient was right. It soon became certain, and before
half the circle had been uncovered, each member of the commission
thought he had himself been the first to discover its
circular shape.</p>

<div class="dsdnote">〈THE MODEL CHAIRMAN.〉</div>

<p>But the chairman was a person of large experience. He
quietly left the Com­mis­sion­ers to fight amongst themselves
about the discovery of the circle, and if they chose, even about
its quadrature. On his return, however, he reported that
from some very extensive calculations of his own he had
anticipated an elliptic cavity; that he had directed the attention
of the Com­mis­sion­ers to the subject; and that they had
succeeded in verifying his prediction. He also stated that
the same theory led him to the knowledge of the fact, that
in certain cases the ellipse might approach very nearly to a
circle, although it could never actually reach it, whilst on
the other hand it might become so flat as to approach a
straight line—an approximation to which nobody ever suggested
that the chairman himself could have attained. The
chairman then, with singular modesty, alluding in his report
to one of his colleagues possessing high rank, great influence
and a very moderate knowledge of science, remarked that it
was fortunate for him (the chairman) that that distinguished
member had been so fully occupied with
much more valuable <span class="xxpn" id="p415">{415}</span>
investigations, otherwise he would certainly have anticipated
the important discovery it had fallen to his own lot to make.</p>

<div class="dsdnote">〈THE COMMISSIONERS OUT-MANŒUVRED.〉</div>

<p>In the meantime the Com­mis­sion­ers, who had each wished
to appropriate to himself the discovery of the circle, <i>now</i>
thought that this usurpation of it by their chairman was most
unjust towards the unpretending member who had really
made it. They therefore advised him to claim his own discovery,
and promised to back him in asserting it.</p>

<p>But their chairman really was a <i>clever fellow</i>,<a class="afnanc" href="#fn56" id="fnanc56">56</a>
and deep
as Silurian rocks. Aware of the importance of the discovery
thus appropriated, he had already visited the modest Com­mis­sion­er—had
overwhelmed him with compliments, and had
also prevailed upon that other influential Com­mis­sion­er whom
he had so well buttered in his Report, to give him a small
piece of preferment, which had been accepted by his victim:—thus
putting a padlock upon his lips, which his brother
Com­mis­sion­ers were unable either to unlock or to pick.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc56" id="fn56">56</a>
A <i>clever fellow</i> may oc­ca­sion­al­ly snatch our applause; but
a <i>clever man</i> can alone command our respect.</p></div>

<p>After the Report was presented, more speeches were made—more
medals given, but the plague con­tin­ued, and their
un­i­verse was de­pop­u­la­ted.</p>

<p>A third Commission was afterwards sent, who reported that
they found at the spot previously reached, on either side,
two vast circles, the diameter of each of which was one
hundred times the height of an ordinary individual; that the
material occupying space within the circle differed slightly
from that without it; and that it appeared as if a vast
cylinder of space had been pushed through without disturbing
the matter external to it. They also reported that the former
Com­mis­sion­ers had never approached the origin of the mischief,
but had simply worked their way, at right angles, to a
<span class="xxpn" id="p416">{416}</span>
line which might terminate in it at the distance of a thousand
miles, more or less, either on the right or on the left hand of
the point they had reached.</p>

<div class="dsdnote">〈DISTURBED VISION.〉</div>

<p>At this moment a sound like the roll of distant thunder
recalled me to this lower world, and interrupted my interesting
communion with the world of Spirits. That noise arose
from the chimes of the cathedral clock. Spending a few
days at Salisbury, I had wandered into the cathedral, and
being much fatigued, had selected the luxurious pew of the
Dean as a place of temporary rest. Reposing on elastic
cushions, with my head resting on an eider-down pillow, the
vision I have related had taken place.</p>

<p>On removing the pillow I observed a small piece of matter
beneath it. This, upon examination, turned out to be a morsel
of decayed Gloucester cheese. The whole vision was now
very clearly explained. The verger had evidently retired to
the most commodious pew to eat his dinner, and had inadvertently
left the small bit of cheese upon the very spot I had
selected for my temporary repose. It was clear that my
Spirit had been put, <i>en rapport</i>, with the soul of a mite, one
of the most cultivated of his race.</p>

<p>If the reader will glance over the following brief explanation,
he will be fully convinced that my solution of this vision
is the true one.</p>

<ul id="ulp416"><li class="li0">
<div><i>Parallel Passages in the Creation of the Universe and in the
Birth and Education of a Gloucester Cheese.</i></div>
<ul>
<li class="li0"><p class="pfirst fsz7">References.</p>
<p class="phanga"><i>a.</i> Milk gushing into the milk-pail at the rate of twenty
gushes per minute. Alternations of greater and
less heat.</p></li>

<li class="li0"><p class="phanga"><i>b.</i> Rennet being thrown in, the milk curdles.</p></li>

<li class="li0"><p class="phanga"><i>c.</i> Curds
compressed into cheese. <span class="xxpn" id="p417">{417}</span></p></li>

<li class="li0"><p class="phanga"><i>d.</i> Cheese turned over daily during
121 days.</p>
   <p class="pinb phanga">A few minutes’ difference in the time of
   the dairyman’s attendance to perform this operation made the days
   slightly unequal.</p></li>

<li class="li0"><p class="phanga"><i>e.</i> Cheese lifted up and pitched
into a cart.</p></li>

<li class="li0"><p class="phanga"><i>f.</i> Cheese <i>jolted</i> in cart during
half a day on its way to to be shipped at Gloucester.</p></li>

<li class="li0"><p class="phanga"><i>g.</i> Cheese pitched from cart into
ship.</p></li>

<li class="li0"><p class="phanga"><i>h.</i> Ship sails with the cheese for
Southampton.</p></li>

<li class="li0"><p class="phanga"><i>i.</i> The motion of the waves makes
the mites sea-sick for three days. Multitudes die.</p></li>

<li class="li0"><p class="phanga"><i>j.</i> Cheese taken from ship and
pitched into a cart; as in the period <i>e</i>.</p></li>

<li class="li0"><p class="phanga"><i>k.</i> Cheese conveyed in cart to
cheesemonger at Salisbury—the mites dreadfully <i>jolted</i>,</p></li>

<li class="li0"><p class="phanga"><i>l.</i> Cheese pitched into
cheesemonger’s shop, as in <i>e</i>.</p></li>

<li class="li0"><p class="phanga"><i>m.</i> Long period of repose of the
cheese on the cheesemonger’s shelf.</p></li>

<li class="li0"><p class="phanga"><i>n.</i> A cylindrical cavity made and
piece taken out for a customer to taste. Portion of cylinder replaced.
Air being let in, a part of the cheese becomes rotten, in which large
worms are produced, giving rise to the story of the dragon.</p>
</li></ul></li></ul>

<div class="dsdnote">〈EXPLANATION.〉</div>

<p>In order to discover the month in which the cheese was
made, I remarked that, since it was turned over on its shelf
in the cheese-room exactly 121 times, it must have been
first placed there in some month which, together with the
three succeeding months, had a number of days exactly equal
to 121. <span class="xxpn" id="p418">{418}</span></p>

<div class="dsdnote">〈CALCULATION.〉</div>

<p>I then computed the following <span class="nowrap">Table:—</span></p>

<div class="dtablebox">
<table summary="">
<caption class="phanga"><i>Table of the number of Days contained in each
four months, commencing on the first day of each month and ending on
the last day of the fourth following month.</i></caption>
<tr>
 <th scope="col" title="time period"></th>
 <th scope="col">Number of Days.</th></tr>
<tr>
 <td class="tdleft">1 January to 30 April</td>
 <td class="tdcntr">120</td></tr>
<tr>
 <td class="tdleft">1 February to 31 May</td>
 <td class="tdcntr">120</td></tr>
<tr>
 <td class="tdleft">1 March to 30 June</td>
 <td class="tdcntr">122</td></tr>
<tr>
 <td class="tdleft">1 April to 31 July</td>
 <td class="tdcntr">122</td></tr>
<tr>
 <td class="tdleft">1 May to 31 August</td>
 <td class="tdcntr">123</td></tr>
<tr>
 <td class="tdleft">1 June to 30 September</td>
 <td class="tdcntr">122</td></tr>
<tr>
 <td class="tdleft">1 July to 31 October</td>
 <td class="tdcntr">123</td></tr>
<tr>
 <td class="tdleft">1 August to 30 November</td>
 <td class="tdcntr">122</td></tr>
<tr>
 <td class="tdleft">1 September to 31 December</td>
 <td class="tdcntr">122</td></tr>
<tr>
 <td class="tdleft">1 October to 31 January</td>
 <td class="tdcntr">123</td></tr>
<tr>
 <td class="tdleft">1 November to 28 February</td>
 <td class="tdcntr">120</td></tr>
<tr>
 <td class="tdleft">1 December to 31 March</td>
 <td class="tdcntr">121</td></tr>
</table></div>

<p>Now, from the preceding Table it appears that there is
only one month in the year fulfilling this condition, namely,
the month of March. It follows, therefore, that the cheese
must have been made four months before, that is, in the
month of December.</p>

<hr class="hrblk" />

<p>Shortly after this vision I received a visit from that great
geologist, the erudite Professor Ponderdunder,<a class="afnanc" href="#fn57" id="fnanc57">57</a>
a member of
all existing Academies, and Secretary of the most celebrated
How-and-wi Academy for the <i>Reconstruction of Primeval
Time</i>. I was anxious to have the opinion of this learned
person upon my recent experience: but he was evidently
envious of my vision, which he
treated disrespectfully. <span class="xxpn" id="p419">{419}</span>
Possessed of an intellect which was anything but precocious, I
had with much labour at last made him apprehend the arithmetic
by which I had discovered the exact month of December
in the date of the great series of 121 cataclysms, and I felt
much mortified that he did not appreciate my ingenuity.
All of a sudden he seemed intuitively to perceive the use
that might be made of this vision. He then asked me with
great earnestness whether I had communicated this new
method of reasoning to any other person. On my answering
in the negative, he entreated me not to say a word about it.
He was especially anxious that Gardner Wilkinson, Layard,
and Rawlinson should not get hold of it, lest they might
anticipate the discovery which it would enable him to complete.
He assured me that he could, by visiting Nineveh, and
taking the Pyramids and Jericho on his road, with the aid of
my formula, restore the true chronology from the creation.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc57" id="fn57">57</a>
Author of the celebrated Treatise “On the Entity of
Space,” the basis of all <i>sound</i> metaphysical reasoning.</p></div>

<div class="dsdnote">〈THE LEARNED PONDERDUNDER STARTS FOR JERICHO.〉</div>

<p>Having given him this promise, he left me, and immediately
telegraphed to a very influential friend, the Vice-President
who <i>managed</i> the How-and-wi Academy, suggesting that not
a moment should be lost in authorizing him to set out on
this expedition, which although painfully laborious to himself
personally and not without peril, he was willing to undertake
for the glory of the Academy, and from the religious conviction
that it would enable him to refute the frightful heresy
of Bishop Colenso. Within twenty-four hours the faithful
telegraph brought him back the order to start and the
credit necessary for his equipment. He soon completed the
latter, and was <i>en route</i> within the time I have mentioned.</p>

<p>It is with deep regret I have now to state, that just ten
days after the active Secretary had started on his pious mission,
I discovered that my reasoning about the month of
December with all its consequences
was completely vitiated <span class="xxpn" id="p420">{420}</span>
by not having taken into consideration the existence of leap
years, in which case the magic number 121 occurs in no less
than four cases; so that nothing at all is decided by it.</p>

<p>I can only add my hope that, if any of my readers should
become acquainted with the whereabouts of the learned
Ponderdunder, he would kindly communicate by electric
telegraph this painful intelligence to that energetic traveller.</p>

<p>I have sub­se­quent­ly been informed that Professor Ponderdunder’s
honorarium is only £800 a-year, and the payment
of all travelling expenses. The former is doubled upon
dangerous travel. I was told that he also enjoys a snug
sinecure of considerable value recently instituted in his own
country; being at the head of the department for the promotion
of “<i>Small Science and Low Art</i>.” The family of the
Ponderdunders possess the peculiar gift of manipulating
learned bodies. The Flowery—Rhetorical, and the Zoo-Ethnological
Societies barely escaped perdition under their costly
autocracy. I regret also to add, (but truth forbids me to
conceal the interesting fact) that Ponderdunder is <i>not</i> a
member of <i>all</i> existing academies as his visiting card indicated.</p>

<p>On searching the list of the members of the Roman Academy
“Dei Lynxcii,” I find that he is not a Lynx. This, the oldest of
European academies, originally existed in the time of Galileo.
About a quarter of a century ago I had the honour of receiving its
diploma.</p></div><!--section-->

<div class="section" id="p421">
<h2 class="h2herein">CHAPTER XXXII.
<span class="hsmall">VARIOUS REMINISCENCES.</span></h2>

<h3 class="h3herein"><i>On Preventing the Forgery of Bank-Notes.</i></h3>

<p class="pfirst"><span class="smcap">I<b>N</b></span>
1836 imitations of bank-notes were so easily made, and
the forgeries so numerous, that the Directors of the Bank of
England resolved on appointing a small committee to
examine the subject, and advise them upon a remedy.</p>

<p>The Governor of the Bank wrote to ask me whether I
would consent to act upon that committee. Not being myself
a pro­fes­sion­al engineer, I entertained some doubts whether
my presence would be agreeable to the profession. Having
consulted Sir Isambard Brunel and the late Mr. Bryan
Donkin, who had been also applied to, they both pressed me
to join them in the inquiry.</p>

<p>We examined the existing means of preventing forgery,
which were certainly very defective. The system of the
Bank of Ireland which had recently been greatly improved,
was then discussed. Not many months before, I had carefully
examined the whole plan at Dublin. After a full deliberation
on the subject, I drew up our Report, which unanimously
recommended its adoption. The identity of the steel plates
from which the bank-notes were to be printed was secured
by Perkins’s plan of multiplying the number of such plates by
impressing them all from one roll of hardened steel.</p>

<p>This plan answered its purpose fully at that
time. It has, <span class="xxpn" id="p422">{422}</span>
however, been superseded within the last few years. I had,
through the kindness of the late Governor of the Bank of
England, an opportunity of examining their most recent
improvement. The discovery of the process of making fac-similes
of a wood engraving, by means of the electro-chemical
deposit of copper, has now enabled the Bank to return to the
more rapid process of surface printing.</p>

<p>It is probable, from the great progress of the mechanical
arts, that these periods for revising methods of preventing
forgery will occur at more frequent intervals.</p>

<p>I derived great pleasure from being permitted, as an
amateur, to join in this interesting inquiry with my pro­fes­sion­al
friends, whose knowledge and character I highly valued.</p>

<p>Subsequently I received the unexpected gratification of a
vote of thanks from the Governor and Company of the Bank
of England—an honour usually reserved for warriors and
statesmen.</p>

<div class="dkeeptgth">
<h3 class="h3herein"><i>An Émeute.</i></h3>

<p>On one of my visits to Paris I had the pleasure of dining at
the Bank of France. During dinner, in the midst of an interesting
conversation, the Chairman received a note: having glanced over it he
put it down by his side on the table.</p></div>

<p>On the occurrence of a pause in the conversation, thinking the note
might possibly require an immediate reply, I inquired whether such was
the case. “No,” said my host, “it is of no consequence. It is only an
émeute;” which he then informed me was occurring in a distant part of
Paris.</p>

<div class="dkeeptgth"> <h3 class="h3herein"><i>Letters of Credit.</i></h3>

<p>Letters of credit are specially addressed to certain bankers at
various places with whom your own banker is in correspondence. <span
class="xxpn" id="p423">{423}</span></p></div>

<div class="dsdnote">〈THE AUTHOR IN WANT OF CASH.〉</div>

<p>It has on several occasions happened to me to want cash
either for myself or to accommodate some friend at places
where my own letters were not addressed to any firm. At
Frankfort I made a purchase of books. I had a certain
amount of the usual circular letters, but as these were payable
in a great many cities, and as I proposed visiting Egypt, I
did not wish to part with them. I therefore went to the
house of Rothschild, hoping to get an advance on my letter
of credit, although it was not addressed to that firm. But it
being Saturday, no business was done. I therefore inquired for
another banker of reputation, and was directed to M. Koch.</p>

<p>I accordingly called at his counting-house, stated my
reason for wanting the money, showed him my circular notes
and letters of credit, and asked whether, under these circumstances,
he would cash my check for twenty pounds. He
immediately remarked that he had frequently visited England,
and that most probably we had several common friends,
as it soon appeared, for the first person he mentioned was
Professor Sedgwick.</p>

<p>M. Koch not only advanced me the money, but he was
so kind as to invite me to dinner on the following day, and to
give me a seat in his box at the opera on the first appearance
of Madamoiselle Sontag on the Frankfort stage.</p>

<p>I remember at least three other occasions in which I got
money for some of my English friends at towns where my
letter of credit was not addressed to any banker. In those
cases I only asked them to take my cheque, send it to London,
and when they had received the amount, to pay it over to me.
I also mentioned that I was known to several persons resident
in Geneva and in Berlin where these occurrences happened.
In each case the banker immediately let me have the money
my friends wanted. <span class="xxpn" id="p424">{424}</span></p>

<div class="dsdnote">〈DIFFICULTY OF GETTING CASH, HANDSOMELY REMOVED.〉</div>

<p>The only instance in which I was refused amused me very
much. I spent a few weeks at Modena, where I had purchased
a microscope and several other philosophical instruments.
One morning I went to the wealthy firm of Sanguinetti,
and mentioning my object to one of the partners, at the
same time showing him my letter of credit, asked if, under
these circumstances, he would give me cash for a draft of
twenty pounds on my banker in London. He replied very
courteously that it was the rule of their house to give credit
only upon letters addressed to them by their <i>own</i> cor­res­pon­dent
in London. I remarked that it was quite necessary
in matters of business to adhere to fixed rules, and that when
made aware of their practice I should be the last person to
ask them to deviate from it.</p>

<p>Early the next morning a carriage drove up to the door of
my lodgings and an elderly gentleman was announced. This
was M. Sanguinetti, the senior partner of the firm. He told
me he came to apologize for the refusal of his junior partner
on the preceding day, and to offer to give me cash for my
cheque to whatever amount I might require.</p>

<p>I replied that, a near relative of my own having formerly
been a banker in London, I was aware of the necessity of a
rigid observance of rules of business, and that his young
partner had not only done his duty, but, I added, that he
had done it in the most courteous manner. M. Sanguinetti
was so obliging and so pressing, that I found it difficult to
accept the advance of so small a sum: however, it was all
arranged, and he left me.</p>

