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
|
<!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">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<title>The Project Gutenberg eBook of The Asteroids, by Daniel Kirkwood</title>
<style type="text/css">
body {
margin-left: 10%;
margin-right: 10%;
}
h1,h2,h3,h4,h5 {
text-align: center; /* all headings centered */
clear: both;
}
p {
margin-top: .75em;
text-align: justify;
margin-bottom: .75em;
}
.big { font-size: 150%; }
.small { font-size: 75%; }
.hanging-indent {
text-indent: -2em;
padding-left: 2em;
}
hr {
width: 33%;
margin-top: 2em;
margin-bottom: 2em;
margin-left: auto;
margin-right: auto;
clear: both;
}
hr.chap {width: 65%}
sub {font-size: .6em; vertical-align: -10%;}
sup {font-size: .6em; vertical-align: 60%;}
.ilb { display: inline-block; vertical-align: middle; }
table {
margin-left: auto;
margin-right: auto;
}
td, th { vertical-align: top; }
.vm td { vertical-align: middle; }
.tdl {text-align: left;}
.tdr {text-align: right;}
.tdrb {text-align: right; vertical-align: bottom; padding-left: 1em; }
.tdc {text-align: center;}
.tdcount {text-align: right; width: 5em;}
.ruled {
margin-top: 1em;
margin-bottom: 1em;
border-collapse: collapse;
border-top: solid 2px;
border-bottom: solid 2px;
border-left: solid 2px;
border-right: solid 2px;
}
.ruled td, th {
border-right: solid 2px;
padding: 0.5em;
}
.ruled td.tdc {text-align: center;}
.ruled td {text-align: left;}
.ruled th {text-align: center; border-bottom: solid 2px;}
.all-center td {text-align: center;}
.ind {display: inline-block; width: 2.5em; text-align: right;}
.ilb2 {display: inline-block; width: 2em; text-align: right;}
.ilb3 {display: inline-block; width: 3em; text-align: right;}
.ilb-deg {display: inline-block; width: 1em; text-align: left;}
.pt1 {padding-top: 1em; }
.vspace td {padding-top: 0.5em; padding-bottom: 0.5em;}
.pagenum { /* uncomment the next line for invisible page numbers */
/* visibility: hidden; */
position: absolute;
left: 92%;
font-size: smaller;
text-align: right;
} /* page numbers */
.bt {border-top: solid 2px;}
.center {text-align: center;}
.right {text-align: right;}
.smcap {font-variant: small-caps;}
.lowercase { text-transform:lowercase; }
/* Images */
.figcenter {
margin: auto;
text-align: center;
}
/* Footnotes */
.footnotes {border: dashed 1px;}
.footnote {margin-left: 10%; margin-right: 10%; font-size: 0.9em;}
.footnote .label {position: absolute; right: 84%; text-align: right;}
.fnanchor {
vertical-align: super;
font-size: small;
text-decoration:
none;
}
/* Transcriber's notes */
.transnote {background-color: #E6E6FA;
color: black;
font-size:smaller;
padding:0.5em;
margin-bottom:5em;
font-family:sans-serif, serif; }
hr.full { width: 100%;
margin-top: 3em;
margin-bottom: 0em;
margin-left: auto;
margin-right: auto;
height: 4px;
border-width: 4px 0 0 0; /* remove all borders except the top one */
border-style: solid;
border-color: #000000;
clear: both; }
</style>
</head>
<body>
<div>*** START OF THE PROJECT GUTENBERG EBOOK 41570 ***</div>
<h1>The Project Gutenberg eBook, The Asteroids, by Daniel Kirkwood</h1>
<p> </p>
<p> </p>
<table border="0" style="background-color: #E6E6FA;margin: 0 auto;" cellpadding="10">
<tr>
<td valign="top">
Note:
</td>
<td>
Images of the original pages are available through
Internet Archive. See
<a href="http://archive.org/details/asteroidsorminor00kirkrich">
http://archive.org/details/asteroidsorminor00kirkrich</a>
</td>
</tr>
</table>
<p> </p>
<div class="transnote">
<p>Transcriber's Note:</p>
<p>Every effort has been made to replicate this text as faithfully
as possible, including non-standard spelling and punctuation.
Some apparent typographical errors in the indices and names of
asteroids in Tables I and II have been corrected.</p>
</div>
<p> </p>
<hr class="full" />
<p> </p>
<p> </p>
<p> </p>
<p><span class="pagenum">[Pg 1]</span></p>
<h1><span class="small">THE</span><br />
ASTEROIDS,<br />
<span class="small">OR</span><br />
MINOR PLANETS<br />
<span class="small">BETWEEN</span><br />
MARS AND JUPITER.</h1>
<p class="center">BY<br />
<span class="big">DANIEL KIRKWOOD, LL.D.,</span><br />
<span class="small">PROFESSOR EMERITUS IN THE UNIVERSITY OF INDIANA; AUTHOR OF "COMETS
AND METEORS," "METEORIC ASTRONOMY," ETC.</span></p>
<p> </p>
<p> </p>
<p> </p>
<p class="center"><span class="small">PHILADELPHIA:</span><br />
J. B. LIPPINCOTT COMPANY.<br />
1888.
</p>
<hr class="chap" />
<p><span class="pagenum">[Pg 2]</span></p>
<p class="center">Copyright, 1887, by <span class="smcap">Daniel Kirkwood</span>.