<p>I then sent for my landlord and inquired whether he had
had any communication with M. Sanguinetti. He replied
that the old gentleman, the head of the firm, had called the
preceding evening, and asked him who I
was. “And what,” <span class="xxpn" id="p425">{425}</span>
said I to my landlord, “was your answer?”—“I told him you
were a Milord Anglais,” replied my host.—“I am not a
Milord Anglais,” I observed; “but why did you tell him so?”—“Because,”
said my landlord, “when the minister paid you
a visit, you sat down in his presence.”</p>

<p>The explanation of the affair was this. Soon after my
arrival at Modena, I called on the Marquis Rangoni, a distinguished
mathematician, who had written a profound comment
on Laplace’s ‘Théorie des Fonctions Génératrices.’ I
had not brought any letter of introduction, but had merely
sent up my card. The Marquis Rangoni received me very
cordially, and we were soon in deep discussion respecting
some of the most abstract questions of analysis. He returned
my visit on the following day, when he resumed the discussion,
and I showed him some papers connected with the subject. I
was aware of the title of the Marquis Rangoni to respect, as
arising from his own profound acquaintance with analysis, but
I was now, for the first time, informed that he was a man of
great importance in the little Dukedom of Modena, for he
was the Prime Minister of the Grand Duke—in fact, the
Palmerston of Modena. This at once explained the attention
I received from the wealthy banker.</p>

<div class="dkeeptgth">
<h3 class="h3herein"><i>The Speaker.</i></h3>

<p>One Saturday morning an American gentleman who had
just arrived from Liverpool, where he had landed from the
United States on the previous day, called in Dorset Street.
He was very anxious to see the Difference Engine, and quite
fitted by his previous studies for understanding it well. I
took him into the drawing-room in which the machine then
resided and gave him a short explanation of its structure.
As I expected a large party of my friends
in the evening, <span class="xxpn" id="p426">{426}</span>
amongst whom were a few men of science, I asked him to
join the party.</p></div>

<div class="dsdnote">〈A CONTRAST—ENGLAND—AMERICA.〉</div>

<p>It so happened on that day that the Speaker had a small
dinner-party. The Silver Lady was accidentally mentioned,
and greatly excited the curiosity of the lady of the house.
As the whole of this small party, comprising three or four of
my most intimate friends, were coming to my house in the
evening, they proposed that the Speaker and his wife should
accompany them to my party, assuring them truly that I
should be much gratified by the visit.</p>

<p>The Silver Lady happened to be in brilliant attire, and
after mentioning the romance of my boyish passion, the
unexpected success of her acquisition, and the devoted
cultivation I bestowed upon her education, I proceeded to
set in action her fascinating and most graceful movements.</p>

<p>A gay but by no means unin­tel­lec­tual crowd surrounded
the automaton. In the adjacent room the Difference Engine
stood nearly deserted: two foreigners alone worshipped at
that altar. One of them, but just landed from the United
States, was engaged in explaining to a learned professor from
Holland what he had himself in the morning gathered from
its constructor.</p>

<p>Leaning against the doorway, I was myself contemplating
the strongly contrasted scene, pleased that my friends were
relaxing from their graver pursuits, and admiring the really
graceful movements produced by mechanism; but still more
highly gratified at observing the deep and almost painful
attention of my Dutch guest, who was questioning his American
instructor about the mechanical means I had devised
for accomplishing some arithmetical object. The deep
thought with which this explanation
was attended to, <span class="xxpn" id="p427">{427}</span>
suddenly flashed into intense delight when the simple means of
its accomplishment were made apparent.</p>

<p>My acute and valued friend, the late Lord Langdale, who had
been observing the varying changes of my own countenance,
as it glanced from one room to the other, now asked me,
“What new mischief are you meditating?”—“Look,” said I,
“in that further room—England. Look again at this—two
Foreigners.”</p>

<div class="dkeeptgth">
<h3 class="h3herein"><i>Ancient Music.</i></h3>

<p>Many years ago some friends of mine invited me to accompany
them to the concert of ancient music, and join their
supper-party after it was over.</p></div>

<p>My love of music is not great, but for the pleasure of the
society I accepted the invitation. On our meeting at the
supper-table, I was overwhelmed with con­grat­u­la­tions upon
my exquisite appreciation of the treat we had just had. I
was assured that though my expression of feeling was of the
quietest order, yet that I was the earliest to approve all the
most beautiful passages.</p>

<p>I accepted modestly my easily-won laurels, and perhaps my
taste for music might have survived in the memory of my
friends, when my taste for mechanism had been forgotten. I
will, however, confide to the public the secret of my success.
Soon after I had taken my seat at the concert, I perceived
Lady Essex at a short distance from me. Knowing well her
exquisitely sensitive taste, I readily perceived by the expression
of her countenance, as well as by the slight and almost
involuntary movement of the hand, or even of a finger, those
passages which gave her most delight. These quiet indications,
unobserved by my friends, formed the electric wire
by which I directed the expressions
of my own <span class="xxpn" id="p428">{428}</span>
countenance and the very modest applause I thought it prudent to
develop.</p>

<p>After receiving the con­grat­u­la­tions of my friends upon
my great musical taste, I informed them how easily that
reputation had been acquired. Such are the feeble bases on
which many a public character rests.</p>

<hr class="hrblk" />

<p>During my residence with my Oxford tutor, whilst I was
working by myself on mathematics, I oc­ca­sion­al­ly arrived at
conclusions which appeared to me to be new, but which from
time to time I afterwards found were already well known.
At first I was much discouraged by these disappointments,
and drew from such occurrences the inference that it was
hopeless for me to attempt to invent anything new. After a
time I saw the fallacy of my reasoning, and then inferred
that when my knowledge became much more extended I
might reasonably hope to make some small additions to my
favourite science.</p>

<div class="dsdnote">〈PHILOSOPHY OF INVENTION.〉</div>

<p>This idea considerably influenced my course during my
residence at Cambridge by directing my reading to the
original papers of the great discoverers in math­e­mat­i­cal
science. I then endeavoured to trace the course of their
minds in passing from the known to the unknown, and to
observe whether various artifices could not be connected
together by some general law. The writings of Euler were
eminently instructive for this purpose. At the period of my
leaving Cambridge I began to see more distinctly the object
of my future pursuit.</p>

<p>It appeared to me that the highest exercise of human
faculties consisted in the endeavour to discover those laws of
thought by which man passes from the known
to that which <span class="xxpn" id="p429">{429}</span>
was unknown. It might with propriety be called the philosophy
of invention. During the early part of my residence
in London, I commenced several essays on Induction, Generalization,
Analogy, with various illustrations from different
sources. The philosophy of signs always occupied my attention,
and to whatever subject I applied myself I was ever on
the watch to perceive and record the links by which the new
was connected with the known.</p>

<div class="dsdnote">〈EARLY ESSAYS.〉</div>

<p>Most of the early essays I refer to were not sufficiently
matured for publication, and several have appeared without
any direct reference to the great object of my life. I may,
however, point out one of my earlier papers in the “Philosophical
Transactions for 1817,” which, whilst it made considerable
additions to a new branch of science, is itself a
very striking instance of the use of analogy for the purpose
of invention. I refer to the “Essay on the Analogy between
the Calculus of Functions and other Branches of Analysis.”—<i>Phil.
Trans.</i> 1817.</p></div><!--section-->

<div class="section" id="p430">
<h2 class="h2herein">CHAPTER XXXIII.
<span class="hsmall">THE AUTHOR’S CONTRIBUTIONS TO HUMAN KNOWLEDGE.</span></h2>

<div class="dsynopsis">
Scientific Societies&#x200a;—&#x200a;Analytical
Society&#x200a;—&#x200a;Astronomical Society&#x200a;—&#x200a;Grand
Duke of Tuscany, Leopold II.&#x200a;—&#x200a;Scientific Meeting
at Florence&#x200a;—&#x200a;Also at Berlin&#x200a;—&#x200a;At
Edinburgh&#x200a;—&#x200a;At Cambridge&#x200a;—&#x200a;Origin of
the Statistical Society&#x200a;—&#x200a;Statistical Congress at
Brussels&#x200a;—&#x200a;Calculus of Functions&#x200a;—&#x200a;Division
of Labour&#x200a;—&#x200a;Verification part of
Cost&#x200a;—&#x200a;Principles of Taxation&#x200a;—&#x200a;Extension
to Elections&#x200a;—&#x200a;The two
Pumps&#x200a;—&#x200a;Monopoly&#x200a;—&#x200a;Miracles.</div>

<h3 class="h3herein"><i>Of the part taken by the Author in the formation of various
Scientific&nbsp;Societies.</i></h3>

<p class="pfirst"><span class="smcap">T<b>HE</b></span> origin of the
Analytical Society has been already explained in the fourth chapter.
In the year 1820 the Author of this volume, joining with several
eminent men attached to astronomical pursuits, instituted the Royal
Astronomical Society. At the present time only three of the original
founders survive. The meetings, and still more the publications of that
society, have contributed largely to extend the taste for astronomy.</p>

<p>In 1827 I visited Italy, and during my residence at
Florence had many opportunities of observing the strong
feeling of the reigning Grand Duke Leopold II., not only for
the fine arts, but for the progress of science, and for its application
to the advancement of the arts of life.</p>

<div class="dsdnote">〈THE GRAND DUKE OF TUSCANY.〉</div>

<p>After a long tour in Italy, I found myself in the following
year again in Florence, and again I was received with a kindness
and consideration which I can never
forget. The Grand <span class="xxpn" id="p431">{431}</span>
Duke was anxious to know my opinion respecting the state of
science in Italy. At one of the many interviews with which
I was honoured, he asked me whether I could point out any
way in which he could assist its progress.</p>

<p>The question was unexpected; but it immediately recalled
to me a recent circumstance, which I then mentioned, namely,
that in three of the great cities of Italy I had been consulted
confidentially by three distinguished men of science upon the
same subject, on which each was separately engaged without
being aware of the fact that the other two were employed on
the same inquiry. The result, I remarked, would probably be
that Italy would thus make <i>one</i> step in science, and that the
discovery might probably be accompanied by painful discussions
respecting priority; whilst with better means of intercommunication
amongst its men of science Italy might have
made <i>three</i> steps in advance. The idea of a periodical meeting
of men engaged in scientific pursuits naturally arose out
of these remarks. At parting, the Grand Duke requested me
to draw up a minute of the conversation. I therefore drew
up a note on the subject, in which I shadowed out an annual
meeting of learned men in the various cities of Italy.</p>

<p>On finally taking leave, previous to my visit to Germany,
the Grand Duke assured me that he had read the minute of
our conversation with much attention, that he saw the evils
pointed out, and agreed with me as to the remedy. He then
observed that “the time for such a meeting had not yet
arrived; but,” added the Grand Duke, “when it does arrive,
you may depend upon me.”</p>

<p>Eleven years after, in 1839, I was honoured by an invitation
from the Grand Duke of Tuscany to meet the men of science
of Italy, then about to assemble at Florence. In this communication
it was observed, that “the time
had <i>now</i> arrived.” <span class="xxpn" id="p432">{432}</span></p>

<p>In the autumn of 1828 I reached Berlin, and unexpectedly
found, from M. Humboldt, that in the course of a few weeks
the phi­los­o­phers of Germany were to hold a meeting in that
capital.</p>

<p>I then learnt for the first time that, some years before,
Dr. Oken had proposed and organized an annual congress of
German naturalists, meeting in each succeeding year in some
great town.</p>

<p>I remained to witness the enlarged meeting at Berlin,
which was very successful, and wrote an account of it to
Sir D. Brewster, who published the description of it in “The
Edinburgh Journal of Science.”<a class="afnanc" href="#fn58" id="fnanc58">58</a>
This was, I believe, the first
communication to the English public of the existence of the
German Society.</p>

<div class="dsdnote">〈BRITISH ASSOCIATION: ITS ORIGIN.〉</div>

<p>A few years after, Sir David Brewster, Sir John Robison,
Secretary of the Royal Society of Edinburgh, and the Rev.
William Vernon Harcourt, undertook the foundation of a
similar periodical and itinerant society in our own country.</p>

<p>It appeared to me that the original organization of the
British Association, as developed at York and at Oxford, was
defective,—that its basis was not sufficiently extended. In
fact, that other sciences besides the physical were wanting for
the harmony and success of the whole. There was no section
to interest the landed proprietors or those members of their
families who sat in either house of parliament. Nor was
there much to attract the man­u­fac­turer or the retail dealer.
A purely accidental circumstance enabled me to remedy one
of these defects.<a class="afnanc" href="#fn59" id="fnanc59">59</a>
<span class="xxpn" id="p433">{433}</span></p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc58" id="fn58">58</a>
Vol. x., p. 225. 1829.</p>

<p class="pfirst padtopc"><a class="afnlabel" href="#fnanc59" id="fn59">59</a>
I afterwards succeeded in getting the British Association
to adopt the plan of having an exhibition of specimens of the various
man­u­fac­tures and commercial products of the districts it successively
visited. This commenced at Newcastle in 1838, and was carried to a much
greater extent in
the following year at Birmingham. I am not aware that this
fact was ever referred to by those who got up the Exhibition of 1851.</p></div>

<div class="dsdnote">〈THE STATISTICAL SOCIETY: ITS ORIGIN.〉</div>

<p>At the Third Meeting of the British Association at Cambridge
in 1833, I happened, one afternoon, to call on my old
and valued friend the Rev. Richard Jones, Professor of Political
Economy at Haileybury, who was then residing in apartments
at Trinity College. He informed me that he had just had
a long conversation with our mutual friend M. Quételet, who
had been sent officially by the Belgian Government to attend
the meeting of the British Association. That M. Quételet
had brought with him a budget of statistical facts, and that
as there was no place for it in any section, he (Professor
Jones) had asked M. Quételet to come to him that evening,
and had invited Sir Charles Lemon, Professor Malthus,
Mr. Drinkwater (afterwards Mr. Bethune),<a class="afnanc" href="#fn60" id="fnanc60">60</a>
and one or two
others interested in the subject, to meet him, at the same
time requesting me to join the party. I gladly accepted
this invitation and departed. I had not, however, reached the
gate of Trinity College before it occurred to me that there
was now an opportunity of doing good service to the British
Association. I returned to the apartments of my friend,
explained to him my views, in which he fully coincided, and
I suggested the formation of a Statistical Section. We both
agreed that unless some <i>unusual</i> course were taken, it would be
impossible to get such a Section organized until the meeting
in the following year. I therefore proposed that when we
met in the evening we should consider the question of constituting
ourselves provisionally a Statistical Section, and afterwards,
at the general meeting in the Senate House, that I
should explain the circumstance which had arisen, and the
<span class="xxpn" id="p434">{434}</span>
great advantage to the British Association of rendering such a
Section a permanent branch of its institution. After further
explanations its utility was fully admitted; certain rather
stringent rules were laid down in order to confine its inquiries
to collections of facts. The sanction of the General Meeting
was then given to the establishment of the Statistical Section,
and before the termination of the Congress, a larger audience
was collected in its meeting-room than in those of any of its
sister sciences.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc60" id="fn60">60</a>
I have reason to believe, from the Note Book of Mr.
Drinkwater (Bethune), that this meeting was held on Wednesday, 26th
June, 1833.</p></div>

<p>The interest of our discussions, and the mass of materials
which now began to open upon our view, naturally indicated
the necessity of forming a more permanent society for their
collection. The British Association approved of the appointment
of a permanent committee of this section. I was requested
to act as chairman, and Mr. Drinkwater as secretary.
On the 15th March, 1834, at a public meeting held in London,
the Marquis of Lansdowne in the Chair, it was resolved to
establish the Statistical Society of London.</p>

<p>The Committee of the British Association, in reporting this
fact to the Council, observe that “though the want of such a
society has been long felt and acknowledged, the successful
establishment of it, after every previous attempt had failed,
has been due altogether to the impulse given by the last
meeting of the Association. The distinguished foreigner
(M. Quételet) who contributed so materially to the formation
of the Statistical Section, was attracted to England principally
with a view of attending that meeting; and the Committee
hail this as a signal instance of the beneficial results
to be expected from that personal intercourse among the
enlightened men of all countries, which it is a principal
object of the British Association to encourage and facilitate.”</p>

<p>M. Quételet, on his return to his own
country, continued to <span class="xxpn" id="p435">{435}</span>
direct by his counsel, and to advance, by his own indefatigable
industry, those statistical inquiries of which the Belgian
Government so well appreciated the advantage.</p>

<p>At length the conviction of the importance of the value of
Statistical Science becoming widely extended in other countries,
M. Quételet saw that a fit time had arrived for summoning
a European Congress. The results of such meetings are
invaluable to all sciences, but more peculiarly to statistics, in
which names have to be defined, signs to be invented, methods
of ob­ser­va­tion to be compared and rendered uniform; thus
enhancing the value of all future ob­ser­va­tions by making them
more comparable as well as more expeditiously collected.</p>

<p>The proposal was adopted by the Belgian Government, and
the first International Statistical Congress was held at Brussels
in September, 1853.</p>

<p>The result was most successful; all the cultivators of Statistical
Science are deeply indebted to M. Quételet for the
unwearied pains he took to insure its success. He was assisted
in this arduous task by the ministers of the crown, and supported
by the high approbation of an enlightened sovereign.</p>

<div class="dkeeptgth">
<h3 class="h3herein"><i>Calculus of Functions.</i></h3>

<p>This was my earliest step, and is still one to which I would
willingly recur if other demands on my time permitted.
Many years ago I recorded, in a small MS. volume, the facts,
and also extracts of letters from Herschel, Bromhead, and
Maule, in which I believe I have done justice to my friends
if not to myself. It is very remarkable that the Analytical
Engine adapts itself with singular facility to the development
and numerical working out of this vast department of analysis.</p></div>

<p>In the list of my printed papers, at the end of this volume, will be
found my various cont­ri­bu­tions to that subject.</p></div><!--section-->

<div class="section"><div class="xxpn"
id="p436">{436}</div>
<h3 class="h3herein"><span class="smcap">P<b>OLITICAL</b></span>
<span class="smcap">E<b>CONOMY.</b></span></h3>

<p>My cont­ri­bu­tions to <i>Political Economy</i> are chiefly to be found
in “The Economy of Machinery and Man­u­fac­tures,” which consists of
illustrations and developments of the principles regulating a very
large section of that important subject.</p>

<h3 class="h3herein"><i>Division of Labour.</i></h3>

<p>It is singular that in the analysis of the <i>division of labour</i>,
given by Adam Smith in “The Wealth of Nations,” the most
efficient cause of its advantage is entirely omitted. The three
causes assigned in that work <span class="nowrap">are—</span></p>