</p>
<div class="figcenter">
<img src="images/i_002.jpg" width="115" height="41" alt="" />
</div>
<hr class="chap" />
<p><span class="pagenum">[Pg 3]</span></p>
<h2><a name="PREFACE" id="PREFACE">PREFACE.</a></h2>
<p>The rapid progress of discovery in the zone of minor planets, the
anomalous forms and positions of their orbits, the small size as well as
the great number of these telescopic bodies, and their peculiar
relations to Jupiter, the massive planet next exterior,—all entitle
this part of the system to more particular consideration than it has
hitherto received. The following essay is designed, therefore, to supply
an obvious want. Its results are given in some detail up to the date of
publication. Part I. presents in a popular form the leading historical
facts as to the discovery of Ceres, Pallas, Juno, Vesta, and Astræa; a
tabular statement of the dates and places of discovery for the entire
group; a list of the names of discoverers, with the number of minor
planets detected by each; and a table of the principal elements so far
as computed.</p>
<p>In Part II. this descriptive summary is followed by questions relating
to the origin of the cluster; the elimination of members from particular
parts; the eccentricities and inclinations of the orbits; and the
relation<span class="pagenum">[Pg 4]</span> of the zone to comets of short period. The elements are those
given in the Paris <i>Annuaire</i> for 1887, or in recent numbers of the
<i>Circular zum Berliner Astronomischen Jahrbuch</i>.</p>
<p class="right">DANIEL KIRKWOOD.</p>
<p><span class="smcap">Bloomington, Indiana</span>, November, 1887.</p>
<hr class="chap" />
<p><span class="pagenum">[Pg 5]</span></p>
<h2><a name="CONTENTS" id="CONTENTS">CONTENTS.</a></h2>
<table summary="Contents">
<tr><td class="tdc"><a href="#PART_I">PART I</a>.</td>
<td class="tdr smcap lowercase">PAGE</td></tr>
<tr><td class="tdl smcap"><a href="#Introductory">Planetary Discoveries before the Asteroids were known</a></td>
<td class="tdrb">9</td></tr>
<tr><td class="tdl smcap"><a href="#Discovery_of_the_First_Asteroids">Discovery of the First Asteroids</a></td>
<td class="tdrb">11</td></tr>
<tr><td class="tdl smcap"><a href="#TABLE_I">Table I.—Asteroids in the Order of their Discovery</a></td>
<td class="tdrb">17</td></tr>
<tr><td class="tdl smcap"><a href="#The_numbers_discovered_by_the_thirty-five_observers">Numbers found by the Respective Discoverers</a></td>
<td class="tdrb">23</td></tr>
<tr><td class="tdl smcap"><a href="#The_numbers_discovered_in_the_several_months">Numbers discovered in the Different Months</a></td>
<td class="tdrb">25</td></tr>
<tr><td class="tdl smcap"><a href="#Mode_of_Discovery">Mode of Discovery</a></td>
<td class="tdrb">25</td></tr>
<tr><td class="tdl smcap"><a href="#NAMES_AND_SYMBOLS">Names and Symbols</a></td>
<td class="tdrb">25</td></tr>
<tr><td class="tdl smcap"><a href="#Magnitudes_of_the_Asteroids">Magnitudes of the Asteroids</a></td>
<td class="tdrb">26</td></tr>
<tr><td class="tdl smcap"><a href="#The_Orbits_of_the_Asteroids">Orbits of the Asteroids</a></td>
<td class="tdrb">28</td></tr>
<tr><td class="tdl smcap"><a href="#TABLE_II">Table II.—Elements of the Asteroids</a></td>
<td class="tdrb">29</td></tr>
<tr><td class="tdc pt1"><a href="#PART_II">PART II.</a></td><td> </td></tr>
<tr><td class="tdl smcap"><a href="#Extent_of_the_Zone">Extent of the Zone</a></td>
<td class="tdrb">37</td></tr>
<tr><td class="tdl smcap"><a href="#theory_of_Olbers">Theory of Olbers</a></td>
<td class="tdrb">38</td></tr>
<tr><td class="tdl smcap"><a href="#The_Small_Mass_of_the_Asteroids">Small Mass of the Asteroids</a></td>
<td class="tdrb">38</td></tr>
<tr><td class="tdl smcap"><a href="#The_Limits_of_Perihelion_Distance">Limits of Perihelion Distance</a></td>
<td class="tdrb">39</td></tr>
<tr><td class="tdl smcap"><a href="#Was_the_Asteroid_Zone_originally_Stable_Distribution_of_the_Members_in_Space">Distribution of the Asteroids in Space</a></td>
<td class="tdrb">40</td></tr>
<tr><td class="tdl smcap"><a href="#The_existence_of_these_blanks_was_thus_predicted">Law of Gap Formation</a></td>
<td class="tdrb">42</td></tr>
<tr><td class="tdl smcap"><a href="#COMMENSURABILITY_OF_PERIODS">Commensurability of Periods with that of Jupiter</a></td>
<td class="tdrb">43</td></tr>
<tr><td class="tdl smcap"><a href="#Do_these_parts_of_the_ring_present_discontinuities">Orders of Commensurability</a></td>
<td class="tdrb">44</td></tr>
<tr><td class="tdl smcap"><a href="#What_then_was_their_physical_cause">Elimination of very Eccentric Orbits</a></td>
<td class="tdrb">46</td></tr>
<tr><td class="tdl smcap"><a href="#Relations_between_certain_Adjacent_Orbits">Relations between certain Adjacent Orbits</a></td>
<td class="tdrb">47<span class="pagenum">[Pg 6]</span></td></tr>
<tr><td class="tdl smcap"><a href="#The_Eccentricities">The Eccentricities</a></td>
<td class="tdrb">48</td></tr>
<tr><td class="tdl smcap"><a href="#The_Inclinations">The Inclinations</a></td>
<td class="tdrb">49</td></tr>
<tr><td class="tdl smcap"><a href="#Longitudes_of_the_Perihelia">Longitudes of the Perihelia and of the Ascending Nodes</a></td>
<td class="tdrb">50</td></tr>
<tr><td class="tdl smcap"><a href="#The_Periods">The Periods</a></td>
<td class="tdrb">51</td></tr>