<ul>
<li>1st. The increase of dexterity in every particular workman.</li>

<li>2nd. The saving of time lost in passing from one species of
work to another.</li>

<li>3rd. The invention of a great number of machines which
facilitate and abridge labour, and enable one man to do the
work of many.</li></ul>

<p>These are undoubtedly true causes, but the most important
cause is entirely omitted.</p>

<p>The most effective cause of the cheapness produced by the
division of labour is <span class="nowrap">this—</span></p>

<p>By dividing the work to be executed into different processes,
each requiring different degrees of skill, or of force,
the master man­u­fac­turer can purchase exactly that precise
quantity of both which is necessary for each process. Whereas
if the whole work were executed by one workman, that person
must possess sufficient skill to perform the most difficult, and
sufficient strength to execute the most laborious, of those
operations into which the art is divided.</p>

<p>Needle-making is perhaps the best illustration of the overpowering
effect of this cause. The
operatives in this <span class="xxpn" id="p437">{437}</span>
man­u­fac­ture consist of children, women, and men, earning wages
varying from three or four shillings up to five pounds per
week. Those who point the needles gain about two pounds.
The man who hardens and tempers the needles earns from
five to six pounds per week. It ought also to be observed
that one man is sufficient to temper the needles for a large
factory; consequently the time spent on each needle by the
most expensive operative is excessively small.</p>

<p>But if a man­u­fac­turer insist on employing one man to
make the whole needle, he must pay at the rate of five pounds
a week for every portion of the labour bestowed upon it.<a class="afnanc" href="#fn61" id="fnanc61">61</a></p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc61" id="fn61">61</a>
See “Economy of Man­u­fac­tures.”</p></div>

<div class="dkeeptgth">
<h3 class="h3herein"><i>Cost of any Article.</i></h3>

<p>Besides the usual elements which contribute to constitute the price
of any thing, there exists another which varies greatly in different
articles. It is <span class="nowrap">this—</span></p></div>
<ul>
<li><i>The cost and difficulty of verifying the fact that the article is
exactly what it professes to be.</i></li></ul>

<p>This is in some cases very small; but in many instances it
is scarcely possible for the purchaser to verify the genuineness
of certain articles. In these cases the public pay a larger
price than they otherwise would do to those tradesmen whose
character and integrity are well established.</p>

<div class="dkeeptgth">
<h3 class="h3herein"><i>Principles of Taxation.</i></h3>

<p>In a pamphlet printed in 1848, I published my views of
taxation, especially with reference to an Income Tax.</p></div>

<p>The principle there supported was entertained and
examined by the French Minister of Finance, M. Passy.
The pamphlet itself was sub­se­quent­ly translated into Italian
and published at Turin, under the auspices of the Sardinian
Finance Minister. <span class="xxpn" id="p438">{438}</span></p>

<div class="dsdnote">〈THE PRINCIPLE OF REPRESENTATION.〉</div>

<p>The principle there maintained admits, I think, of an
extension to the election of rep­re­sen­ta­tives.</p>

<p>In that case, each person would have one vote on the
ground of his personality, and other votes in proportion to
his income. Whenever any further extension of our rep­re­sen­ta­tive
system becomes necessary, the dangers arising from
the extension of the personal suffrage may fairly be
counterbalanced by giving a plurality of votes to property.
Such a course would have a powerful tendency to good, by
supporting the national credit and by preventing the
destructive waste of capital by war, and it might even make
us a highly conservative people.</p>

<p>As the subject of political economy will be considered
rather dry by most readers, I will endeavour to enliven
it by an extract from that pamphlet, which singularly
illustrates the question of direct and indirect taxation.
I had mentioned the productive pump of my Italian
friend to the late Lord Lansdowne, who supplied me with
the counterpart in the unproductive pump erected by the
late William Edgeworth, at Edgeworth Town, in Ireland.</p>

<p>That proprietor, whose country residence was much frequented
by beggars, resolved to establish a test for discriminating
between the idle and the industrious, and also to
obtain some small return for the alms he was in the habit of
bestowing. He accordingly added to the pump by which the
upper part of his house was supplied with water, a piece of
mechanism so contrived that, at the end of a certain number of
strokes of the pump-handle, a penny fell out from an aperture
to repay the labourer for his work. This was so arranged,
that labourers who continued at the work, obtained very
nearly the usual daily wages of labour in that part of the
country. The idlest of the vagabonds of course refused this
new labour test: but the greater part of
the beggars, whose <span class="xxpn" id="p439">{439}</span>
constant tale was that ‘<i>they could not earn a fair day’s wages
for a fair days work</i>,’ after earning a few pence, usually went
away <i>cursing</i> the hardness of their taskmaster.</p>

<div class="dsdnote">〈STORY OF THE TWO PUMPS.〉</div>

<p>An Italian gentleman, with greater sagacity, devised a more
productive pump, and kept it in action at far less expense.
The garden wall of his villa adjoined the great high road leading
from one of the capitals of northern Italy<a class="afnanc" href="#fn62" id="fnanc62">62</a>, from which it
was distant but a few miles. Possessing within his garden a
fine spring of water, he erected on the outside of the wall a
pump for public use, and chaining to it a small iron ladle, he
placed near it some rude seats for the weary traveller, and by
a slight roof of climbing plants protected the whole from the
mid-day sun. In this delightful shade the tired and thirsty
travellers on that well-beaten road ever and anon reposed and
refreshed themselves, and did not fail to put in requisition
the service of the pump so opportunely presented to them.
From morning till night many a dusty and wayworn pilgrim
plied the handle, and went on his way, <i>blessing</i> the liberal
proprietor for his kind consideration of the passing stranger.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc62" id="fn62">62</a>
Turin.</p></div>

<p>But the owner of the villa was deeply acquainted with
human nature. He knew in that sultry climate that the
liquid would be more valued from its scarcity, and from the
difficulty of acquiring it. He therefore, to enhance the value
of the gift, wisely arranged the pump, so that its spout was of
rather contracted dimensions, and the handle required a
moderate application of force to work it. Under these
circumstances the pump raised far more water than could
pass through its spout; and, to prevent its being wasted, the
surplus was conveyed by an invisible channel to a large
reservoir judiciously placed for watering the proprietor’s own
house, stables, and garden,—into which about five pints were
poured for every spoonful passing out of the spout for the
<span class="xxpn" id="p440">{440}</span>
benefit of the weary traveller. Even this latter portion was
not entirely neglected, for the waste-pipe conveyed the part
which ran over from the ladle to some delicious strawberry
beds at a lower level. Perhaps, by a small addition to this
ingenious arrangement, some kind-hearted travellers might
be enabled to indulge their mules and asses with a taste of
the same cool and refreshing fluid; thus paying an additional
tribute to the skill and sagacity of the benevolent proprietor.
My accomplished friend would doubtless make a most popular
Chancellor of the Exchequer, should his Sardinian Majesty
require his services in that department of administration.</p>

<div class="dkeeptgth">
<h3 class="h3herein"><i>Monopoly.</i></h3>

<p>In the course of my examination of this question I arrived
at what I conceive to be a demonstration of the following
<span class="nowrap">principle:—</span></p></div>
<ul>
<li><i>That even under circumstances of the most absolute monopoly,
the monopolist will, if he</i>
<span class="smmaj">KNOWS</span> <i>his own interest and</i>
<span class="smmaj">PURSUES</span>
<i>it, sell the article he produces at exactly the same price as the
freest competition would produce</i>.</li></ul>

<p>I devoted a chapter to this subject in an edition which I
prepared several years ago for a new Italian translation of the
“Economy of Man­u­fac­tures;” but I am not aware whether it
has yet been published.</p>

<div class="dkeeptgth">
<h3 class="h3herein"><i>Miracles.</i></h3>

<p>The explanation which I gave of the nature of miracles in
“The Ninth Bridgewater Treatise,” published in May, 1837,
has now stood the test of more than a quarter of a century,
during which it has been examined by some of the deepest
thinkers in many countries. Its adoption by those writers
who have referred to it has, as far as my information goes,
been unanimous.</p></div></div><!--section-->

<div class="section" id="p441">
<h2 class="h2herein">CHAPTER XXXIV.
<span class="hsmall">
THE AUTHOR’S FURTHER CONTRIBUTIONS TO HUMAN
KNOWLEDGE.</span></h2>

<div class="dsynopsis">
Glaciers&#x200a;—&#x200a;Uniform Postage&#x200a;—&#x200a;Weight
of the Bristol Bags&#x200a;—&#x200a;Parcel
Post&#x200a;—&#x200a;Plan for trans­mit­ting Letters along
Aërial Wires&#x200a;—&#x200a;Cost of Verification is part of
Price&#x200a;—&#x200a;Sir Rowland Hill&#x200a;—&#x200a;Submarine
Navigation&#x200a;—&#x200a;Difference Engine&#x200a;—&#x200a;Analytical
Engine&#x200a;—&#x200a;Cause of Magnetic and Electric
Rotations&#x200a;—&#x200a;Mechanical Notation&#x200a;—&#x200a;Occulting
Lights&#x200a;—&#x200a;Semi-oc­cul­ta­tion may determine
Distances&#x200a;—&#x200a;Distinction of Lighthouses
numerically&#x200a;—&#x200a;Application from the United
States&#x200a;—&#x200a;Proposed Voyage&#x200a;—&#x200a;Loss
of the Ship and Mr. Reid&#x200a;—&#x200a;Congress of
Naval Officers at Brussels in 1853&#x200a;—&#x200a;My
Portable Occulting Light exhibited&#x200a;—&#x200a;Night
Signals&#x200a;—&#x200a;Sun Signals&#x200a;—&#x200a;Solar
Occulting Lights&#x200a;—&#x200a;Afterwards used
at Sebastopol&#x200a;—&#x200a;Numerical Signals
applicable to all Dictionaries&#x200a;—&#x200a;Zenith
Light Signals&#x200a;—&#x200a;Telegraph for Ships on
Shore&#x200a;—&#x200a;Greenwich Time Signals&#x200a;—&#x200a;Theory
of Isothermal Surfaces to account for the Geological Facts
of the successive Uprising and Depression of various
parts of the Earth’s Surface&#x200a;—&#x200a;Games of
Skill&#x200a;—&#x200a;Tit-tat-to&#x200a;—&#x200a;Exhibitions&#x200a;—&#x200a;Problem
of the Three Magnetic Bodies.</div>

<h3 class="h3herein"><i>Of Glaciers.</i></h3>

<p class="pfirst"><span class="smcap">M<b>UCH</b></span>
has been written upon the subject of glaciers. The
view which I took of the question on my first acquaintance
with them still seems to me to afford a sufficient explanation
of the phenomena. It is probable that I may have been
anticipated in it by Saussure and others; but, having no time
to inquire into its history, I shall give a very brief statement
of those views.</p>

<p>The greater part of the material which ultimately constitutes
a glacier arises from the rain falling and the snow
deposited in the higher portions of
mountain ranges, which <span class="xxpn" id="p442">{442}</span>
naturally first fill up the ravines and valleys, and rests on
the tops of the mountains, covering them to various depths.</p>

<p>The chief facts to be explained are—first, the causes of
the descent of these glaciers into the plains; second, the
causes of the transformation of the opaque consolidated snow
at the sources of the glacier into pure transparent ice at its
termination.</p>

<p>The glaciers usually lying in valleys having a steep descent,
gravity must obviously have a powerful influence; but its
action is considerably increased by another cause.</p>

<p>The heat of the earth and that derived from the friction
of the glacier and its broken fragments against the rock on
which it rests, as well as from the friction of its own fragments,
slowly melts the ice, and thus diminishing the amount
of its support, the ice above cracks and falls down upon the
earth, again to be melted and again to be broken.</p>

<p>But as the ice is upon an inclined plane, the pressure from
above, on the upper side of the fragment, will be greater than
that on the lower; consequently, at every fall the fallen mass
will descend by a very small quantity further into the valley.
Another consequence of the melting of the lower part of the
centre of the glacier will be that the centre will advance
faster than the sides, and its termination will form a curve
convex towards the valley.</p>

<p>The above was, I believe, the common explanation of the
formation of glaciers. The following part explains my own
<span class="nowrap">views:—</span></p>

<div class="dkeeptgth">
<h3 class="h3herein"><i>Of the Causes of the Transformation of Condensed Snow into
Transparent Ice.</i></h3>

<p>It is a well-known fact that water rapidly frozen retains all
the air it held in solution, and is opaque. <span class="xxpn"
id="p443">{443}</span></p></div>

<p>It is also known that water freezing very slowly is transparent.</p>

<p>Whenever, by the melting of the lower portion of any part
of a glacier, a piece of it cracks and falls to a lower level, the
friction of the broken sides will produce heat, and melt a
small portion of water. This water, trickling down very
slowly, will form a thin layer on the broken surface, and a
portion will be retained in the narrowest part of the crack.
But, since the temperature of a glacier is very near the freezing
point, that water will freeze very slowly. It will, therefore,
become transparent ice, and will, as it were, solder together
the two adjacent surfaces by a thin layer of transparent ice.</p>

<p>But the transparent ice is much stronger and more difficult
to break than opaque ice; consequently, the next time the
soldered fragments are again broken, they will not break in
the strongest part, which is the transparent ice: but the next
fracture will occur in the opaque ice, as it was at first.</p>

<p>Thus, by the continued breaking and falling downward of
the fragments of the glacier, as it proceeds down the valley,
a series of vertical, rudely-parallel veins of transparent ice
will be formed. As these masses descend the valley, fresh
vertical layers of transparent ice will be interposed between
those already existing until the whole takes that beautiful
transparent cerulean tint which we so frequently see at the
lower termination of a glacier. Another effect of this vertical
fracture at the surfaces of least resistance will be alternate
vertical layers of opaque and transparent ice shading into each
other. This would, in some of its stages, give a kind of ribboned
appearance to the ice. Probably traces of it would
still be exhibited even in the most transparent ice. Speaking
roughly, this ribboned structure ought to be closer together
the nearer the piece examined is to the end of
the glacier. It <span class="xxpn" id="p444">{444}</span>
ought also to be more apparent towards the centre of the glacier
than towards the sides. The effect of this progress downward
is to produce a very powerful friction between the masses
of ice and the earth over which they are pushed, and, consequently,
a continual accession to that stream of water which
is found issuing from all glaciers.</p>

<p>The result of this continual breaking up is to cause all the
water melted by the friction of the blocks of ice which is not
retained in the interstices to fall towards the lowest part of the
descending valley, and thus increase the stream, and so take
away more and more of the support of the central part of the
glacier. Hence the advance of the surface of the glacier
will be much quicker towards its middle than near the
sides.</p>

<div class="dsdnote">〈CRACKS IN GLACIERS PERPENDICULAR.〉</div>

<p>The consequence of these actions is, that cracks in the ice
will occur generally in planes perpendicular to its surface.
The rain which falls upon the glacier, the water produced
from its surface by the sun’s rays and by the effect of the
temperature of the atmosphere, as well as the water produced
by the friction of its descending fragments, will penetrate
through these cracks, and be retained by capillary action on
the surfaces, and still more where the distance of the adjacent
surfaces is very small. The rest of this unfrozen water will
reach the rocky bottom of the glacier, and give up some of its
heat to the bed over which it passes, to be again employed in
melting away the lowest support of the glacier ice. Although
the temperature of the glacier should differ but by a very
small quantity from that of the freezing point of water, yet
these films will only freeze the more slowly, and therefore become
more solid and transparent ice. Their very thinness will
enable all the air to be more readily extricated by freezing.</p>

<p>The question of the <i>regelation</i> of pounded ice,
if by that <span class="xxpn" id="p445">{445}</span>
term is meant anything more than welding ice by heat, or of
joining its parts by a process analogous to that which is called
<i>burning together</i> two separate portions of a bronze statue, has
always appeared to me unsat­is­fac­tory.</p>

<div class="dsdnote">〈BURNING TOGETHER BRONZE.〉</div>

<p>The process of “burning together” is as follows:—Two
portions of a large statue, which have been cast separately,
are placed in a trough of sand, with their corresponding ends
near to each other. A channel is made in the sand, leading
through the junction of the parts to be united.</p>

<p>A stream of melted bronze is now allowed to run out from
the furnace through the channel between the contiguous ends
which it is proposed to unite. The first effect of this is to
heat the ends of the two fragments. After the stream of
melted metal has continued some time, the ends of those fragments
themselves begin to melt. When a small quantity of
each end is completely melted, the further flow of the melted
metal is stopped, and as soon as the pool of melted metal
connects, the two ends of the pieces to be united begins to
consolidate: the whole is covered up with sand and allowed
to cool gradually. When cold, the unnecessary metal is cut
away, and the fragments are as perfectly united as if they
had been originally cast in one piece.</p>

<p>The sudden consolidation, by physical force, of pounded ice
or snow appears to me to arise from the first effect of the
pressure producing heat, which melts a small portion into
water, and brings the particles of ice or snow nearer to each
other. The portion of water thus produced then, having its
heat abstracted by the ice, connects the particles of the latter
more firmly together by freezing.</p>

<p>If two flat surfaces of clear ice had a heated plate of metal
put between them, two very thin layers of water would be
formed between the ice and the heated plate.
If the hot <span class="xxpn" id="p446">{446}</span>
plate were suddenly withdrawn, and the two plates of ice
pressed together, they would then be frozen together. This
would be equivalent to welding. In all these cases the temperature
of the ice must be a very little lower than the freezing-point.
The more nearly it approached that point the
slower the process of freezing would be, and therefore the
more transparent the ice thus formed.</p>

<div class="dsdnote">〈ICE FROZEN IN THE EXHIBITION, 1862.〉</div>

<p>In the Exhibition of 1862 there were two different processes
by which ice was produced in abundance, even in the
heat of the Machinery Annex, in which they were placed.</p>

<p>In both the water was quickly converted into ice, and in
both cases the ice was opaque.</p>

<p>In one of them the ice was produced in the shape of long
hollow cylinders. These were quite opaque, and were piled
up in stacks. The temperature of the place caused the ice to
melt slowly; consequently, the interstices where the cylinders
rested upon each other, received and retained a small
portion of the water, which, trickling down, was detained by
capillary attraction. Here it was very slowly frozen, and
formed at the junction of the cylinders a thin film of transparent
ice. This gradually increased as the upper cylinders
of the ice melted away, and, after several hours’ exposure, I
have seen clear transparent ice a quarter of an inch thick,
where, at the commencement, there had not been even a
trace of translucency.</p>

<p>On inquiring of the operator why the original cylinders
were opaque, he told me, because they were frozen quickly.
I then pointed out to him the small portions of transparent
ice, which I have described, and asked him the cause. He
immediately said, because they had been frozen slowly.</p>

<p>It appeared to be an axiom, derived from his own experience,
that water quickly frozen is always
opaque, and water <span class="xxpn" id="p447">{447}</span>
slowly frozen always transparent. I pointed out this practical
illustration to many of the friends I accompanied in their
examination of the machinery of the Annex.</p>

<p>It would follow from this explanation, that glaciers on lofty
mountains and in high latitudes may, by their own action, keep the
surface of the earth on which they rest at a higher temperature than it
would otherwise attain.</p></div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Book and Parcel Post.</i></h3>

<p>When my friend, the late General Colby, was preparing the
materials and instruments for the intended Irish survey, he
generally visited me about once a week to discuss and talk
over with me his various plans. We had both of us turned
our attention to the Post-office, and had both considered and
advocated the question of a uniform rate of postage. The
ground of that opinion was, that the actual <i>transport</i> of a
letter formed but a small item in the expense of trans­mit­ting
it to its destination; whilst the heaviest part of the cost arose
from the <i>collection</i> and <i>distribution</i>, and was, therefore, almost
independent of the length of its journey. I got some returns
of the weight of the Bristol mail-bag for each night during
one week, with a view to ascertain the possibility of a more
rapid transmission. General Colby arrived at the conclusion
that, supposing every letter paid sixpence, and that the same
number of letters were posted, then the revenue would remain
the same. I believe, when an official comparison was
sub­se­quent­ly made, it was found that the equivalent sum
was fivepence halfpenny. I then devised means for trans­mit­ting
letters enclosed in small cylinders, along wires suspended
from posts, and from towers, or from church steeples.
I made a little model of such an apparatus, and thus trans­mit­ted
notes from my front drawing-room,
through the house, <span class="xxpn" id="p448">{448}</span>
into my workshop, which was in a room above my stables.
The date of these experiments I do not exactly recollect,
but it was certainly earlier than 1827.</p>

<div class="dsdnote">〈COST OF VERIFICATION.〉</div>

<p>I had also, at a still earlier period, arrived at the
remarkable economical principle, <i>that one element in the price
of every article is the cost of its verification</i>. It arose <span
class="nowrap">thus:—</span></p>

<p>In 1815 I became possessed of a house in London, and commenced
my residence in Devonshire Street, Portland Place,
in which I resided until 1827. A kind relative of mine sent
up a constant supply of game. But although the game cost
nothing, the expense charged for its carriage was so great
that it really was more expensive than butchers’ meat. I
endeavoured to get redress for the constant overcharges, but
as the game was transferred from one coach to another I
found it practically impossible to discover where the overcharge
arose, and thus to remedy the evil. These efforts,
however, led me to the fact that <i>verification</i>, which in this
instance constituted a considerable part of the <i>price of the
article, must form a portion of its price in every case</i>.</p>

<p>Acting upon this, I suggested that if the Government were
to become, through the means of the Post-office, parcel carriers,
they would derive a greater profit from it than any private
trader, because the whole price of verification would be saved
by the public. I therefore recommended the enlargement of
the duties of the Post-office by employing it for the conveyance
of books and parcels.</p>

<p>I mention these facts with no wish to disparage the <i>subsequent</i>
exertions of Sir Rowland Hill. His devotion to the
subject, his unwearied industry, and his long and at last successful
efforts to overcome the notorious official friction of
that department, required all the enduring energy he so
constantly bestowed upon the
subject. The benefit <span class="xxpn" id="p449">{449}</span>
conferred upon the country by the improvements he introduced
is as yet scarcely sufficiently estimated.</p>

<p>These principles were published afterwards in the
“Economy of Man­u­fac­tures.”—See First Edition, 8th June,
1832; Second Edition, 22nd November, 1832. See chap.
on the “Influence of Verification on Price,” p. 134, and
“Conveyance of Letters,” p. 273.</p></div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Submarine Navigation.</i></h3>

<p>Of this it is not necessary to do more than mention the
title and refer for the detail to the chapter on Experience by
Water: and also to the article Diving Bell in the “Encyclopædia
Metropolitana.”</p>

<p>I have only to add my opinion that in open inverted vessels
it may probably be found, under certain circumstances,
of important use.</p>

<h3 class="h3herein"><i>Difference Engine.</i></h3>

<p>Enough has already been said about that unfortunate
discovery in the previous part of this volume. The first
and great cause of its discontinuance was the inordinately
extravagant demands of the person whom I had employed to
construct it for the Government. Even this might, perhaps,
by great exertions and sacrifices, have been surmounted.
There is, however, a limit beyond which human endurance
cannot go. If I survive some few years longer, the Analytical
Engine will exist, and its works will afterwards be
spread over the world. If it is the will of that Being,
who gave me the endowments which led to that discovery,
that I should not survive to complete my work, I bow
to that decision with intense gratitude for those gifts: conscious
that through life I have never hesitated
to make the <span class="xxpn" id="p450">{450}</span>
severest sacrifices of fortune, and even of feelings, in order to
accomplish my imagined mission.</p>

<p>The great principles on which the Analytical Engine
rests have been examined, admitted, recorded, and dem­on­strated.
The mechanism itself has now been reduced to
unexpected simplicity. Half a century may probably elapse
before any one without those aids which I leave behind me,
will attempt so unpromising a task. If, unwarned by my
example, any man shall undertake and shall succeed in really
constructing an engine embodying in itself the whole of the
executive department of math­e­mat­i­cal analysis upon
different principles or by simpler mechanical means, I have
no fear of leaving my reputation in his charge, for he
alone will be fully able to appreciate the nature of my
efforts and the value of their results.</p>

<div class="dkeeptgth">
<h3 class="h3herein"><i>Explanation of the Cause of Magnetic and Electric Rotations.</i></h3>

<p>In 1824 Arago published his experiments on the magnetism manifested
by various substances during rotation. I was much struck with the
announcement, and immediately set up some apparatus in my own workshop
in order to witness the facts thus announced.</p></div>

<p>My friend Herschel, who assisted at some of the earliest
experiments, joined with me in repeating and varying those of
Arago. The results were given in a joint paper on that
subject, published in the “Transactions of the Royal Society”
in 1825.</p>

<p>I had previously made some magnetic experiments on a
large magnet which would, under peculiar management,
sustain about 32½ lbs. It was necessary to commence with a
weight of about 28 lbs., and then to add at successive intervals
additional weights, but each less and less
than the former. <span class="xxpn" id="p451">{451}</span></p>

<div class="dsdnote">〈ON ELECTRIC ROTATIONS.〉</div>

<p>This led me to an explanation of the cause of those rotations,
which I still venture to think is the true cause, although it is
not so recognized by English phi­los­o­phers.</p>

<p>The history is a curious one, and whether the cause which I
assigned is right or wrong, the train of thought by which I was
led to it is valuable as an illustration of the mode in which the
human mind works in its progress towards new discoveries.</p>

<p>The first experiment, showing that the weight suspended
might be increased at successive intervals of time, was stated
in most treatises on magnetism. But the visible fact impressed
strongly on my mind the conclusion that the production
and discharge of magnetism is not instantaneous,
but requires time for its complete action. It appeared,
therefore, to me that this principle was sufficient for the
explanation of the rotations observed by Arago.</p>

<p>In the following year it occurred to me that electricity
possessed the same property, namely, that of requiring time
for its communication. I then instituted a new series of
experiments, and succeeded, as I had anticipated, in producing
electric rotations. But a new fact now presented itself:
in certain cases the electric needle moved back in the contrary
direction to that indicated by the influences to which it
was subjected. Whenever this occurred the retrograde
motion was always very slow. After eliminating successively
by experiment every cause which I could imagine, the fact
which remained was, that in certain cases there occurred a
motion in the direction opposite to that which was expected.
But whenever such a motion occurred it was always very
slow. Upon further reflection, I conjectured that it might
arise from the screen, interposed between the electric and
the needle itself, becoming electrified possibly in the opposite
direction. New experiments confirmed this
view and proved <span class="xxpn" id="p452">{452}</span>
that the original cause was sufficient for the production of all
the observed effects.</p>

<p>These experiments and their explanation were printed in
the “Phil. Trans.” 1826. But they met with so little acceptance
in England that I had ceased to contend for them
against more popular doctrines, and was too deeply occupied
with other inquiries to enter on their defence. Several
years after, during a visit to Berlin, taking a morning walk
with Mitscherlich, I asked what explanation he adopted
of the magnetic rotations of Arago. He instantly replied,
“There can be no doubt that yours is the true one.”</p>

<p>It will be a curious circumstance in the history of science,
if an erroneous explanation of new and singular experiments
in one department should have led to the prevision of another
similar set of facts in a different department, and even to
the explanation of new facts at first apparently contradicting
it.</p></div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Mechanical Notation.</i></h3>

<p>This also has been described in a former chapter. I look
upon it as one of the most important additions I have made
to human knowledge. It has placed the construction of
machinery in the rank of a demonstrative science. The day
will arrive when no school of mechanical drawing will be
thought complete without teaching it.</p>

<h3 class="h3herein"><i>Occulting Lights.</i></h3>

<div class="dsdnote">〈PRINCIPLE OF INVENTION.〉</div>

<p>The great object of all my inquiries has ever been to endeavour to
ascertain those laws of thought by which man makes discoveries. It was
by following out one of the principles which I had arrived at that I
was led to the system of occulting numerical lights for distinguishing
lighthouses <span class="xxpn" id="p453">{453}</span> and for night
signals at sea, which I published about twelve years ago. The principle
I allude to is <span class="nowrap">this:—</span></p>

<ul><li class="li0">
<p>Whenever we meet with any defect in the means we are
contriving for the accomplishing a given object, that defect
should be noted and reserved for future consideration, and
inquiry should be <span class="nowrap">made—</span></p>

<p><i>Whether that which is a defect as regards the object in view
may not become a source of advantage in some totally different
subject.</i></p></li></ul>

<p>I had for a long series of years been watching the progress
of electric, magnetic, and other lights of that order, with the
view of using them for domestic purposes; but their want of
uniformity seemed to render them hopeless for that object.
Returning from a brilliant exhibition of voltaic light, I
thought of applying the above rule. The accidental in­ter­rup­tions
might, by breaking the circuit, be made to recur at
any required intervals. This remark suggested their adaptation
to a system of signals. But it was immediately followed
by another, namely: that the in­ter­rup­tions were equally
applicable to all lights, and might be effected by simple mechanism.</p>

<div class="dsdnote">〈UNEXPECTED DIFFICULTY.〉</div>

<p>I then, by means of a small piece of clock-work and an
argand lamp, made a <i>numerical</i> system of oc­cul­ta­tion, by
which any number might be trans­mit­ted to all those within
sight of the source of light. Having placed this in a window
of my house, I walked down the street to the distance of
about 250 yards. On turning round I perceived the number
32 clearly indicated by its oc­cul­ta­tions. There was, however,
a small defect in the apparatus. After each oc­cul­ta­tion there
was a kind of semi-oc­cul­ta­tion. This arose from the arm
which carried the shade rebounding from the stop on which
it fell. Aware that this defect could be
easily remedied, I <span class="xxpn" id="p454">{454}</span>
continued my onward course for about 250 yards more, with
my back towards the light. On turning round I was much
surprised to observe that the signal 32 was repeated distinctly
without the slightest trace of any semi-oc­cul­ta­tion or
blink.</p>

<p>I was very much astonished at this change; and on returning
towards my house had the light constantly in view. After
advancing a short distance I thought I perceived a very faint
trace of the blink. At thirty or forty paces nearer it was
clearly visible, and at the half-way point it was again perfectly
distinct. I knew that the remedy was easy, but I was
puzzled as to the cause.</p>

<p>After a little reflection I concluded that it arose from the
circumstance that the small hole through which the light
passed was just large enough to be visible at five hundred
yards, yet that when the same hole was partially covered by
the rebound there did not remain sufficient light to be seen
at the full distance of five hundred yards.</p>

<p>Thus prepared, I again applied the principle I had commenced
with and proceeded to examine whether this defect
might not be converted into an advantage.</p>

<div class="dsdnote">〈OCCULTING SIGNALS.〉</div>

<p>I soon perceived that a lighthouse, whose number was
continually repeated with a blink, obscuring just half its
light, would be seen <i>without any blink</i> at all distances beyond
half its range; but that at all distances within its half range
that fact would be indicated by a blink. Thus with two
blinks, properly adjusted, the distance of a vessel from a
first-class light would be distinguished at from twenty to thirty
miles by oc­cul­ta­tions indicating its number without any blink;
between ten and twenty miles by an occultation with one blink,
and within ten miles by an oc­cul­ta­tion with two blinks.</p>

<p>But another advantage was also suggested by this defect. <span
class="xxpn" id="p455">{455}</span> If the opaque cylinder which
intercepts the light consists of two cylinders, A and B, connected
together by rods: <span class="nowrap">thus—</span></p>

<ul class="fsz7">
<li>If the compound cylinder descend to <i>a</i>, and then rise again, there
will be a single oc­cul­ta­tion.</li>

<li>If the compound cylinder descend to <i>b</i>, and then rise again, there
will be a double oc­cul­ta­tion.</li>

<li>If the compound cylinder descend to <i>c</i>, and then rise again, there
will be a triple oc­cul­ta­tion.</li></ul>

<p class="pcontinue">Such oc­cul­ta­tions are very distinct, and are
specially applicable to lighthouses.</p>

<div class="dctr01"><img src="images/i455.png" width="800"
height="547" alt="" /></div>

<p>In the year 1851, during the Great Exhibition, the light
I have described was exhibited from an upper window of
my house in Dorset Street during many weeks. It had
not passed unnoticed by foreigners, who frequently reminded
me that they had passed my door when I was asleep by
writing upon their card the number exhibited by the occulting
light and dropping it into my letter-box.</p>

<p>About five or six weeks after its first appearance I received
a letter from a friend of mine in the United States, expressing
great interest about it, and inquiring whether its construction
was a secret.  My answer was, that
I made no <span class="xxpn" id="p456">{456}</span>
secret of it, and would prepare and send him a short description
of it.</p>

<p>I then prepared a description, of which I had a very
few copies printed. I sent twelve of these to the proper
authorities of the great maritime countries. Most of them
were accompanied by a private note of my own to some
person of influence with whom I happened to be acquainted.</p>

<p>One of these was addressed to the present Emperor of the
French, then a member of their Representative Chamber. It
was dated the 30th November, 1852. Three days after I
read in the newspapers the account of the <i>coup</i> of December
2, and smiled at the inopportune time at which my
letter had accidentally been forwarded. However, three
days after I received from M. Mocquard the prettiest note,
saying that he was commanded by the Prince President to
thank me for the communication, and to assure me that the
Prince was as much attached as ever to science, and should
always continue to promote its cultivation.</p>

<div class="dsdnote">〈EXPERIMENTS IN AMERICA.〉</div>

<p>The letter which was sent to the United States was placed
in the hands of the Coast Survey. The plan was highly approved,
and Congress made a grant of 5,000 dollars, in order
to try it experimentally. After a long series of experiments,
in which its merits were severely tested, a report was made to
Congress strongly recommending its adoption. I then received
a very pressing invitation to visit the United States, for the
purpose of assisting to put it in action. It was conveyed to
me by an amiable and highly cultivated person, the late Mr.
Reed, Professor of English Literature at Philadelphia, who, on
his arrival in London, proposed that I should accompany him
on his return in October, the best season for the voyage, and
in the finest vessel of their mercantile navy. I had long
had a great wish to visit the American continent,
but I did <span class="xxpn" id="p457">{457}</span>
not think it worth crossing the Atlantic, unless I could have
spent a twelvemonth in America. Finding this impossible
under the then circumstances, about a month before the
time arrived I resigned with great reluctance the pleasure of
accompanying my friend to his own country.</p>

<div class="dsdnote">〈THE AUTHOR’S ESCAPE.〉</div>

<p>It was most fortunate that I was thus prevented from
embarking on board the Arctic, a steamer of the largest class.</p>

<p>Steaming at the rate of thirteen knots an hour over the
banks of Newfoundland during a dense fog, the Arctic was
run into by a steamer of about half its size, moving at the
rate of seven knots. The concussion was in this instance fatal
to the larger vessel.</p>

<p>This sad catastrophe was thus described by the brother of
my lost <span class="nowrap">friend:—</span></p>

<div class="dblockquote">
<p>“On the 20th of September, 1854, Mr. Reed, with his
sister, embarked at Liverpool for New York, in the United
States steamship Arctic. Seven days afterwards, at noon, on
the 27th, when almost in sight of his native land, a fatal
collision occurred, and before sundown every human being
left upon the ship had sunk under the waves of the ocean.
The only survivor who personally acquainted with my
brother, saw him about two o’clock,
<span class="smmaj">P.M.</span>, after the collision,
and not very long before the ship sank, sitting with his sister
in the small passage aft of the dining-saloon. They were
tranquil and silent, though their faces wore the look of
painful anxiety. They probably afterwards left this position,
and repaired to the promenade deck. For a selfish struggle
for life, with a helpless companion dependent upon him, with
a physical frame unsuited for such a strife, and above all,
with a sentiment of religious resignation which taught him
in that hour of agony, even with the memory of his wife and
children thronging in his mind, to bow
his head in <span class="xxpn" id="p458">{458}</span>
submission to the will of God,—for such a struggle he was
wholly unsuited; and his is the praise, that he perished
with the women and children.”</p></div>

<div class="dsdnote">〈OCCULTING LIGHT AT BRUSSELS.〉</div>

<p>In 1853 I spent some weeks at Brussels. During my residence
in that city a Congress of naval officers from all the
maritime nations assembled to discuss and agree upon certain
rules and ob­ser­va­tions to be arranged for the common benefit
of all. One evening I had the great pleasure of receiving
the whole party at my house for the purpose of witnessing
my occulting lights.</p>

<p>The portable occulting light which I had brought with
me was placed in the verandah on the first floor, and we then
went along the Boulevards to see its effect at different distances
and with various numerical signals. On our return
several papers relating to the subject were lying upon the
table.  The Russian rep­re­sen­ta­tive, M. <span class="nowrap">———,</span> took up one
of the original printed descriptions and was much interested
in it. On taking leave he asked, with some hesitation,
whether I would lend it to him for a few hours. I told him
at once that if I possessed another copy I would willingly
give it to him; but that not being the case I could only
offer to lend it. M. <span class="nowrap">———</span> therefore took it home with him,
and when I sat down to breakfast the next morning I found
it upon my table. In the course of the day I met my
Russian friend in the Park. I expressed my hope that he
had been interested by the little tract he had so speedily
returned. He replied that it had interested him so much
that he had sat up all night, had copied the whole of it, and
that his transcript and a despatch upon the subject was now
on its way by the post to his own Government.</p>