<tr><td class="tdl smcap"><a href="#Origin_of_the_Asteroids">Origin of the Asteroids</a></td>
<td class="tdrb">52</td></tr>
<tr><td class="tdl smcap"><a href="#Variability_of_Certain_Asteroids">Variability of Certain Asteroids</a></td>
<td class="tdrb">53</td></tr>
<tr><td class="tdl smcap"><a href="#The_Average_Asteroid_Orbit">The Average Asteroid Orbit</a></td>
<td class="tdrb">54</td></tr>
<tr><td class="tdl smcap"><a href="#The_Relation_of_Short-Period_Comets_to_the_Zone_of_Asteroids">The Relation of Short-Period Comets to the Zone of Asteroids</a></td>
<td class="tdrb">55</td></tr>
<tr><td class="tdl smcap"><a href="#APPENDIX">Appendix</a></td>
<td class="tdrb">59</td></tr>
</table>
<hr class="chap" />
<p><span class="pagenum">[Pg 7]<br />[Pg 8]</span></p>
<h2><a name="PART_I" id="PART_I">PART I.</a></h2>
<p><span class="pagenum">[Pg 9]</span></p>
<h2><a name="THE_ASTEROIDS_OR_MINOR_PLANETS_BETWEEN_MARS_AND_JUPITER" id="THE_ASTEROIDS_OR_MINOR_PLANETS_BETWEEN_MARS_AND_JUPITER">THE ASTEROIDS, OR MINOR PLANETS BETWEEN MARS AND JUPITER.</a></h2>
<h3><a name="Introductory" id="Introductory">1. Introductory.</a><br />
<span class="small">PLANETARY DISCOVERIES BEFORE THE ASTEROIDS WERE KNOWN.</span></h3>
<p>The first observer who watched the skies with any degree of care could
not fail to notice that while the greater number of stars maintained the
same relative places, a few from night to night were ever changing their
positions. The planetary character of Mercury, Venus, Mars, Jupiter, and
Saturn was thus known before the dawn of history. The names, however, of
those who first distinguished them as "wanderers" are hopelessly lost.
Venus, the morning and evening star, was long regarded as two distinct
bodies. The discovery that the change of aspect was due to a single
planet's change of position is ascribed to Pythagoras.</p>
<p>At the beginning of the seventeenth century but six primary planets and
one satellite were known as members of the solar system. Very few, even
of the learned, had then accepted the theory of Copernicus; in fact,
before the invention of the telescope the evidence in its favor was not
absolutely conclusive. On<span class="pagenum">[Pg 10]</span> the 7th of January, 1610, Galileo first saw
the satellites of Jupiter. The bearing of this discovery on the theory
of the universe was sufficiently obvious. Such was the prejudice,
however, against the Copernican system that some of its opponents denied
even the reality of Galileo's discovery. "Those satellites," said a
Tuscan astronomer, "are invisible to the naked eye, and therefore can
exercise no influence on the earth, and therefore would be useless, and
therefore do not exist. Besides, the Jews and other ancient nations, as
well as modern Europeans, have adopted the division of the week into
<i>seven</i> days, and have named them from the seven planets; now, if we
increase the number of planets this whole system falls to the ground."</p>
<p>No other secondary planet was discovered till March 25, 1655, when
Titan, the largest satellite of Saturn, was detected by Huyghens. About
two years later (December 7, 1657) the same astronomer discovered the
true form of Saturn's ring; and before the close of the century
(1671-1684) four more satellites, Japetus, Rhea, Tethys, and Dione, were
added to the Saturnian system by the elder Cassini. Our planetary
system, therefore, as known at the close of the seventeenth century,
consisted of six primary and ten secondary planets.</p>
<p>Nearly a century had elapsed from the date of Cassini's discovery of
Dione, when, on the 13th of March, 1781, Sir William Herschel enlarged
the dimensions of our system by the detection of a
planet—Uranus—exterior to Saturn. A few years later (1787-1794) the
same distinguished observer discovered the first and second satellites
of Saturn, and also the four Uranian satellites. He was the only planet
discoverer of the eighteenth century.</p>
<p><span class="pagenum">[Pg 11]</span></p>
<h3><a id="Discovery_of_the_First_Asteroids"></a>2. Discovery of the First Asteroids.</h3>
<p>As long ago as the commencement of the seventeenth century the
celebrated Kepler observed that the respective distances of the planets
from the sun formed nearly a regular progression. The series, however,
by which those distances were expressed required the interpolation of a
term between Mars and Jupiter,—a fact which led the illustrious German
to predict the discovery of a planet in that interval. This conjecture
attracted but little attention till after the discovery of Uranus, whose
distance was found to harmonize in a remarkable manner with Kepler's
order of progression. Such a coincidence was of course regarded with
considerable interest. Towards the close of the last century Professor
Bode, who had given the subject much attention, published the law of
distances which bears his name, but which, as he acknowledged, is due to
Professor Titius. According to this formula the distances of the planets
from Mercury's orbit form a geometrical series of which the ratio is
two. In other words, if we reckon the distances of Venus, the earth,
etc., from the orbit of Mercury, instead of from the sun, we find
that—interpolating a term between Mars and Jupiter—the distance of any
member of the system is very nearly half that of the next exterior.