<p>Several years after I was informed that <i>occulting solar lights</i>
<span class="xxpn" id="p459">{459}</span> were used by the Russians
during the siege of Sebastopol.</p></div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Night Signals.</i></h3>

<p>The system of occulting light applies with remarkable facility
to night signals, either on shore or at sea. If it is used
numerically, it applies to all the great dictionaries of the
various maritime nations. I may here remark, that there
exist means by which all such signals may, if necessary, be
communicated in cipher.</p>

<h3 class="h3herein"><i>Sun Signals.</i></h3>

<p>The distance at which such signals can be rendered visible
exceeds that of any other class of signals by means of light.
During the Irish Trigonometrical Survey, a mountain in
Scotland was observed, with an angular instrument from
a station in Ireland, at the distance of 108 miles. This was
accomplished by stationing a party on the summit of the
mountain in Scotland with a looking-glass of about a foot
square, directing the sun’s image to the opposite station. No
oc­cul­ta­tions were used; but if the mirror had been larger,
and oc­cul­ta­tion employed, messages might have been sent, and
the time of residence upon the mountain considerably diminished.
When I was occupied with occulting signals, I made
this widely known. I afterwards communicated the plan,
during a visit to Paris, to many of my friends in that capital,
and, by request, to the Minister of Marine.</p>

<p>I have observed in the “Comptes Rendus” that the system has
to a certain extent been since used in the south of Algeria,
where, during eight months of the year, the sun is generally
unobscured by clouds as long as it is above the horizon. I have
not, however, noticed in those communications to the Institute
any reference to my own previous publication.</p></div><!--section-->

<div class="section"><div class="xxpn" id="p460">{460}</div>
<h3 class="h3herein"><i>Zenith-light Signals.</i></h3>

<p>Another form of signal, although not capable of use at very great
distances, may, however, be employed with considerable advantage,
under certain circumstances. Universality and economy are its great
advantages. It consists of a looking-glass, making an angle of 45°
with the horizon, placed just behind an opening in a vertical board.
This being stuck into the earth, the light of the sky in the zenith,
which is usually the brightest, will be projected horizontally through
the opening, in whatever direction the person to be communicated with
may be placed. The person who makes the signals must stand on one side
in front of the instrument; and, by passing his hat slowly before the
aperture any number of times, may thus express each unit’s figure of
his signal.</p>

<p>He must then, leaving the light visible, pause whilst he
deliberately counts to himself ten.</p>

<p>He must then with his hat make a number of oc­cul­ta­tions
equal to the tens figure he wishes to express.</p>

<p>This must be continued for each figure in the number of
the signal, always pausing between each during the time of
counting ten.</p>

<p>When the end of the signal is terminated, he must count
sixty in the same manner; and if the signal he gave has
not been acknowledged, he should repeat it until it has been
observed.</p>

<p>The same simple telegraph may be used in a dark night,
by substituting a lantern for the looking-glass. The whole
apparatus is simple and cheap, and can be easily carried even
by a small boy.</p>

<p>I was led to this contrivance many years ago by reading an
account of a vessel stranded within thirty yards
of the shore. <span class="xxpn" id="p461">{461}</span>
Its crew consisted of thirteen people, ten of whom got into
the boat, leaving the master, who thought himself safer in the
ship, with two others of the crew.</p>

<p>The boat put off from the ship, keeping as much out of the
breakers as it could, and looking out for a favourable place
for landing. The people on shore followed the boat for several
miles, urging them not to attempt landing. But not a
single word was audible by the boat’s crew, who, after rowing
several miles, resolved to take advantage of the first favourable
lull. They did so—the boat was knocked to pieces, and
the whole crew were drowned. If the people on the shore
could at that moment have communicated with the boat’s crew,
they could have informed them that, by continuing their
course for half a mile further, they might turn into a cove,
and land almost dry.</p>

<p>I was much impressed by the want of easy communication
between stranded vessels and those on shore who might
rescue them.</p>

<div class="dsdnote">〈SHIPWRECK SIGNALS.〉</div>

<p>I can even now scarcely believe it credible that the very
simple means I am about to mention has not been adopted
years ago. A list of about a hundred questions, relating to
directions and inquiries required to be communicated between
the crew of a stranded ship and those on shore who wish to
aid it, would, I am told, be amply sufficient for such purposes.
Now, if such a list of inquiries were prepared and printed by
competent authority, any system of signals by which a number
of two places of figures can be expressed might be used. This
list of inquiries and answers ought to be printed on cards, and
nailed up on several parts of every vessel. It would be still
better, by conference with other maritime nations, to adopt
the same system of signs, and to have them printed in each
language. A looking-glass, a board with a hole in
it, and a <span class="xxpn" id="p462">{462}</span>
lantern would be all the apparatus required. The lantern
might be used for night, and the looking-glass for day
signals.</p>

<p>These simple and inexpensive signals might be oc­ca­sion­al­ly
found useful for various social purposes.</p>

<div class="dsdnote">〈SHORT DISTANCE SIGNALS.〉</div>

<p>Two neighbours in the country whose houses, though reciprocally
visible, are separated by an interval of several miles,
might oc­ca­sion­al­ly telegraph to each other.</p>

<p>If the looking-glass were of large size, its light and its
oc­cul­ta­tion might be seen perhaps from six to ten miles, and
thus become by daylight a cheap guiding light through channels
and into harbours.</p>

<p>It may also become a question whether it might not in
some cases save the expense of buoying certain channels.</p>

<p>For railway signals during daylight it might in some cases
be of great advantage, by saving the erection of very lofty
poles carrying dark frames through which the light of the sky
is admitted.</p>

<p>Amongst my early experiments, I made an occulting hand-lantern,
with a shade for occulting by the pressure of the
thumb, and with two other shades of red and of green glass.
This might be made available for military purposes, or for
the police.</p>

<div class="dkeeptgth">
<h3 class="h3herein"><i>Greenwich Time Signals.</i></h3>

<p>It has been thought very desirable that a signal to indicate
Greenwich time should be placed on the Start Point, the
last spot which ships going down the Channel on distant
voyages usually sight.</p></div>

<p>The advantage of such an arrangement arises from this—that
chronometers having had their rates ascertained on
shore, may have them somewhat altered by
the motions to <span class="xxpn" id="p463">{463}</span>
which they are submitted at sea. If, therefore, after a run
of above two hundred miles, they can be informed of the
exact Greenwich time, the sea rate of their chronometers
will be obtained.</p>

<p>Of course no other difficulty than that of expense occurs
in trans­mit­ting Greenwich time by electricity to any points
on our coast. The real difficulty is to convey it to the passing
vessels. The firing of a cannon at certain fixed hours has
been proposed, but this plan is encumbered by requiring the
knowledge of the distance of the vessel from the gun, and
also from the variation of the velocity of the transmission of
sound under various circumstances.</p>

<p>During the night the flash arising from ignited gunpowder
might be employed. But this, in case of rain or other atmospheric
circumstances, might be impeded. The best plan for
night-signals would be to have an occulting light, which
might be that of the lighthouse itself, or another specially
reserved for the purpose.</p>

<p>During the day, and when the sun is shining, the time
might be trans­mit­ted by the oc­cul­ta­tions of reflected solar
light, which would be seen at any distance the curvature of
the earth admitted.</p>

<p>The application of my Zenith Light might perhaps fulfil
all the required conditions during daylight.</p>

<p>I have found that, even in the atmosphere of London, an
opening only five inches square can be distinctly seen, and its
oc­cul­ta­tions counted by the naked eye at the distance of a
quarter of a mile. If the side of the opening were double
the former, then the light trans­mit­ted to the eye would be
four times as great, and the oc­cul­ta­tions might be observed
at the distance of one mile.</p>

<p>The looking-glass employed must have its
side nearly in <span class="xxpn" id="p464">{464}</span>
the proportion of three to two, so that one of five feet by
seven and a half ought to be seen at the distance of about
eight or nine miles.</p></div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Geological Theory of Isothermal Surfaces.</i></h3>

<p>During one portion of my residence at Naples my attention
was con­cen­trat­ed upon what in my opinion is the most remarkable
building upon the face of the earth, the Temple of
Serapis, at Puzzuoli.<a class="afnanc" href="#fn63" id="fnanc63">63</a></p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc63" id="fn63">63</a>
In this inquiry I profited by the assistance of Mr.
Head, now the Right Hon. Sir Edmund Head, Bart., K.C.B., late
Governor-General of Canada. An abstract of my own ob­ser­va­tions was
printed in the “Abstracts of Proceedings” of the Geological Society,
vol. ii. p. 72. My friend’s historical views were printed in the
“Transactions” of the Antiquarian Society.</p></div>

<div class="dsdnote">〈TEMPLE OF SERAPIS.〉</div>

<p>It was obviously built at or above the level of the Mediterranean
in order to profit by a hot spring which supplied
its numerous baths. There is unmistakable evidence that it
has subsided below the present level of the sea, at least
twenty-five feet; that it must have remained there during many
years; that it then rose gradually up, probably to its former
level, and that during the last twenty years it has been again
slowly subsiding.</p>

<p>The results of this survey led me in the following year to
explain the various elevations and depressions of portions of
the earth’s surface, at different periods of time, by a theory
which I have called the theory of the earth’s isothermal
surfaces.</p>

<p>I do not think the importance of that theory has been well
understood by geologists, who are not always sufficiently
acquainted with physical science. The late Sir Henry De la
Beche perceived at an early period the great light those
sciences might throw upon his own favourite pursuit, and
<span class="xxpn" id="p465">{465}</span>
was himself always anxious to bring them to bear upon
geology.</p>

<p>I am still more confirmed in my opinion of the importance
of the “Theory of Isothermal Surfaces in Geology” from the
fact that a few years afterwards my friend Sir John Herschel
arrived independently at precisely the same theory. I have
stated this at length in the notes to the “Ninth Bridgewater
Treatise.”</p></div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Games of Skill.</i></h3>

<p>A considerable time after the translation of Menabrea’s
memoir had been published, and after I had made many
drawings of the Analytical Engine and all its parts, I began
to meditate upon the in­tel­lec­tual means by which I had
reached to such advanced and even to such unexpected
results. I reviewed in my mind the various principles which
I had touched upon in my published and unpublished papers,
and dwelt with sat­is­fac­tion upon the power which I possessed
over mechanism through the aid of the Mechanical Notation.
I felt, however, that it would be more sat­is­fac­tory to the
minds of others, and even in some measure to my own, that
I should try the power of such principles as I had laid down,
by assuming some question of an entirely new kind, and
endeavouring to solve it by the aid of those principles which
had so successfully guided me in other cases.</p>

<div class="dsdnote">〈GAMES OF SKILL CAN BE PLAYED BY AN AUTOMATON.〉</div>

<p>After much consideration I selected for my test the contrivance
of a machine that should be able to play a game of
purely in­tel­lec­tual skill successfully; such as tit-tat-to, drafts,
chess, &amp;c.</p>

<p>I endeavoured to ascertain the opinions of persons in every
class of life and of all ages, whether they thought it required
human reason to play games of skill.
The almost constant <span class="xxpn" id="p466">{466}</span>
answer was in the affirmative. Some supported this view of
the case by observing, that if it were otherwise, then an
automaton could play such games. A few of those who had
considerable acquaintance with math­e­mat­i­cal science allowed
the possibility of machinery being capable of such work;
but they most stoutly denied the possibility of contriving
such machinery on account of the myriads of combinations
which even the simplest games included.</p>

<p>On the first part of my inquiry I soon arrived at a demonstration
that every game of skill is susceptible of being played
by an automaton.</p>

<p>Further consideration showed that if <i>any position</i> of the
men upon the board were assumed (whether that position
were possible or impossible), then if the automaton could
make the first move rightly, he must be able to win the
game, always supposing that, under the given position of the
men, that conclusion were possible.</p>

<p>Whatever move the automaton made, another move would
be made by his adversary. Now this altered state of the
board is <i>one</i> amongst the <i>many positions</i> of the men in which,
by the previous paragraph, the automaton was supposed
capable of acting.</p>

<p>Hence the question is reduced to that of making the best
move under any possible combinations of positions of the men.</p>

<p>Now the several questions the automaton has to consider
are of this <span class="nowrap">nature:—</span></p>

<ul>
<li>1. Is the position of the men, as placed before him on
the board, a possible position? that is, one which
is consistent with the rules of the game?</li>

<li>2. If so, has Automaton himself already lost the game?</li>

<li>3. If not, then has Automaton
won the game? <span class="xxpn" id="p467">{467}</span></li>

<li>4. If not, can he win it at the next move? If so, make
that move.</li>

<li>5. If not, could his adversary, if he had the move, win
the game.</li>

<li>6. If so, Automaton must prevent him if possible.</li>

<li>7. If his adversary cannot win the game at his next
move, Automaton must examine whether he can
make such a move that, if he were allowed to
have two moves in succession, he could at the
second move have <i>two</i> different ways of winning
the game;</li></ul>

<p class="pcontinue">and each of these cases failing, Automaton must
look forward to three or more successive moves.</p>

<p>Now I have already stated that in the Analytical Engine I
had devised mechanical means equivalent to memory, also
that I had provided other means equivalent to foresight, and
that the Engine itself could act on this foresight.</p>

<div class="dsdnote">〈NUMBER OF THE COMBINATIONS.〉</div>

<p>In consequence of this the whole question of making an
automaton play any game depended upon the possibility of
the machine being able to represent all the myriads of combinations
relating to it. Allowing one hundred moves on each
side for the longest game at chess, I found that the combinations
involved in the Analytical Engine enormously surpassed
any required, even by the game of chess.</p>

<div class="dsdnote">〈GAME OF TIT-TAT-TO.〉</div>

<p>As soon as I had arrived at this conclusion I commenced an
examination of a game called “tit-tat-to,” usually played by little
children. It is the simplest game with which I am acquainted.
Each player has five counters, one set marked with a <span
class="fsz4">+</span>, the other set with an 0. The board consists of
a square divided into nine smaller squares, and the object of each
player is to get three of his own men in a straight <span class="xxpn"
id="p468">{468}</span> line. One man is put on the board by each
player alternately. In practice no board is used, but the children
draw upon a bit of paper, or on their slate, a figure like any of the
following.</p>

<p>The successive moves of the two players may be represented
as <span class="nowrap">follow:—</span></p>

<div class="dctr01"><img src="images/i468.png"
width="800" height="104" alt="" /></div>

<p class="pcontinue">In this case + wins at the seventh move.</p>

<p>The next step I made was to ascertain what number of
combinations were required for all the possible variety of
moves and situations. I found this to be comparatively
insignificant.</p>

<p>I therefore easily sketched out mechanism by which such
an automaton might be guided. Hitherto I had considered
only the philosophical view of the subject, but a new idea
now entered my head which seemed to offer some chance of
enabling me to acquire the funds necessary to complete the
Analytical Engine.</p>

<p>It occurred to me that if an automaton were made to play
this game, it might be surrounded with such attractive circumstances
that a very popular and profitable exhibition might
be produced. I imagined that the machine might consist of
the figures of two children playing against each other,
accompanied by a lamb and a cock. That the child who
won the game might clap his hands whilst the cock was
crowing, after which, that the child who was beaten might cry
and wring his hands whilst the lamb began bleating.</p>

<p>I then proceeded to sketch various mechanical means by
which every action could be produced. These, when compared
with those I had employed for
the Analytical Engine, <span class="xxpn" id="p469">{469}</span>
were remarkably simple. A difficulty, however, arose of a
novel kind. It will have been observed, in the explanation I
gave of the Analytical Engine, that cases arose in which it
became necessary, on the occurrence of certain conditions,
that the machine itself should select one out of two or more
distinct modes of calculation. The particular one to be
adopted could only be known when those calculations on
which the selection depended had been already made.</p>

<div class="dsdnote">〈DIFFICULTY ARISING FROM CHOICE.〉</div>

<p>The new difficulty consisted in this, that when the automaton
had to move, it might occur that there were two different
moves, each equally conducive to his winning the game. In
this case no reason existed within the machine to direct his
choice: unless, also, some provision were made, the machine
would attempt two contradictory motions.</p>

<p>The first remedy I devised for this defect was to make the
machine keep a record of the number of games it had won
from the commencement of its existence. Whenever two
moves, which we may call A and B, were equally conducive
to winning the game, the automaton was made to consult the
record of the number of the games he had won. If that
number happened to be even, he was directed to take the
course A; if it were odd, he was to take the course B.</p>

<p>If there were three moves equally possible, the automaton
was directed to divide the number of games he had won by
three. In this case the numbers 0, 1, or 2 might be the
remainder, and the machine was directed to take the course
A, B, or C accordingly.</p>

<p>It is obvious that any number of conditions might be thus
provided for. An inquiring spectator, who observed the
games played by the automaton, might watch a long time
before he discovered the principle upon which it acted. It
is also worthy of remark how
admirably this illustrates <span class="xxpn" id="p470">{470}</span>
the best definitions of chance by the phi­los­o­pher and the
<span class="nowrap">poet:—</span></p>

<div class="dblockquote">
<div>“Chance is but the expression of man’s ignorance.”—<span
 class="smcap">L<b>APLACE.</b></span></div>

<div>“All chance, design ill understood.”—<span
 class="smcap">P<b>OPE.</b></span></div></div>

<div class="dsdnote">〈EXHIBITION OF AUTOMATON.〉</div>

<p>Having fully satisfied myself of the power of making such
an automaton, the next step was to ascertain whether there
was any probability, if it were exhibited to the public, of its
producing, in a moderate time, such a sum of money as would
enable me to construct the Analytical Engine. A friend, to
whom I had at an early period com­mun­i­cat­ed the idea, en­ter­tained
great hopes of its pecuniary success. When it became
known that an automaton could beat not merely children but
even papa and mamma at a child’s game, it seemed not
unreasonable to expect that every child who heard of it would
ask mamma to see it. On the other hand, every mamma,
and some few papas, who heard of it would doubtless take
their children to so singular and interesting a sight. I
resolved, on my return to London, to make inquiries as to
the relative productiveness of the various exhibitions of recent
years, and also to obtain some rough estimate of the probable
time it would take to construct the automaton, as well as
some approximation to the expense.</p>

<p>It occurred to me that if half a dozen were made, they
might be exhibited in three different places at the same time.
Each exhibitor might then have an automaton in reserve in
case of accidental injury. On my return to town I made the
inquiries I alluded to, and found that the English machine for
making Latin verses, the German talking-machine, as well as
several others, were entire failures in a pecuniary point of
view. I also found that the most profitable exhibition which
had occurred for many years was that of the little dwarf,
General Tom Thumb. <span class="xxpn" id="p471">{471}</span></p>