Baron De Zach, an enthusiastic astronomer, was greatly interested in
Bode's empirical scheme, and undertook to determine the elements of the
hypothetical planet. In 1800 a number of astronomers met at Lilienthal,
organized an astronomical society, and assigned one twenty-fourth part
of the zodiac to each of twenty-four observers, in order to detect, if
possible, the unseen planet. When it is remembered that at this time no
primary planet had<span class="pagenum">[Pg 12]</span> been discovered within the ancient limits of the
solar system, that the object to be looked for was comparatively near
us, and that the so-called law of distances was purely empirical, the
prospect of success, it is evident, was extremely uncertain. How long
the watch, if unsuccessful, might have been continued is doubtful. The
object of research, however, was fortunately brought to light before the
members of the astronomical association had fairly commenced their
labors.<a name="FNanchor_1" id="FNanchor_1"></a><a href="#Footnote_1" class="fnanchor">[1]</a></p>
<p>On the 1st of January, 1801, Professor Giuseppe Piazzi, of Palermo,
noticed a star of the eighth magnitude, not indicated in Wollaston's
catalogue. Subsequent observations soon revealed its planetary
character, its mean distance corresponding very nearly with the
calculations of De Zach. The discoverer called it Ceres Ferdinandea, in
honor of his sovereign, the King of Naples. In this, however, he was not
followed by astronomers, and the planet is now known by the name of
Ceres alone. The discovery of this body was hailed by astronomers with
the liveliest gratification as completing the harmony of the system.
What, then, was their surprise when in the course of a few months this
remarkable order was again interrupted! On the 28th of March, 1802, Dr.
William Olbers, of Bremen, while examining the relative positions of the
small stars along the path of Ceres, in order to find that planet with
the greater facility, noticed a star of the seventh or eighth magnitude,
forming with two others an equilateral triangle where he was certain no
such configuration ex<span class="pagenum">[Pg 13]</span>isted a few months before. In the course of a few
hours its motion was perceptible, and on the following night it had very
sensibly changed its position with respect to the neighboring stars.
Another planet was therefore detected, and Dr. Olbers immediately
communicated his discovery to Professor Bode and Baron De Zach. In his
letter to the former he suggested Pallas as the name of the new member
of the system,—a name which was at once adopted. Its orbit, which was
soon computed by Gauss, was found to present several striking anomalies.
The inclination of its plane to that of the ecliptic was nearly
thirty-five degrees,—an amount of deviation altogether extraordinary.
The eccentricity also was greater than in the case of any of the old
planets. These peculiarities, together with the fact that the mean
distances of Ceres and Pallas were nearly the same, and that their
orbits approached very near each other at the intersection of their
planes, suggested the hypothesis that they are fragments of a single
original planet, which, at a very remote epoch, was disrupted by some
mysterious convulsion. This theory will be considered when we come to
discuss the tabulated elements of the minor planets now known.</p>
<p>For the convenience of astronomers, Professor Harding, of Lilienthal,
undertook the construction of charts of all the small stars near the
orbits of Ceres and Pallas. On the evening of September 1, 1804, while
engaged in observations for this purpose, he noticed a star of the
eighth magnitude not mentioned in the great catalogue of Lalande. This
proved to be a third member of the group of asteroids. The discovery was
first announced to Dr. Olbers, who observed the planet at Bremen on the
evening of September 7.</p>
<p><span class="pagenum">[Pg 14]</span></p>
<p>Before Ceres had been generally adopted by astronomers as the name of
the first asteroid, Laplace had expressed a preference for Juno. This,
however, the discoverer was unwilling to accept. Mr. Harding, like
Laplace, deeming it appropriate to place Juno near Jupiter, selected the
name for the third minor planet, which is accordingly known by this
designation.</p>
<p>Juno is distinguished among the first asteroids by the great
eccentricity of its orbit, amounting to more than 0.25. Its least and
its greatest distances from the sun are therefore to each other very
nearly in the ratio of three to five. The planet consequently receives
nearly three times as much light and heat in perihelion as in aphelion.
It follows, also, that the half of the orbit nearest the sun is
described in about eighteen months, while the remainder, or more distant
half, is not passed over in much less than three years. Schroeter
noticed a variation in the light of Juno, which he supposed to be
produced by an axial rotation in about twenty-seven hours.</p>
<p>The fact that Juno was discovered not far from the point at which the
orbit of Pallas approaches very near that of Ceres, was considered a
strong confirmation of the hypothesis that the asteroids were produced
by the explosion of a large planet; for in case this hypothesis be
founded in truth, it is evident that whatever may have been the forms of
the various orbits assumed by the fragments, they must all return to the
point of separation. In order, therefore, to detect other members of the
group, Dr. Olbers undertook a systematic examination of the two opposite
regions of the heavens through which they must pass. This search was
prosecuted with great industry and perseverance till ultimately crowned
with success. On the 29th of March, 1807, while<span class="pagenum">[Pg 15]</span> sweeping over one of
those regions through which the orbits of the known asteroids passed, a
star of the sixth magnitude was observed where none had been seen at
previous examinations. Its planetary character, which was immediately
suspected, was confirmed by observation, its motion being detected on
the very evening of its discovery. This fortunate result afforded the
first instance of the discovery of two primary planets by the same
observer.</p>
<p>The astronomer Gauss having been requested to name the new planet, fixed
upon Vesta, a name universally accepted. Though the brightest of the
asteroids, its apparent diameter is too small to be accurately
determined, and hence its real magnitude is not well ascertained.
Professor Harrington, of Ann Arbor, has estimated the diameter at five
hundred and twenty miles. According to others, however, it does not
exceed three hundred. If the latter be correct, the volume is about
1/20000 that of the earth. It is remarkable that notwithstanding its
diminutive size it may be seen under favorable circumstances by the
naked eye.</p>
<p>Encouraged by the discovery of Vesta (which he regarded as almost a
demonstration of his favorite theory), Dr. Olbers continued his
systematic search for other planetary fragments. Not meeting, however,
with further success, he relinquished his observations in 1816. His
failure, it may here be remarked, was doubtless owing to the fact that
his examination was limited to stars of the seventh and eighth
magnitudes.</p>
<p>The search for new planets was next resumed about 1831, by Herr Hencke,
of Driessen. With a zeal and perseverance worthy of all praise, this
amateur astronomer employed himself in a strict examination of the<span class="pagenum">[Pg 16]</span>
heavens represented by the Maps of the Berlin Academy. These maps extend
fifteen degrees on each side of the equator, and contain all stars down
to the ninth magnitude and many of the tenth. Dr. Hencke rendered some
of these charts still more complete by the insertion of smaller stars;
or rather, "made for himself special charts of particular districts." On
the evening of December 8, 1845, he observed a star of the ninth
magnitude where none had been previously seen, as he knew from the fact
that it was neither found on his own chart nor given on that of the
Academy. On the next morning he wrote to Professors Encke and Schumacher
informing them of his supposed discovery. "It is very improbable," he
remarked in his letter to the latter, "that this should prove to be
merely a variable star, since in my former observations of this region,
which have been continued for many years, I have never detected the
slightest trace of it." The new star was soon seen at the principal
observatories of Europe, and its planetary character satisfactorily
established. The selection of a name was left by the discoverer to
Professor Encke, who chose that of Astræa.</p>
<p>The facts in regard to the very numerous subsequent discoveries may best
be presented in a tabular form.</p>
<p><span class="pagenum">[Pg 17]</span></p>
<h3><a id="TABLE_I"></a>TABLE I.<br />
<span class="small"><i>The Asteroids in the Order of their Discovery.</i></span></h3>
<table class="ruled" summary="The Asteroids in the Order of their Discovery">
<tr><th>Asteroids.</th><th>Date of<br />Discovery.</th><th>Name of<br />Discoverer.</th><th>Place of<br />Discovery.</th></tr>
<tr><td><span class="ind">1.</span> Ceres</td><td>1801, Jan. 1</td><td>Piazzi</td><td>Palermo</td></tr>
<tr><td><span class="ind">2.</span> Pallas</td><td>1802, Mar. 28</td><td>Olbers</td><td>Bremen</td></tr>
<tr><td><span class="ind">3.</span> Juno</td><td>1804, Sept. 1</td><td>Harding</td><td>Lilienthal</td></tr>
<tr><td><span class="ind">4.</span> Vesta</td><td>1807, Mar. 29</td><td>Olbers</td><td>Bremen</td></tr>
<tr><td><span class="ind">5.</span> Astræa</td><td>1845, Dec. 8</td><td>Hencke</td><td>Driessen</td></tr>
<tr><td><span class="ind">6.</span> Hebe</td><td>1847, July 1</td><td>Hencke</td><td>Driessen</td></tr>
<tr><td><span class="ind">7.</span> Iris</td><td>1847, Aug. 14</td><td>Hind</td><td>London</td></tr>
<tr><td><span class="ind">8.</span> Flora</td><td>1847, Oct. 18</td><td>Hind</td><td>London</td></tr>
<tr><td><span class="ind">9.</span> Metis</td><td>1848, Apr. 26</td><td>Graham</td><td>Markree</td></tr>
<tr><td><span class="ind">10.</span> Hygeia</td><td>1849, Apr. 12</td><td>De Gasparis</td><td>Naples</td></tr>
<tr><td><span class="ind">11.</span> Parthenope</td><td>1850, May 11</td><td>De Gasparis</td><td>Naples</td></tr>
<tr><td><span class="ind">12.</span> Victoria</td><td>1850, Sept. 13</td><td>Hind</td><td>London</td></tr>
<tr><td><span class="ind">13.</span> Egeria</td><td>1850, Nov. 2</td><td>De Gasparis</td><td>Naples</td></tr>
<tr><td><span class="ind">14.</span> Irene</td><td>1851, May 19</td><td>Hind</td><td>London</td></tr>
<tr><td><span class="ind">15.</span> Eunomia</td><td>1851, July 29</td><td>De Gasparis</td><td>Naples</td></tr>
<tr><td><span class="ind">16.</span> Psyche</td><td>1852, Mar. 17</td><td>De Gasparis</td><td>Naples</td></tr>
<tr><td><span class="ind">17.</span> Thetis</td><td>1852, Apr. 17</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">18.</span> Melpomene</td><td>1852, June 24</td><td>Hind</td><td>London</td></tr>
<tr><td><span class="ind">19.</span> Fortuna</td><td>1852, Aug. 22</td><td>Hind</td><td>London</td></tr>
<tr><td><span class="ind">20.</span> Massalia</td><td>1852, Sept. 19</td><td>De Gasparis</td><td>Naples</td></tr>
<tr><td><span class="ind">21.</span> Lutetia</td><td>1852, Nov. 15</td><td>Goldschmidt</td><td>Paris</td></tr>
<tr><td><span class="ind">22.</span> Calliope</td><td>1852, Nov. 16</td><td>Hind</td><td>London</td></tr>
<tr><td><span class="ind">23.</span> Thalia</td><td>1852, Dec. 15</td><td>Hind</td><td>London</td></tr>
<tr><td><span class="ind">24.</span> Themis</td><td>1853, Apr. 5</td><td>De Gasparis</td><td>Naples</td></tr>
<tr><td><span class="ind">25.</span> Phocea</td><td>1853, Apr. 6</td><td>Chacornac</td><td>Marseilles</td></tr>
<tr><td><span class="ind">26.</span> Proserpine</td><td>1853, May 5</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">27.</span> Euterpe</td><td>1853, Nov. 8</td><td>Hind</td><td>London</td></tr>