<p>On considering the whole question, I arrived at the conclusion,
that to conduct the affair to a successful issue it would
occupy so much of my own time to contrive and execute the
machinery, and then to superintend the working out of the
plan, that even if successful in point of pecuniary profit, it
would be too late to avail myself of the money thus acquired
to complete the Analytical Engine.</p></div><!--section-->

<div class="section">
<h3 class="h3herein"><i>Problem of the Three Magnetic Bodies.</i></h3>

<p>The problem of the three bodies, which has cost such unwearied
labour to so many of the highest intellects of this
and the past age, is simple compared with another which is
opening upon us. We now possess a very extensive series of
well-recorded ob­ser­va­tions of the positions of the magnetic
needle, in various parts of our globe, during about thirty
years.</p>

<div class="dsdnote">〈CAUSES OF MAGNETIC CHANGES.〉</div>

<p>Certain periods of changes of about ten or eleven years are
said to be indicated as connected with changes in the amount
of solar spots; but the inductive evidence scarcely rests upon
three periods, and it seems more probable that these effects
arise from some common cause.</p>

<ul>
<li>(1.) It has been long known that the earth has at least two if not
more magnetic poles.</li>

<li>(2.) It is probable, therefore, that the sun and moon also have
several magnetic poles.</li>

<li>(3.) In 1826 I proved that when a magnet is brought into proximity
to a piece of matter capable of becoming magnetic, the magnetism
communicated by it requires <i>time</i> for its full development in the body
magnetized. Also that when the influence of the magnet is removed,
the magnetized body requires <i>time</i> to regain its former state. <span
class="xxpn" id="p472">{472}</span></li></ul>

<p>This being the case, it is required, having assumed certain
positions for the poles of these various magnetic bodies, to
calculate their reciprocal influences in changing the positions
of those poles on the other bodies. The development of the
equations representing these forces will indicate cycles which
really belong to the nature of the subject. The comparisons
of a long series of ob­ser­va­tions with recorded facts will
ultimately enable us to determine both the number and
position of those poles upon each body.</p>

<div class="dsdnote">〈ELECTRIC CHANGES.〉</div>

<p>Electricity possesses an analogous property with respect to
time being required for its full action. If the bodies of our
system influence each other electrically, other developments
will be required and other cycles discovered.</p>

<p>When the equations resulting from the actions of these
causes are formed, and means of developing them arranged,
the whole of the rest of the work comes under the domain of
machinery.</p></div><!--section-->

<div class="section" id="p473">
<h2 class="h2herein">CHAPTER XXXV.
<span class="hsmall">RESULTS OF SCIENCE.</span></h2>

<div class="dsynopsis">
Board of Longitude&#x200a;—&#x200a;Professorship of Mathematics
at the East India College&#x200a;—&#x200a;Professorship
of Mathematics at Edinburgh&#x200a;—&#x200a;Secretaryship
of the Royal Society&#x200a;—&#x200a;Master of the
Mint&#x200a;—&#x200a;Ditto&#x200a;—&#x200a;Ditto&#x200a;—&#x200a;Registrar-General
of Births, Deaths, and
Marriages&#x200a;—&#x200a;Ditto&#x200a;—&#x200a;Com­mis­sion­er of
Railways&#x200a;—&#x200a;Ditto&#x200a;—&#x200a;Ditto Abolished.</div>

<p class="pfirst"><span class="smcap">A<b>T</b></span>
the commencement of life I had hoped that, whilst I
indulged in the pursuits of science, I might derive from it
some advantages for my family, or at least, that it might
enable me to replace a small portion of the large expenditure,
without which one of my most important discoveries could
not be practically worked out.</p>

<p>I shall now mention briefly several of those appointments
for which I had the vanity to suppose myself qualified, and
the simplicity to believe that fitness for the office was of the
slightest use without interest to get the appointment.</p>

<p>1. In the early part of 1816 the Professorship of Mathematics
at the East India College at Haileybury became vacant. The
salary, I believe, was 500&#x200a;<i>l</i>. a-year. I became a candidate, and
had strong recommendations from Ivory and Playfair. I was
informed that it was usual for the candidates to call on the
Directors. I did so. One of them was an honest man, for
he was kind enough to tell me the truth. He said, “If you
have interest, you will get it; if not, you
will not succeed.” <span class="xxpn" id="p474">{474}</span></p>

<p>2. In 1819 the Professorship of Mathematics at Edinburgh
became vacant by the death of Playfair, and the succession
of Professor Leslie to his chair. I immediately became a
candidate, and received testimony of my fitness from Lacroix,
Biot, and Laplace.</p>

<p>These communications, though gratifying to myself, were
useless for the object. Not being a Scot, I was rejected at
Edinburgh. That visit, however, led to a very agreeable incident.
I spent a delightful week at Kinneil with Dugald
Stewart. The second volume of his “Philosophy of the
Human Mind” had fortunately fallen into my hands at an
early period during my residence at Cambridge, and I had
derived much in­struc­tion from that valuable work.</p>

<div class="dsdnote">〈BOARD OF LONGITUDE.〉</div>

<p>3. About this time, in a conversation with Sir Joseph
Banks, I mentioned my wish to have a seat at the Board of
Longitude—an office to which a salary of 100&#x200a;<i>l.</i> a-year was
attached. Although not then appointed, hopes were held out
by Sir Joseph that at some future occasion I might be more
successful. In 1820 another vacancy occurred in the Board
of Longitude. I called on Sir Joseph Banks to ask his
influence with the Admiralty; this he declined, alleging as
a reason for withholding it,—the part I had taken in the institution
of the Astronomical Society.</p>

<p>I was one of its founders, had been one of its first Honorary
Secretaries, and had taken an active part in that Committee,
by which the “Nautical Almanac” was remodelled.</p>

<p>4. In 1824 an opportunity unexpectedly presented itself. I
was invited to take the entire organization and management
of an office for the assurance of lives, then about to be established.</p>

<p>It is sufficient to state that amongst our officers were the
late Marquis of Lansdowne, the late
Lord Abercrombie, the <span class="xxpn" id="p475">{475}</span>
present Master of the Rolls, and the present Judge of the
Admiralty Court; and that our direction included some of
the first merchants in the City, two or three Directors of
the Bank of England, and about an equal number of India
Directors.</p>

<div class="dsdnote">〈LIFE ASSURANCE OFFICE.〉</div>

<p>The proposition made to me was that I should have the entire
man­age­ment of the concern as Director and Actuary, with a salary of
1,500&#x200a;<i>l.</i> a-year, and apartments in the es­tab­lish­ment, with
liberty to practise as an Actuary.</p>

<p>On consulting my friend the late Francis Baily, F.R.S.,
who had himself practised as an Actuary, he strongly advised
me to accept the office. He assured me that the profit arising
from private practice could scarcely be less than 1,000&#x200a;<i>l.</i> a
year, and would probably be much more.</p>

<p>Under these circumstances, I accepted the proposition. On
examining the materials which existed for a Table of the value
of lives, I found in one of the addresses of Mr. Morgan, the
Actuary of the Equitable, materials with which to construct,
by the aid of various calculations, a very tolerable Table of
the actual mortality in that Society. Upon this basis I calculated
the Tables of our new Institution. After three months’
labour, when the whole of the arrangements had been completed,
and the day for our opening had been fixed, circumstances
occurred which induced us to give up the plan. After
the experience I had now had of the amount of time occupied
by such an office, I was unwilling to renew the engagement
with other parties. I hoped by great exertions to complete
the Difference Engine after the lapse of a few years, and that I
should not be allowed to become a serious loser by that course.</p>

<p>The Institution was therefore given up, and we each contributed
about 100&#x200a;<i>l.</i> to discharge the expenses incurred.</p>

<p>Within the subsequent twelvemonth, an
application to take <span class="xxpn" id="p476">{476}</span>
the management of another Life Assurance Society was made
to me, which I declined. That office is still in existence.</p>

<p>The information and experience I had thus gained led me
to think that the public were not sufficiently informed
respecting the nature of assurances on lives, and that a small
popular work on the subject might be useful. I prepared
such a work as intervals of leisure admitted, and early in
1826 published it under the title of “A Comparative View of
the various Institutions for the Assurance of Lives.” This
little volume was soon translated into German, and became
the groundwork upon which the Great Life Assurance Society
of Gotha was founded. Every year since that event I have
received a copy of the report of the state of the Institution—a
gratifying attention which I am happy to have this
opportunity of acknowledging.</p>

<p>The wish expressed by my translator, in his Preface,<a class="afnanc" href="#fn64" id="fnanc64">64</a>
has
also been fulfilled by the establishment of many other excellent
Life Assurance Offices, founded on similar principles.</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc64" id="fn64">64</a>
“May this book soon give rise to many flourishing life
assurance companies in our beloved fatherland, by which proportionate
wealth and happiness may be promoted amongst us, and at the same time
prepare for the decline of lotteries.”—<i>German translation of Babbage
on Life Assurance.</i></p></div>

<div class="dsdnote">〈GERMAN ASSURANCE COMPANIES.〉</div>

<p>In Germany alone there were, in 1860, twenty-four Life
Assurance Companies, in which about 260,000 persons were
assured to the amount of upwards of forty millions sterling.
The oldest and most successful of these institutions have
adopted my Table of the Equitable experience, and I am
informed that it agrees very well with the results of their own
experience up to about the fifty-seventh year. After this the
deaths are rather more frequent than those of the Equitable.</p>

<p>Another still more gratifying result arose. My father,
whose acquaintance with mercantile
affairs was very <span class="xxpn" id="p477">{477}</span>
extensive, was so pleased with the little book that, during the two
last years of his life, he read it through three times.</p>

<div class="dsdnote">〈MASTERSHIP OF THE MINT.〉</div>

<p>5. In 1846 the Mastership of the Mint became vacant. In
former days it was held by Newton. I had pointed it out in
“The Decline of Science” as one of those offices to which
men of science might reasonably aspire. A complete acquaintance
with the most advanced state of mechanical science,
which the demands of my own machinery had compelled me
to improve, added to a knowledge of the internal economy of
manufactories, appeared to me to constitute fair claims to that
office.</p>

<p>In the event of my succeeding, I had proposed to let the
whole of my salary accumulate, so that at the end of ten or
twelve years I might retire from the office, and be enabled,
with the 20,000&#x200a;<i>l.</i> thus earned, to construct the Analytical
Engine.</p>

<p>I wrote to Lord Melbourne on the subject, but I did not
mention that circumstance even to my most intimate friends.
It came, however, to the knowledge of one of them, who took
a very warm interest in my success; and I believe that at
first I had a very fair chance. The appointment remained
for a short time in abeyance; but it was found necessary to
detach Sheil from O’Connell, and the appointment was therefore
given to Sheil.</p>

<p>Some years after, when Sheil was appointed our Minister
at the court of Tuscany, he asked me to give him a letter of
introduction to the Grand Duke Leopold II. Of course I
treated the application as a joke; but Sheil assured me that
he was quite serious, and that he knew it would be of use to
him. I therefore gave him a letter of introduction to a
sovereign from whom both before and sub­se­quent­ly I have
been honoured by
many gratifying attentions. <span class="xxpn" id="p478">{478}</span></p>

<p>6. In 1849, on the promotion of Sheil, the Mastership of
the Mint again became vacant. I thought my own claims
sufficiently known to the public; but I had no political interest.
My friend Sir John Herschel was more fortunate,
and he received the appointment.</p>

<p>7. After a few years, the office again became vacant by the
resignation of Sir John Herschel. The Government had now
for the third time an opportunity of partially repairing its
former neglect. I had, however, no political party to support
me, and the present Master of the Mint, Mr. Graham, then
received the appointment.</p>

<div class="dkeeptgth">
<h3 class="h3herein"><i>Registrar-General of Births, Deaths, &amp;c.</i></h3>

<p>8. In 1835 a new office was created, that of Registrar-General
of Births, Deaths, and Marriages. Mr. Francis Baily
and others of my friends suggested to me that, being known
to the public as qualified for this situation by my previous
publications, I had a fair claim to the appointment. Having
made inquiries on this subject, I found that it would be
useless to make any application, as the place was intended for
the brother-in-law of a Secretary of State.</p></div>

<p>9. On the death of Mr. Lister, a few years after, the same
office again became vacant, when other friends then made a
similar suggestion.</p>

<p>On making preliminary inquiries, I found, as before, that
all applications would be useless, as the appointment was
intended for a military officer, Major Graham, the brother of
another Secretary of State.</p>

<div class="dkeeptgth">
<h3 class="h3herein"><i>Com­mis­sion­ers of Railways.</i></h3>

<p>10. Some years ago, the alarm created by accidents
occurring upon railways, induced the
Government to consider <span class="xxpn" id="p479">{479}</span>
about the appointment of a Commission to examine into their
causes, and to lay down rules for the guidance of the Companies
in the prevention of those dangers.</p></div>

<p>In 1846 an Act of Parliament was passed appointing Com­mis­sion­ers
for the supervision of railways. Having myself
thought much upon the subject, and having had personally
some experience on railways, I had the vanity to think that
the mechanical knowledge of the author of “The Economy
of Man­u­fac­tures” would justify his appointment as one of
those Com­mis­sion­ers.</p>

<p>Applying, under such circumstances, for a Com­mis­sion­ership
of the Railway Board, I expected that I should find few
competitors with higher claims. But I had no interest—a
military engineer was appointed, who already held a civil
appointment, and who died in less than two years after.</p>

<p>11. On the occurrence of this vacancy another military
officer was appointed. I was again passed over, under circumstances
which at the time I thought must have caused
deep regret in the mind of the Minister who made the appointment.</p>

<p>After an existence of a few years, public opinion was so
strongly expressed against the Railway Commission that it
was dissolved.</p>

<p>I am satisfied that in each of these cases, the appointment
was entirely due to family or political influence.</p>

<p>I have, in the course of my experience, frequently heard of
appointments made in the most flattering and unexpected
manner; of titles offered, in fact, in such a way, that it was
impossible to decline them. Having myself seen a good deal
behind the scenes of the drama of life, I have repeatedly
found that these unsolicited honours have been obtained by
the most persevering applications, and by
the most servile <span class="xxpn" id="p480">{480}</span>
flattery. Indeed, to the great scandal of public life, success
has in some instances been attained by a man condescending
for a time to oppose his own party, and, as some observer has
wittily remarked, “of attempting to break into the shop for
the purpose of serving behind the counter.”</p>

<div class="dsdnote">〈REFLECTIONS ON PATRONAGE.〉</div>

<p>It cannot be doubted that patronage entrusted to the disposition
of a Minister often proves an onerous and ungrateful
trust, demanding powers of discrimination and forbearance
not always found in public men; whilst a careful ob­ser­va­tion
of the manner in which patronage is usually dispensed does
not lead to the conclusion that its exercise is always free from
the influence of corrupt motives.  Even in the cases in
which such impure motives <i>seem</i> absent, it too frequently
happens that other influences beside a just and honest discrimination
appear to have taken a part in regulating the
distribution of public favour. It would be invidious to speculate
on the motives or discuss the merits of the appointments
to which I have had occasion to refer: with their propriety
or otherwise I have individually no concern: of the positive
motives which induced them I have no knowledge, at least
not sufficient to justify me in condemning them on that score.
But I cannot help thinking that such appointments have not
always been made without some degree of pain or misgiving,
and perhaps a conscientious scruple on the part of the Minister;
indeed I have sometimes indulged a suspicion that a
little firmness to resist external pressure would oc­ca­sion­al­ly
secure more fairness to candidates for public employment,
and tend to retain the services of more efficient agents of the
public weal.</p>

<div class="dsdnote">〈THE WEIGHT OF NEPOTISM.〉</div>

<p>Although mankind may differ among one another individually
<i>ad infinitum</i>, they possess certain moral elements
which are common to the race. Such belong
to the animal, <span class="xxpn" id="p481">{481}</span>
and are never obliterated, though they may oc­ca­sion­al­ly be
concealed by the ermine of office or the robe of state. Self-interest
is the great lever of society; and though the patriot
profess to sacrifice it for the public good, or the cynic affect
to despise its influence as opposed to his philosophy, both
these may claim our respect, but neither should be permitted
to deceive us. A Minister who professes to cast off the attributes
of humanity is either a victim of delusion who has succeeded
in deceiving himself, or a knave who is bent upon
deceiving others. He may spurn the temptation of a bribe,
because his wants do not lie in that direction; and, not­with­stand­ing
his generous pretensions, he will never discern
merit unless accompanied by popular suffrage or political
influence: in <i>his</i> balance one grain of <i>nepotism</i> will weigh
down all the <i>honesty</i> he has
at his disposal.</p></div><!--section-->

<div class="section" id="p482">
<h2 class="h2herein">CHAPTER XXXVI.
<span class="hsmall">AGREEABLE RECOLLECTIONS.</span></h2>

<p class="pfirst"><span class="smcap">I<b>N</b></span>
the course of this volume I have mentioned, under other
heads, many agreeable circumstances, and many others remain
unwritten. I shall now confine myself to two.</p>

<p>On one occasion when I was engaged in my workshop in
arranging some machinery for experiments on a difficult part
of the Analytical Engine, an intimate friend called, and I
went into the library to see him. An unopened letter lying
on the table, he asked whether I usually treated my letters
in that way. I looked at the letter, which appeared to be a
printed one. When my friend had left me, I opened it,
and found that it professed to be from the Institute of
France, announcing my nomination as a corresponding
member of that distinguished body. On looking at the conclusion
for the well-known signature of my friend Arago, I
found another name which I could not read. I therefore
concluded that some wag had played me a trick. I however
doubted whether the joke was intended to hit me or the
Academy of Sciences.</p>

<p>Having left the paper on my table, I returned to my
experiments. After dinner I took up the neglected document,
and then for the first time perceived that it professed
to be from the Academy of Moral Sciences. On re-examining
the signature, I found it to be that
of its eminent <span class="xxpn" id="p483">{483}</span>
secretary, M. Mignet, and that it was the official announcement of
my election as a Corresponding Member of that Academy.</p>

<div class="dsdnote">〈ACADEMY OF MORAL SCIENCES.〉</div>

<p>Now the first impression on my own mind was one of
sincere regret. I felt for a moment that the Academy might
have thus honoured me not solely for my labours in their
own, but in other departments of science. This painful
feeling was, however, only momentary. It then occurred to
me that I had written the “Economy of Man­u­fac­tures,” which
related to Political Economy, one section; and the “Ninth
Bridgewater Treatise,” which related to Philosophy, another
section of the Academy of Moral Sciences. I now felt a real
pleasure, which amply compensated me for the transitory
regret; and I am sure no member of the many academies
who have honoured me by enrolling my name on their list
will reproach me for stating the fact,—that no other nomination
ever gave me greater sat­is­fac­tion than the one to
which I have now adverted.</p>

<p>Some years ago my eldest son, Mr. B. Herschel Babbage,
was employed by the Government of South Australia to explore
and survey part of the north-western portion of that
colony. After an absence of about six months, a considerable
portion of which time he spent in a desert, he reached a
small station at the head of Spencer’s Gulf, intending to wait
there until the arrival of a steamer from Adelaide, which was
expected in about a week to carry back the wool of the
distant and scattered colonists.</p>

<p>It so happened that, a few days before, a Swedish merchant-vessel,
commanded by Capt. Orling, a part owner of the ship,
had also arrived in search of a freight of wool. Captain
Orling on going ashore heard of the arrival at the settlement
of a stranger from the interior, and on inquiry found that he
bore my name. <span class="xxpn" id="p484">{484}</span></p>

<div class="dsdnote">〈GRATEFUL SWEDES.〉</div>

<p>He immediately went in search of my son, and having
found him, said, “I am not personally acquainted with your
father, but I am well acquainted with his name: he has
shown such kindness to a countryman of mine<a class="afnanc" href="#fn65" id="fnanc65">65</a>
that every
Swede would be proud of an opportunity of acknowledging
it. The steamer for which you are waiting cannot arrive
until a week hence. There are no accommodations in this
station, not even a public-house; I entreat you to come on
board my ship and be my guest until the steamer arrives
and is ready to take you to Adelaide.”</p>

<div class="dftnt">
<p class="pfirst"><a class="afnlabel" href="#fnanc65" id="fn65">65</a>
It had been my good fortune to have an opportunity of rendering
justice to the merits of Mr. Scheütz, the inventor of the Swedish Difference
Engine.</p></div>

<p>My son, who during the six previous months had slept
under no canopy but that of heaven, accepted this delightful
invitation, and enjoyed, during a week, the society of a very
agreeable and highly-informed gentleman.</p>

<p>I have received many marks of attention of various kinds
from natives of Sweden—paragraphs translated from Swedish
newspapers which were peculiarly interesting to me, engravings,
and printed volumes. I have been honoured with
these attentions by persons in various classes of society up to
the highest, and I am confident that the enlightened and
accomplished Prince to whom I allude will not think me
ungrateful when I avow that the most gratifying of all these
attentions to a father, whose name in his own country has
been useless to himself and to his children, was to hear from
England’s antipodes of a grateful Swede welcoming and
giving hospitality on the part of his countrymen to my son
for the sake of the name he bore.</p></div><!--section-->

<div class="section">
<div><span class="xxpn" id="p485">{485}</span></div>

<h3 class="h3herein"><i>Conclusion.</i></h3>

<p>I will now conclude, as I began, by invoking the attention
of my reader to a subject which, if he is young, may be of
importance to him in after-life. He may reasonably ask what
peculiarities of mind enabled me to accomplish what even
the most instructed in their own sciences deemed impossible.</p>

<p>I have always carefully watched the exercise of my own
faculties, and I have also endeavoured to collect from the
light reflected by other minds some explanation of the question.</p>

<p>I think one of the most important guiding principles has
been this:—that every moment of my waking hours has
always been occupied by <i>some train of inquiry</i>. In far the
largest number of instances the subject might be simple or
even trivial, but still work of inquiry, of some kind or other,
was always going on.</p>

<p>The difficulty consisted in adapting the work to the state of
the body. The necessary training was difficult. Whenever
at night I found myself sleepless, and wished to sleep, I took
a subject for examination that required little mental effort,
and which also had little influence on worldly affairs by its
success or failure.</p>

<p>On the other hand, when I wanted to con­cen­trate my whole
mind upon an important subject, I studied during the day all
the minor accessories, and after two o’clock in the morning I
found that repose which the nuisances of the London streets
only allow from that hour until six in the morning.</p>

<p>At first I had many a sleepless night before I could thus
train myself.</p>

<p>I believe my early perception of the immense power of
signs in aiding the reasoning faculty
contributed much to <span class="xxpn" id="p486">{486}</span>
whatever success I may have had. Probably a still more
important element was the intimate conviction I possessed
that the highest object a reasonable being could pursue was
to endeavour to discover those laws of mind by which man’s
intellect passes from the known to the discovery of the
unknown.</p>

<p>This feeling was ever present to my own mind, and I endeavoured to
trace its principle in the minds of all around me, as well as in the
works of my predecessors.</p></div><!--section-->

<div class="section" id="p487">
<h2 class="h2herein">APPENDIX.</h2>

<hr class="hr10" />

<h3 class="h3herein"><span class="smcap">M<b>IRACLES.</b></span>
<span class="hsmall">
<i>Note (A), page <a href="#p394" title="go to pag&#x65; 394">394</a>.</i></span></h3>

<p class="pfirst"><span class="smcap">I<b>T</b></span>
has always occurred to my mind that many difficulties touching
Miracles might be reconciled, if men would only take the trouble
to agree upon the nature of the phenomenon which they call
“Miracle.” That writers do not always mean the same thing
when treating of miracles is perfectly clear; because what may
appear a miracle to the unlearned is to the better instructed only
an effect produced by some unknown law hitherto unobserved.
So that the idea of miracle is in some respect dependent upon
the opinion of man. Much of this confusion has arisen from the
definition of Miracle given in Hume’s celebrated Essay, namely,
that it is the “violation of a law of nature.”</p>

<p>Now a miracle is not necessarily a violation of any law of
nature, and it involves no physical absurdity.</p>

<p>As Brown well observes, “the laws of nature surely are not
violated when a new antecedent is followed by a new consequent;
they are violated only when the antecedent, being exactly
the same, a different consequent is the result;” so that a miracle
has nothing in its nature inconsistent with our belief of the
uniformity of nature. All that we see in a miracle is an effect
which is new to our ob­ser­va­tion, and whose cause is concealed.</p>

<p>The cause may be beyond the sphere of our ob­ser­va­tion, and
would be thus beyond the familiar sphere of nature; but this
does not make the event a violation of any law of nature. The
limits of man’s ob­ser­va­tion lie within
very narrow boundaries, <span class="xxpn" id="p488">{488}</span>
and it would be arrogance to suppose that the reach of man’s
power is to form the limits of the natural world. The universe
offers daily proof of the existence of power of which we know
nothing, but whose mighty agency nevertheless manifestly
appears in the most familiar works of creation. And shall we
deny the existence of this mighty energy simply because it
manifests itself in delegated and feeble subordination to God’s
omnipotence?</p>

<p>There is nothing in the nature of a miracle that should render
it incredible: its credibility depends upon the nature of the
evidence by which it is supported. An event of extreme probability
will not necessarily command our belief unless upon a
sufficiency of proof; and so an event which we may regard as
highly improbable may command our belief if it is sustained by
sufficient evidence. So that the credibility or incredibility of an
event does not rest upon the nature of the event itself, but
depends upon the nature and sufficiency of the proof which sustains
it.</p>

<p>Mill, in speaking of Hume’s celebrated principle, “that nothing
is credible which is contradictory to experience, or at variance
with the laws of nature,” calls it a very plain and harmless proposition,
being, in effect, nothing more than that whatever is
contradictory to a complete induction is incredible.</p>

<p>Admit the existence of a Deity, and the possibility of a miracle
is the natural consequence. No doubt our examination of the
evidence which sustains an unusual phenomenon should be most
carefully conducted; but we must not measure the credibility or
incredibility of an event by the narrow sphere of our own experience,
nor forget that there is a Divine energy which overrides
what we familiarly call the laws of nature.</p>

<p>If a miracle is not a suspension or a violation of the laws of
nature, it may fairly be asked, What is it?</p>

<p>If we define a miracle as an effect of which the cause is
unknown to us, then we make our ignorance the source of
miracles! and the universe itself would be
a standing miracle. <span class="xxpn" id="p489">{489}</span>
A miracle might be perhaps defined more exactly as an effect
which is not the consequence or effect of any known laws of
nature. Dr. Clarke defines a miracle as a singular event produced
contrary to the ordinary laws of nature by the intervention
of an intelligent Being superior to man. The Abbé Houteville
defines a miracle as the result of the general order of the mechanism
of the universe. “It is,” he says, “a result of the harmony
of the general laws which God has decreed for the working out
of the system of the universe.” Spinosa says, “As men call that
science Divine which surpasses the reach of the human mind, so
they detect the hand of God in every phenomenon of which the
cause is unknown to them.” And certain it is that men attach
more importance to an apparent suspension or violation of the
ordinary laws of nature than to the wonderful harmony and
uniformity of the laws of the universe; as though it implied a
greater degree of power to suspend or interfere with such laws
than to establish them and preserve their uniformity in the
economy of the universe. Whilst Nature follows out her ordinary
course, man, familiarized with the movement of the celestial
orbs, sees myriads of globes revolve in moving harmony about
their spheres with a kind of vacant indifference, nor imagines for
a moment that he sees aught to excite his wonder or stimulate
his intelligence into inquiry; in fact, he does not see God in His
works. But if this harmony and uniformity are interrupted for
a moment, man detects the power of God in the in­ter­rup­tion,
albeit he could not perceive it in the uniformity of natural cause
and effect. This singular obtuseness of the human mind I leave
to the discussion of theologians and phi­los­o­phers; for my own
part, I confess my utter inability to comprehend it. Whatever
truly exists must emanate from the will of God, whether the
event falls within what we understand by the uniformity of
nature, or whether it is otherwise. A miracle must fall within
one of these categories; and in either case it is the effect of the
will of God. Such an in­ter­rup­tion does not imply any notion
of caprice or imperfection in the Deity; but, on
the contrary, it <span class="xxpn" id="p490">{490}</span>
is one of the attributes of His power, and quite consistent with
our notions of the liberty of His will, unrestrained by any laws
which it may be His pleasure to promulgate for the government
of the universe.</p>

<p>“Opera mutat, consilia non mutat,” says St. Augustin. Miracles
may be, for anything we know to the contrary, phenomena of a
higher order of God’s laws, superior to, and, under certain conditions,
controlling the inferior order known to us as the ordinary
laws of nature.</p>

<p>The great difficulty in the consideration of miracles is, that
being in the nature of things incapable of verification, the
evidence which would be sufficient to establish the truth of an
ordinary event within the sphere of natural phenomena would
not be sufficient to command our assent in the case of a miracle.
And this does not arise from a miracle being opposed to nature, but
on account of the infirmity of our nature; for we are always liable
to be deceived, not only by others, but even by our own senses.</p>

<p>The extraordinary character of an event, although it does not
necessarily render the truth of its existence incredible, should,
nevertheless, put us upon our guard, and render us par­tic­u­lar­ly
cautious in examining the evidence upon which its truth is
asserted. We should even examine with care and caution the
evidence of phenomena of the most ordinary character before we
yield our complete assent to the apparent truth of their manifestation;
and <i>à fortiori</i> in the examination of the evidence
which sustains extraordinary phenomena we should require much
stronger evidence, and such as rebuts the possibility of being
deceived by other persons, or even by our senses.</p>

<p>But we must be careful to discriminate between our own
incapacity to test truth and the necessary improbability of an
event. It is plain that from our ignorance of the remote spheres
of God’s action we cannot judge of His works removed from our
experience; but a fact is not necessarily doubtful because it
cannot be reached by our ordinary senses. To recapitulate, we
may lay down
the following <span class="nowrap">propositions:—</span>
<span class="xxpn" id="p491">{491}</span></p>

<ul><li>1. That there is no real physical distinction between miracles
and any other operations of the Divine energy: that we regard them
differently is because we are familiar with one order of events and not
the other.</li>

<li>2. There is nothing incredible in a miracle, and the credibility
of a miraculous event is to be measured only by the evidence which
sustains it. And although the extraordinary character of a phenomenon
may render the event itself improbable, it does not, therefore,
necessarily render it either incredible or untrue.</li></ul>
</div><!--section-->

<div class="section">
<h3 class="h3herein"><span class="smcap">R<b>ELIGION.</b></span>
<span class="hsmall">
 <i>Note (B), page <a href="#p403" title="go to pag&#x65; 403">403</a>.</i></span></h3>

<p>St. Athanasius is not the author of the Creed which bears his
name. It did not, in fact, exist within a century after his death.
It originally appeared in a Latin text, and consequently in the
Western provinces.  Gennadius, Patriarch of Constantinople,
was less tolerant of its eccentricities, or more sensible to its
sublimity even than myself, for he was so amazed at the extraordinary
character of its composition that he frankly pronounced
it to be the work of a drunken man. See ‘Petav. Dogmat. Theologica,’
tom. II. lvii. c. 8, p. 687; and Gibbon’s ‘Decline and Fall,’
vol. iv. p. 335. If we may trust La Bletterie for the character
of Athanasius, nothing is more improbable than that he could be
the author of the Creed still preserving his name. “He was,”
says La Bletterie, “the greatest man of his age, and perhaps the
greatest that the Church has ever possessed. He was endued
with a well-balanced, a lively, and penetrating mind; a generous
and disinterested heart; a courage and heroism always
equal; a lively faith, and a charity without bounds; a profound
humility; a Christianity bold, but simple and noble as
the Gospel.  His eloquence was natural, distinguished by
a rare precision of speech.”</p>

<p>The foundation of all religion is the belief in a God, and that
He exists in certain relation with His
creatures.  Such belief <span class="xxpn" id="p492">{492}</span>
necessarily leads to the consciousness of some obligation towards
the Deity; and this consciousness suggests the duty of worship;
and in the selection of the form of this worship originates the
various creeds which distinguish and distract mankind. There
is a sort of geography of religion; and I regret to think that the
majority of mankind take their creed from the clime in which
they happen to be born; and that many, and not an inconsiderable
portion of mankind, suffer the sacred torch to burn out
altogether, in their contact with the world, and then vainly
imagine that they can recover the sacred fire by striking a spark
out of dogmatic theology!</p>
<hr class="hr20" />

<div class="dkeeptgth">
<h3 class="h3herein"><span class="smcap">A<b>DDITION</b></span>
<span class="smmaj">TO THE</span>
<span class="smcap">C<b>HAPTER</b></span>
<span class="smmaj">ON</span>
<span class="smcap">R<b>AILROADS.</b></span></h3>

<p>One of the most important facts which the engine-driver ought
to know is the exact time since the preceding train has passed
the point of railroad on which his own engine is.</p></div>

<p>This may be done by placing signals, about to be described,
by the side of or across the road at all places where such knowledge
is most important.</p>

<p>The principle to be employed is, that at the passage of those
places the engine itself should, in its transit, wind up a weight
or spring. That this weight should act upon an arm standing
perpendicularly, which would immediately commence moving
slowly to the horizontal position. This it should attain by an
equable motion at the end of three, five, or any desirable number
of minutes.</p>

<p>The means of raising the weight may be derived either from
a projection below the engine or by one above it. The latter,
which seems preferable, might be attached to a light beam traversing
the road to which the apparatus
should be fixed.</p></div><!--section-->

<div class="section" id="p493">
<h2 class="h2herein">LIST OF MR. BABBAGE’S PRINTED PAPERS.</h2>

<p class="phanga"><i>Many applications having been made to the Author and
to his Publishers, for detached Papers which he has from time to time
printed, he takes this opportunity of giving a list of those Papers,
with references to the Works in which they may be found.</i></p>
<hr class="hr20" />
<p>1. The Preface; jointly with Sir John Herschel.—<i>Memoirs
of the Analytical Society. 4to. Cambridge, 1813.</i></p>

<p>2. On Continued Products.—<i>Ibid.</i></p>

<p>3. An Essay towards the Calculus of Functions.—<i>Phil. Trans.</i> 1815.</p>

<p>4. An Essay towards the Calculus of Functions, Part. 2.—<i>Phil. Trans.</i> 1816.
P. 179.</p>

<p>5. Demonstrations of some of Dr. Matthew Stewart’s General Theorems, to
which is added an Account of some New Properties of the Circle.—<i>Roy. Inst.
Jour.</i> 1816. Vol. i. p. 6.</p>

<p>6. Ob­ser­va­tions on the Analogy which subsists between the Calculus of
Functions and other branches of Analysis.—<i>Phil. Trans.</i> 1817. P. 179.</p>

<p>7. Solution of some Problems by means of the Calculus of Functions.—<i>Roy.
Inst. Jour.</i> 1817. P. 371.</p>

<p>8. Note respecting Elimination.—<i>Roy. Inst. Jour.</i> 1817. P. 355.</p>

<p>9. An Account of Euler’s Method of Solving a Problem relating to the
Knight’s Move at Chess.—<i>Roy. Inst. Jour.</i> 1817. P. 72.</p>

<p>10. On some new Methods of Investigating the Sums of several Classes of
Infinite Series.—<i>Phil. Trans.</i> 1819. P. 245.</p>

<p>11. Demonstration of a Theorem relating to Prime Numbers.—<i>Edin. Phil.
Jour.</i> 1819. P. 46.</p>

<p>12. An Examination of some Questions connected with Games of Chance.—<i>Trans.
of Roy. Soc. of Edin.</i> 1820. Vol. ix. p. 153.</p>

<p>13. Ob­ser­va­tions on the Notation employed in the Calculus of Functions.—<i>Trans.
of Cam. Phil. Soc.</i> 1820. Vol. i. p. 63.</p>

<p>14. On the Application of Analysis, &amp;c. to the Discovery of Local Theorems
and Porisms.—<i>Trans. of Roy. Soc. of Edin.</i> Vol. ix. p. 337. 1820.</p>

<p>15. Translation of the Differential and Integral Calculus of La Croix,
1 vol. 1816.</p>

<p>16. Examples to the Differential and Integral Calculus. 2 vols. 8vo.
1820.</p>

<div id="dp493a">
The above two works were executed in conjunction with the Rev. G.
Peacock (Dean of Ely) and Sir John Herschel, Bart.</div>

<p>17. Examples of the Solution of Functional Equations. Extracted from the
preceding. 8vo. 1820.</p>

<p>18. Note respecting the Application of Machinery to the Calculation of
Math­e­mat­i­cal Tables.—<i>Memoirs of the Astron. Soc.</i> <i>June, 1822.</i> Vol. i. p. 309.</p>

<p>19. A Letter to Sir H. Davy, P.R.S., on the Application of Machinery to the
purpose of calculating and printing Math­e­mat­i­cal Tables. 4to. <i>July, 1822.</i></p>