<tr><td><span class="ind">28.</span> Bellona</td><td>1854, Mar. 1</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">29.</span> Amphitrite</td><td>1854, Mar. 1</td><td>Marth</td><td>London</td></tr>
<tr><td><span class="ind">30.</span> Urania</td><td>1854, July 22</td><td>Hind</td><td>London</td></tr>
<tr><td><span class="ind">31.</span> Euphrosyne</td><td>1854, Sept. 1</td><td>Ferguson</td><td>Washington</td></tr>
<tr><td><span class="ind">32.</span> Pomona</td><td>1854, Oct. 26</td><td>Goldschmidt</td><td>Paris</td></tr>
<tr><td><span class="ind">33.</span> Polyhymnia</td><td>1854, Oct. 28</td><td>Chacornac</td><td>Paris</td></tr>
<tr><td><span class="ind">34.</span> Circe</td><td>1855, Apr. 6</td><td>Chacornac</td><td>Paris</td></tr>
<tr><td><span class="ind">35.</span> Leucothea</td><td>1855, Apr. 19</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">36.</span> Atalanta</td><td>1855, Oct. 5</td><td>Goldschmidt</td><td>Paris</td></tr>
<tr><td><span class="ind">37.</span> Fides</td><td>1855, Oct. 5</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">38.</span> Leda</td><td>1856, Jan. 12</td><td>Chacornac</td><td>Paris</td></tr>
<tr><td><span class="ind">39.</span> Lætitia</td><td>1856, Feb. 8</td><td>Chacornac</td><td>Paris</td></tr>
<tr><td><span class="ind">40.</span> Harmonia</td><td>1856, Mar. 31</td><td>Goldschmidt</td><td>Paris</td></tr>
<tr><td><span class="ind">41.</span> Daphne</td><td>1856, May 22</td><td>Goldschmidt</td><td>Paris</td></tr>
<tr><td><span class="ind">42.</span> Isis</td><td>1856, May 23</td><td>Pogson</td><td>Oxford</td></tr>
<tr><td><span class="ind">43.</span> Ariadne</td><td>1857, Apr. 15</td><td>Pogson</td><td>Oxford<span class="pagenum">[Pg 18]</span></td></tr>
<tr><td><span class="ind">44.</span> Nysa</td><td>1857, May 27</td><td>Goldschmidt</td><td>Paris</td></tr>
<tr><td><span class="ind">45.</span> Eugenia</td><td>1857, June 27</td><td>Goldschmidt</td><td>Paris</td></tr>
<tr><td><span class="ind">46.</span> Hestia</td><td>1857, Aug. 16</td><td>Pogson</td><td>Oxford</td></tr>
<tr><td><span class="ind">47.</span> Aglaia</td><td>1857, Sept. 15</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">48.</span> Doris</td><td>1857, Sept. 19</td><td>Goldschmidt</td><td>Paris</td></tr>
<tr><td><span class="ind">49.</span> Pales</td><td>1857, Sept. 19</td><td>Goldschmidt</td><td>Paris</td></tr>
<tr><td><span class="ind">50.</span> Virginia</td><td>1857, Oct. 4</td><td>Ferguson</td><td>Washington</td></tr>
<tr><td><span class="ind">51.</span> Nemausa</td><td>1858, Jan. 22</td><td>Laurent</td><td>Nismes</td></tr>
<tr><td><span class="ind">52.</span> Europa</td><td>1858, Feb. 4</td><td>Goldschmidt</td><td>Paris</td></tr>
<tr><td><span class="ind">53.</span> Calypso</td><td>1858, Apr. 4</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">54.</span> Alexandra</td><td>1858, Sept. 10</td><td>Goldschmidt</td><td>Paris</td></tr>
<tr><td><span class="ind">55.</span> Pandora</td><td>1858, Sept. 10</td><td>Searle</td><td>Albany</td></tr>
<tr><td><span class="ind">56.</span> Melete</td><td>1857, Sept. 9</td><td>Goldschmidt</td><td>Paris</td></tr>
<tr><td><span class="ind">57.</span> Mnemosyne</td><td>1859, Sept. 22</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">58.</span> Concordia</td><td>1860, Mar. 24</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">59.</span> Olympia</td><td>1860, Sept. 12</td><td>Chacornac</td><td>Paris</td></tr>
<tr><td><span class="ind">60.</span> Echo</td><td>1860, Sept. 16</td><td>Ferguson</td><td>Washington</td></tr>
<tr><td><span class="ind">61.</span> Danaë</td><td>1860, Sept. 9</td><td>Goldschmidt</td><td>Paris</td></tr>
<tr><td><span class="ind">62.</span> Erato</td><td>1860, Sept. 14</td><td>Foerster and Lesser</td><td>Berlin</td></tr>
<tr><td><span class="ind">63.</span> Ausonia</td><td>1861, Feb. 10</td><td>De Gasparis</td><td>Naples</td></tr>
<tr><td><span class="ind">64.</span> Angelina</td><td>1861, Mar. 4</td><td>Tempel</td><td>Marseilles</td></tr>
<tr><td><span class="ind">65.</span> Maximiliana</td><td>1861, Mar. 8</td><td>Tempel</td><td>Marseilles</td></tr>
<tr><td><span class="ind">66.</span> Maia</td><td>1861, Apr. 9</td><td>Tuttle</td><td>Cambridge, U.S.</td></tr>
<tr><td><span class="ind">67.</span> Asia</td><td>1861, Apr. 17</td><td>Pogson</td><td>Madras</td></tr>
<tr><td><span class="ind">68.</span> Leto</td><td>1861, Apr. 29</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">69.</span> Hesperia</td><td>1861, Apr. 29</td><td>Schiaparelli</td><td>Milan</td></tr>
<tr><td><span class="ind">70.</span> Panopea</td><td>1861, May 5</td><td>Goldschmidt</td><td>Paris</td></tr>
<tr><td><span class="ind">71.</span> Niobe</td><td>1861, Aug. 13</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">72.</span> Feronia</td><td>1862, May 29</td><td>Peters and Safford</td><td>Clinton</td></tr>
<tr><td><span class="ind">73.</span> Clytie</td><td>1862, Apr. 7</td><td>Tuttle</td><td>Cambridge</td></tr>
<tr><td><span class="ind">74.</span> Galatea</td><td>1862, Aug. 29</td><td>Tempel</td><td>Marseilles</td></tr>
<tr><td><span class="ind">75.</span> Eurydice</td><td>1862, Sept. 22</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">76.</span> Freia</td><td>1862, Oct. 21</td><td>D'Arrest</td><td>Copenhagen</td></tr>
<tr><td><span class="ind">77.</span> Frigga</td><td>1862, Nov. 12</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">78.</span> Diana</td><td>1863, Mar. 15</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">79.</span> Eurynome</td><td>1863, Sept. 14</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">80.</span> Sappho</td><td>1864, May 2</td><td>Pogson</td><td>Madras</td></tr>
<tr><td><span class="ind">81.</span> Terpsichore</td><td>1864, Sept. 30</td><td>Tempel</td><td>Marseilles</td></tr>
<tr><td><span class="ind">82.</span> Alcmene</td><td>1864, Nov. 27</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">83.</span> Beatrix</td><td>1865, Apr. 26</td><td>De Gasparis</td><td>Naples</td></tr>
<tr><td><span class="ind">84.</span> Clio</td><td>1865, Aug. 25</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">85.</span> Io</td><td>1865, Sept. 19</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">86.</span> Semele</td><td>1866, Jan. 14</td><td>Tietjen</td><td>Berlin</td></tr>
<tr><td><span class="ind">87.</span> Sylvia</td><td>1866, May 16</td><td>Pogson</td><td>Madras</td></tr>
<tr><td><span class="ind">88.</span> Thisbe</td><td>1866, June 15</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">89.</span> Julia</td><td>1866, Aug. 6</td><td>Stephan</td><td>Marseilles</td></tr>
<tr><td><span class="ind">90.</span> Antiope</td><td>1866, Oct. 1</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">91.</span> Ægina</td><td>1866, Nov. 4</td><td>Borelly</td><td>Marseilles</td></tr>
<tr><td><span class="ind">92.</span> Undina</td><td>1867, July 7</td><td>Peters</td><td>Clinton<span class="pagenum">[Pg 19]</span></td></tr>
<tr><td><span class="ind">93.</span> Minerva</td><td>1867, Aug. 24</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">94.</span> Aurora</td><td>1867, Sept. 6</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">95.</span> Arethusa</td><td>1867, Nov. 24</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">96.</span> Ægle</td><td>1868, Feb. 17</td><td>Coggia</td><td>Marseilles</td></tr>
<tr><td><span class="ind">97.</span> Clotho</td><td>1868, Feb. 17</td><td>Coggia</td><td>Marseilles</td></tr>
<tr><td><span class="ind">98.</span> Ianthe</td><td>1868, Apr. 18</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">99.</span> Dike</td><td>1868, May 28</td><td>Borelly</td><td>Marseilles</td></tr>
<tr><td><span class="ind">100.</span> Hecate</td><td>1868, July 11</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">101.</span> Helena</td><td>1868, Aug. 15</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">102.</span> Miriam</td><td>1868, Aug. 22</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">103.</span> Hera</td><td>1868, Sept. 7</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">104.</span> Clymene</td><td>1868, Sept. 13</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">105.</span> Artemis</td><td>1868, Sept. 16</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">106.</span> Dione</td><td>1868, Oct. 10</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">107.</span> Camilla</td><td>1868, Nov. 17</td><td>Pogson</td><td>Madras</td></tr>
<tr><td><span class="ind">108.</span> Hecuba</td><td>1869, Apr. 2</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">109.</span> Felicitas</td><td>1869, Oct. 9</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">110.</span> Lydia</td><td>1870, Apr. 19</td><td>Borelly</td><td>Marseilles</td></tr>
<tr><td><span class="ind">111.</span> Ate</td><td>1870, Aug. 14</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">112.</span> Iphigenia</td><td>1870, Sept. 19</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">113.</span> Amalthea</td><td>1871, Mar. 12</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">114.</span> Cassandra</td><td>1871, July 23</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">115.</span> Thyra</td><td>1871, Aug. 6</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">116.</span> Sirona</td><td>1871, Sept. 8</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">117.</span> Lomia</td><td>1871, Sept. 12</td><td>Borelly</td><td>Marseilles</td></tr>
<tr><td><span class="ind">118.</span> Peitho</td><td>1872, Mar. 15</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">119.</span> Althea</td><td>1872, Apr. 3</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">120.</span> Lachesis</td><td>1872, Apr. 10</td><td>Borelly</td><td>Marseilles</td></tr>
<tr><td><span class="ind">121.</span> Hermione</td><td>1872, May 12</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">122.</span> Gerda</td><td>1872, July 31</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">123.</span> Brunhilda</td><td>1872, July 31</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">124.</span> Alceste</td><td>1872, Aug. 23</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">125.</span> Liberatrix</td><td>1872, Sept. 11</td><td>Prosper Henry</td><td>Paris</td></tr>
<tr><td><span class="ind">126.</span> Velleda</td><td>1872, Nov. 5</td><td>Paul Henry</td><td>Paris</td></tr>
<tr><td><span class="ind">127.</span> Johanna</td><td>1872, Nov. 5</td><td>Prosper Henry</td><td>Paris</td></tr>
<tr><td><span class="ind">128.</span> Nemesis</td><td>1872, Nov. 25</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">129.</span> Antigone</td><td>1873, Feb. 5</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">130.</span> Electra</td><td>1873, Feb. 17</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">131.</span> Vala</td><td>1873, May 24</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">132.</span> Æthra</td><td>1873, June 13</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">133.</span> Cyrene</td><td>1873, Aug. 16</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">134.</span> Sophrosyne</td><td>1873, Sept. 27</td><td>Luther</td><td>Bilk</td></tr>