<p>20. On the Theoretical Principles of the Machinery for calculating Tables.—<i>Brewster’s
Edin. Jour. of Science.</i> Vol. viii. p. 122. 1822.</p>

<p>21. Ob­ser­va­tions on the application of Machinery to the Computations of
Math­e­mat­i­cal Tables, Dec. 1822.—<i>Memoirs of Astron. Soc.</i> 1824. Vol. i.
p. 311.</p>

<p>22. On the Determination of the General Term of a new Class of Infinite
Series.—<i>Trans. Cam. Phil. Soc.</i> 1824. Vol.
ii. p. 218. <span class="xxpn" id="p494">{494}</span></p>

<p>23. Ob­ser­va­tions on the Measurement of Heights by the Barometer.—<i>Brewster’s
Edin. Jour. of Science</i>, 1824. P. 85.</p>

<p>24. On a New Zenith Micrometer.—<i>Mem. Astro. Soc.</i> March, 1825.</p>

<p>25. Account of the repetition of M. Arago’s Experiments on the Magnetism
manifested by various substances during Rotation. By C. Babbage, Esq. and
Sir John Herschel.—<i>Phil. Trans.</i> 1825. P. 467.</p>

<p>26. On the Diving Bell.—<i>Ency. Metrop.</i> 4to. 1826.</p>

<p>27. On Electric and Magnetic Rotation.—<i>Phil. Trans.</i> 1826. Vol. ii.
p. 494.</p>

<p>28. On a method of expressing by Signs the Action of Machinery.—<i>Phil.
Trans.</i> 1826. Vol. ii. p. 250.</p>

<p>29. On the Influence of Signs in Math­e­mat­i­cal Reasoning.—<i>Trans. Cam.
Phil. Soc.</i> 1826. Vol. ii. p. 218.</p>

<p>30. A Comparative View of the different Institutions for the Assurance of
Life. 1 vol. 8vo. 1826. German Translation. Weimar, 1827.</p>

<p>31. On Notation.—<i>Edinburgh Encyclopedia.</i> 4to.</p>

<p>32. On Porisms.—<i>Edinburgh Encyclopedia.</i> 4to.</p>

<p>33. A Table of the Logarithms of the Natural Numbers, from 1 to 108,000.
Stereotyped. 1 vol. 8vo. 1826.</p>

<p>34. Three editions on coloured paper, with the Preface and Instructions
translated into German and Hungarian, by Mr. Chas. Nagy, have been published
at Pesth and Vienna. 1834.</p>

<p>35. Notice respecting some Errors common to many Tables of Logarithms.—<i>Mem.
Astron. Soc.</i> 4to. 1827. Vol. iii. p. 65.</p>

<p>Evidence on Savings-Banks, before a Committee of the House of Commons,
1827.</p>

<p>36. Essay on the general Principles which regulate the Application of
Machinery.—<i>Ency. Metrop.</i> 4to. 1829.</p>

<p>37. Letter to T. P. Courtenay on the Proportion of Births of the two Sexes
amongst Legitimate and Illegitimate Children.—<i>Brewster’s Edin. Jour. of
Science.</i> Vol. ii. p. 85. 1829. This letter was translated into French and
published by M. Villermé, Member of the Institute of France.</p>

<p>38. Account of the great Congress of Phi­los­o­phers at Berlin, on 18 Sept.
1828.—Communicated by a Correspondent [C. B.]. <i>Edin. Journ. of Science by
David Brewster.</i> Vol. x. p. 225. 1829.</p>

<p>39. Note on the Description of Mammalia.—<i>Edin. Jour. of Science</i>, 1829.
Vol. i. p. 187. <i>Ferussac Bull</i>, vol. xxv. p. 296.</p>

<p>40. Reflections on the Decline of Science in England, and on some of its
Causes. 4to. and 8vo. 1830.</p>

<p>41. Sketch of the Philosophical Characters of Dr. Wollaston and Sir H.
Davy. Extracted from the <i>Decline of Science</i>. 1830.</p>

<p>42. On the Proportion of Letters occurring in Various Languages, in a letter
to M. Quételet.—<i>Correspondence Mathematique et Physique.</i> Tom. vi. p. 136.</p>

<p>43. Specimen of Logarithmic Tables, printed with different coloured inks
and on variously-coloured papers, in twenty-one volumes 8vo. London. 1831.</p>

<p class="pp494a">The object of this Work, of which <i>one single copy only</i> was printed, is to ascertain by experiment
the tints of the paper and colours of the inks least fatiguing to the eye.</p>

<p class="pp494a">One hundred and fifty-one variously-coloured papers were chosen, and the same two pages of
my stereotype Table of Logarithms were printed upon them in inks of the following colours:
light blue, dark blue, light green, dark green, olive, yellow, light red, dark red, purple, and
black.</p>

<p class="pp494a">Each of these twenty volumes contains papers of the same colour, numbered in the same order,
and there are two volumes printed with each
kind of ink. <span class="xxpn" id="p495">{495}</span></p>

<p class="pp494a">The twenty-first volume contains metallic printing of the same specimen in gold, silver, and
copper, upon vellum and on variously-coloured papers.</p>

<p class="pp494a">For the same purpose, about thirty-five copies of the complete table of logarithms were printed
on thick drawing paper of various tints.</p>

<p class="pp494a">An account of this work may be found in the <i>Edin. Journ. of Science</i> (<i>Brewster’s</i>), 1832.
Vol. vi. p. 144.</p>

<p>44. Economy of Man­u­fac­tures and Machinery. 8vo. 1832.</p>

<p class="pp494a">There are many editions and also American reprints,
and several Translations of this Work into German, French, Italian,
Spanish, &amp;c.</p>

<p>45. Letter to Sir David Brewster, on the Advantage of a Collection
of the Constants of Nature and Art.—<i>Brewster’s Edin. Jour. of
Science.</i> 1832. Vol. vi. p. 334. Reprinted by order of the British
Association for the Promotion of Science. Cambridge, 1833. See also
pp. 484, 490, Report of the Third Meeting of the British Association.
Reprinted in Compte Rendu des Traveaux du Congres Général de
Statistique, Bruxelles, Sept. 1853.</p>

<p>46. Barometrical Ob­ser­va­tions, made at the Fall of the Staubbach, by Sir
John Herschel, Bart., and C. Babbage, Esq.—<i>Brewster’s Edin. Jour. of Science.</i>
Vol. vi. p. 224. 1832.</p>

<p>47. Abstract of a Paper, entitled Ob­ser­va­tions on the Temple of Serapis, at
Pozzuoli, near Naples; with an attempt to explain the causes of the frequent
elevation and depression of large portions of the earth’s surface in remote
periods, and to prove that those causes continue in action at the present time.
Read at Geological Society, 12 March, 1834. See <i>Abstract of Proceedings of
Geol. Soc.</i> Vol. ii. p. 72.</p>

<p class="pp494a">This was the first <i>printed</i> publication of Mr. Babbage’s Geological Theory of the Isothermal
Surfaces of the Earth.</p>

<p>48. The Paper itself was published in the <i>Proceedings of the Geological Soc.</i>
1846.</p>

<p>49. Reprint of the same, with Supplemental Conjectures on the Physical
State of the Surface of the Moon. 1847.</p>

<p>50. Letter from Mr. Abraham Sharpe to Mr. J. Crosthwait, Hoxton, 2 Feb.
1721–22. Deciphered by Mr. Babbage. See <i>Life of Flamsteed</i>, by Mr. F.
Baily. Appendix, pp. 348, 390. 1835.</p>

<p>51. The Ninth Bridgewater Treatise. 8vo. May, 1837; Second Edition,
Jan. 1838.</p>

<p>52. On some Impressions in Sandstone.—<i>Proceedings of Geological Society.</i>
Vol. ii. p. 439. Ditto, <i>Phil. Mag.</i> Ser. 3. Vol. x. p. 474. 1837.</p>

<p>52*. Short account of a method by which Engraving on Wood may be rendered
more useful for the Illustration and Description of Machinery.—<i>Report of
Meeting of British Association at Newcastle.</i> 1838. P. 154.</p>

<p>53. Letter to the Members of the British Association. 8vo. 1839.</p>

<p>54. General Plan, No. 25, of Mr. Babbage’s Great Calculating or Analytical
Engine, lithographed at Paris. 24 by 36 inches. 1840.</p>

<p>55. Statement of the circumstances respecting Mr. Babbage’s Calculating
Engines. 8vo. 1843.</p>

<p>56. Note on the Boracic Acid Works in Tuscany.—<i>Murray’s Handbook of
Central Italy.</i> First Edition, p. 178. 1843.</p>

<p>57. On the Principles of Tools for Turning and Planing Metals,
by Charles Babbage. Printed in the Appendix of Vol. ii. Holtzapffel
Turning and Mechanical Manipulation. 1846.</p>

<p>58. On the Planet Neptune.—<i>The Times</i>, 15th March, 1847.</p>

<p>59. Thoughts on the Principles of Taxation, with reference to a
Property Tax and its Exceptions. 8vo. 1848. Second Edition, 1851. Third
Edition, 1852.</p>

<p class="pp494a">An Italian translation of the first edition,
with notes, was published at Turin, in 1851. <span class="xxpn"
id="p496">{496}</span></p>

<p>60. Note respecting the pink projections from the Sun’s disc
observed during the total solar eclipse in 1851.—<i>Proceedings of the
Astron. Soc.</i>, vol. xii., No. 7.</p>

<p>61. Laws of Mechanical Notation, with Lithographic Plate. Privately
printed for distribution. 4to. July, 1851.</p>

<p>62. Note respecting Lighthouses (Occulting Lights). 8vo. Nov.
1851.</p>

<p class="pp494a">Communicated to the Trinity House, 30 Nov.
1851.</p>

<p class="pp494a">Reprinted in the Appendix to the Report on Lighthouses presented to
the Senate of the United States, Feb. 1852.</p>

<p class="pp494a">Reprinted in the <i>Mechanics’ Magazine</i>, and in various other
periodicals and newspapers. 1852–3.</p>

<p class="pp494a">It was reprinted in various parts of the Report of Com­mis­sion­ers
appointed to examine into the state of Lighthouses. Parliamentary
Paper. 1861.</p>

<p>63. The Exposition of 1851; or, Views of the Industry, the Science, and the
Government of England. 6&#x200a;<i>s.</i> 6&#x200a;<i>d.</i> Second Edition, 1851.</p>

<p>64. On the Statistics of Light-houses. Compte Rendu des Traveaux du
Congres Général, Bruxelles, Sept. 1853.</p>

<p>65. A short description of Mr. Babbage’s Ophthalmoscope is contained in
the Report on the Ophthalmoscope by T. Wharton Jones, F.R.S.—<i>British and
Foreign Medical Review.</i> Oct. 1854. Vol. xiv. p. 551.</p>

<p>66. On Secret or Cipher Writing. Mr. T.’s Cipher Deciphered by C.—<i>Jour.
Soc. Arts</i>, July, 1854, p. 707.</p>

<p>67. On Mr. T.’s Second Inscrutable Cipher Deciphered by C.—<i>Jour. Soc.
Arts</i>, p. 777, Aug. 1854.</p>

<p>68. On Submarine Navigation.—<i>Illustrated News</i>, 23rd June, 1855.</p>

<p>69. Letter to the Editor of the Times, on Occulting Lights for Lighthouses
and Night Signals. Flashing Lights at Sebastopol. 16th July, 1855.</p>

<p>70. On a Method of Laying Guns in a Battery without exposing the men
to the shot of the enemy. <i>The Times</i>, 8 Aug., 1855.</p>

<p>71. Sur la Machine Suédoise de M. Scheutz pour Calculer les Tables Mathématiques.
4to. <i>Comptes Rendus et l’Académie des Sciences.</i> Paris, Oct. 8, 1855.</p>

<p>72. On the Action of Ocean-currents in the Formation of the Strata of the Earth.—<i>Quarterly
Journal Geological Society</i>, Nov. 1856.</p>

<p>73. Ob­ser­va­tions by Charles Babbage, on the Mechanical Notation of
Scheutz’s Difference Engine, prepared and drawn up by his Son, Major Henry
Prevost Babbage, addressed to the Institution of Civil Engineers. <i>Minutes of
Proceedings</i>, vol. xv. 1856.</p>

<p>74. Statistics of the Clearing-House. Reprinted from <i>Trans. of Statistical
Soc.</i> 8vo. 1856.</p>

<p>75. Ob­ser­va­tions on Peerage for Life. July, 1833. Reprinted, 1856.</p>

<p>76. Ob­ser­va­tions addressed to the President and Fellows of the Royal Society
on the Award of their Medals for 1856. 8vo.</p>

<p>77. Table of the Relative Frequency of Occurrence of the Causes of Breaking
Plate-glass Windows.—<i>Mech. Mag.</i> 24th Jan. 1857.</p>

<p>78. On Remains of Human Art, mixed with the Bones of Extinct Races of
Animals. <i>Proceedings of Roy. Soc.</i> 26th May, 1859.</p>

<p>79. Passages from the Life of a Phi­los­o­pher. 8vo. 1864.</p>

<div class="dkeeptgth">
<p>80. [In the press]. History of the Analytical Engine. 4to. It will
contain Chapters V., VI., VII., and VIII., of the present Volume.
Reprint of The Translation of General Menabrea’s Sketch of the
Analytical Engine invented by Charles Babbage. From the <i>Bibliothèque
Universelle de Genève</i>, No. 82, Oct. 1842. Translated by the late
Countess of Lovelace, with extensive Notes by the Translator.</p>

<div class="fsz8 padtopa"> LONDON: PRINTED BY W. CLOWES AND SONS,
STAMFORD STREET AND CHARING CROSS.</div>
</div></div><!--section-->

<div id="dtransnote">
TRANSCRIBER’S NOTE

<p class="pfirst">Original spelling and grammar have been generally
retained, with some exceptions noted below. Original printed page
numbers are shown in curly brackets like this: {52}. Footnotes have
been relabeled 1–65, and moved from within paragraphs to nearby
locations between paragraphs. Many of the page headers in the original
book were significant as text headings, and have been retained,
formatted as all capital letters in angle brackets, e.g.
<span class="nowrap">“〈DIFFICULTIES</span>
NOT <span class="nowrap">ANSWERED.〉”.</span>
These have been inserted into the running text at
the appropriate places between paragraphs. Oc­ca­sion­al­ly such
location might be somewhere in the page preceding the original page
header. The transcriber produced the cover image and hereby assigns it
to the public domain. Large curly brackets, intended to graphically
indicate the combination of information on two or more lines of text,
were eliminated. The related text was restructured appropriately to
retain the original meaning. Instances include page <a href="#p061"
title="go to pag&#x65; 61">61</a>, page <a href="#p276" title="go
to pag&#x65; 276">276</a>, and page <a href="#p364" title="go to
pag&#x65; 364">364</a>. Original page images are available from
archive.org—search for “passagesfromlife03char”.</p>

<ul>
<li>Page &#x2007;<a href="#p019" title="go to pag&#x65; 19">19</a>:
“twelvemouth” to “twelvemonth”, and “acccomplished” to “accomplished”.</li>

<li>Page &#x2007;<a href="#p022" title="go to pag&#x65; 22">22</a>:
“appeard” to “appeared”, and “hankerchiefs” to
“handkerchiefs”.</li>

<li>Page &#x2007;<a href="#p054" title="go to pag&#x65; 54">54</a>.
The archaic practice of placing a left double
quotation mark at the beginning of each quoted line has been
relinquished in favor of modern English practice. Also, the right
double quotation mark after “composing it.” was removed, to conform
with such practice.</li>

<li>Page &#x2007;<a href="#p058" title="go to pag&#x65; 58">58</a>. In
order to make the lines of the text following “The person adding says
to <span class="nowrap">himself—</span>” align properly in the html, epub, and mobi editions, some
faux invisible text had to be inserted. This invisible text, “and carry
non”, may be visible if the css (cascading style sheet) is disabled,
and should be ignored. Also, the lines will not align properly if
the viewing window is too narrow at the user-chosen font-size.</li>

<li>Page &#x2007;<a href="#p071" title="go to pag&#x65; 71">71</a>.
The footnote said “See Note on next page.”. This
footnote has been replaced by the referenced Note.</li>

<li>Page &#x2007;<a href="#p089" title="go to pag&#x65; 89">89</a>:
“gradully” to “gradually”.</li>

<li>Page <a href="#p116" title="go to pag&#x65; 116">116</a>:
“impossibilty” to “impossibility”.</li>

<li>Page <a href="#p190" title="go to pag&#x65; 190">190</a>:
“Albermarle-street” to “Albemarle-street”.</li>

<li>Page <a href="#p195" title="go to pag&#x65; 195">195</a>:
“HUMBOLT” to “HUMBOLDT”.</li>

<li>Page <a href="#p234" title="go to pag&#x65; 234">234</a>:
“Hobb’s” to “Hobbs’s”</li>

<li>Page <a href="#p240" title="go to pag&#x65; 240">240</a>.
The first "table" on the original printed page was not a
well-structured data table. This table has been considerably
altered, forming a new table followed by a list.</li>

<li>Page <a href="#p245" title="go to pag&#x65; 245">245</a>:
“villanons” to “villanous”.</li>

<li>Page <a href="#p283" title="go to pag&#x65; 283">283</a>:
“Tursntile” to “Turnstile”, (in small caps or all caps,
depending on the ebook edition).</li>

<li>Page <a href="#p324" title="go to pag&#x65; 324">324</a>.
The unmatched right double quotation mark after ‘but had
missed it.’ was removed.</li>

<li>Page <a href="#p338" title="go to pag&#x65; 338">338</a>:
“elevavation” to “elevation”.</li>

<li>Page <a href="#p348" title="go to pag&#x65; 348">348</a>:
“philospher” to “philosopher”.</li>

<li>Page <a href="#p384" title="go to pag&#x65; 384">384</a>:
“eylids” to “eyelids”.</li>

<li>Page <a href="#p427" title="go to pag&#x65; 427">427</a>.
A matching right double quotation mark was inserted after
‘two Foreigners.’.</li>

<li>Page <a href="#p435" title="go to pag&#x65; 435">435</a>:
“obvervations” to “observations”.</li>

<li>Page <a href="#p495" title="go to pag&#x65; 495">495</a>.
There are two entries numbered “52”, the second one has
an asterisk following.
The reason for the asterisk is not clear to the transcriber, unless
perhaps to point to the duplicated entry number.</li></ul>



</div><!--dtransnote-->







<div>*** END OF THE PROJECT GUTENBERG EBOOK 57532 ***</div>

</body>
</html>
generated by cgit v1.2.3 (git 2.25.1) at 2026-01-06 00:12:13 +0000