<tr><td><span class="ind">135.</span> Hertha</td><td>1874, Feb. 18</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">136.</span> Austria</td><td>1874, Mar. 18</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">137.</span> Melibœa</td><td>1874, Apr. 21</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">138.</span> Tolosa</td><td>1874, May 19</td><td>Perrotin</td><td>Toulouse</td></tr>
<tr><td><span class="ind">139.</span> Juewa</td><td>1874, Oct. 10</td><td>Watson</td><td>Pekin</td></tr>
<tr><td><span class="ind">140.</span> Siwa</td><td>1874, Oct. 13</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">141.</span> Lumen</td><td>1875, Jan. 13</td><td>Paul Henry</td><td>Paris<span class="pagenum">[Pg 20]</span></td></tr>
<tr><td><span class="ind">142.</span> Polana</td><td>1875, Jan. 28</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">143.</span> Adria</td><td>1875, Feb. 23</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">144.</span> Vibilia</td><td>1875, June 3</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">145.</span> Adeona</td><td>1875, June 3</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">146.</span> Lucina</td><td>1875, June 8</td><td>Borelly</td><td>Marseilles</td></tr>
<tr><td><span class="ind">147.</span> Protogenea</td><td>1875, July 10</td><td>Schulhof</td><td>Vienna</td></tr>
<tr><td><span class="ind">148.</span> Gallia</td><td>1875, Aug. 7</td><td>Prosper Henry</td><td>Paris</td></tr>
<tr><td><span class="ind">149.</span> Medusa</td><td>1875, Sept. 21</td><td>Perrotin</td><td>Toulouse</td></tr>
<tr><td><span class="ind">150.</span> Nuwa</td><td>1875, Oct. 18</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">151.</span> Abundantia</td><td>1875, Nov. 1</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">152.</span> Atala</td><td>1875, Nov. 2</td><td>Paul Henry</td><td>Paris</td></tr>
<tr><td><span class="ind">153.</span> Hilda</td><td>1875, Nov. 2</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">154.</span> Bertha</td><td>1875, Nov. 4</td><td>Prosper Henry</td><td>Paris</td></tr>
<tr><td><span class="ind">155.</span> Scylla</td><td>1875, Nov. 8</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">156.</span> Xantippe</td><td>1875, Nov. 22</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">157.</span> Dejanira</td><td>1875, Dec. 1</td><td>Borelly</td><td>Marseilles</td></tr>
<tr><td><span class="ind">158.</span> Coronis</td><td>1876, Jan. 4</td><td>Knorre</td><td>Berlin</td></tr>
<tr><td><span class="ind">159.</span> Æmilia</td><td>1876, Jan. 26</td><td>Paul Henry</td><td>Paris</td></tr>
<tr><td><span class="ind">160.</span> Una</td><td>1876, Feb. 20</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">161.</span> Athor</td><td>1876, Apr. 19</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">162.</span> Laurentia</td><td>1876, Apr. 21</td><td>Prosper Henry</td><td>Paris</td></tr>
<tr><td><span class="ind">163.</span> Erigone</td><td>1876, Apr. 26</td><td>Perrotin</td><td>Toulouse</td></tr>
<tr><td><span class="ind">164.</span> Eva</td><td>1876, July 12</td><td>Paul Henry</td><td>Paris</td></tr>
<tr><td><span class="ind">165.</span> Loreley</td><td>1876, Aug. 9</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">166.</span> Rhodope</td><td>1876, Aug. 15</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">167.</span> Urda</td><td>1876, Aug. 28</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">168.</span> Sibylla</td><td>1876, Sept. 27</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">169.</span> Zelia</td><td>1876, Sept. 28</td><td>Prosper Henry</td><td>Paris</td></tr>
<tr><td><span class="ind">170.</span> Maria</td><td>1877, Jan. 10</td><td>Perrotin</td><td>Toulouse</td></tr>
<tr><td><span class="ind">171.</span> Ophelia</td><td>1877, Jan. 13</td><td>Borelly</td><td>Marseilles</td></tr>
<tr><td><span class="ind">172.</span> Baucis</td><td>1877, Feb. 5</td><td>Borelly</td><td>Marseilles</td></tr>
<tr><td><span class="ind">173.</span> Ino</td><td>1877, Aug. 1</td><td>Borelly</td><td>Marseilles</td></tr>
<tr><td><span class="ind">174.</span> Phædra</td><td>1877, Sept. 2</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">175.</span> Andromache</td><td>1877, Oct. 1</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">176.</span> Idunna</td><td>1877, Oct. 14</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">177.</span> Irma</td><td>1877, Nov. 5</td><td>Paul Henry</td><td>Paris</td></tr>
<tr><td><span class="ind">178.</span> Belisana</td><td>1877, Nov. 6</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">179.</span> Clytemnestra</td><td>1877, Nov. 11</td><td>Watson</td><td>Ann Arbor</td></tr>
<tr><td><span class="ind">180.</span> Garumna</td><td>1878, Jan. 29</td><td>Perrotin</td><td>Toulouse</td></tr>
<tr><td><span class="ind">181.</span> Eucharis</td><td>1878, Feb. 2</td><td>Cottenot</td><td>Marseilles</td></tr>
<tr><td><span class="ind">182.</span> Elsa</td><td>1878, Feb. 7</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">183.</span> Istria</td><td>1878, Feb. 8</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">184.</span> Deiopea</td><td>1878, Feb. 28</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">185.</span> Eunice</td><td>1878, Mar. 1</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">186.</span> Celuta</td><td>1878, Apr. 6</td><td>Prosper Henry</td><td>Paris</td></tr>
<tr><td><span class="ind">187.</span> Lamberta</td><td>1878, Apr. 11</td><td>Coggia</td><td>Marseilles</td></tr>
<tr><td><span class="ind">188.</span> Menippe</td><td>1878, June 18</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">189.</span> Phthia</td><td>1878, Sept. 9</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">190.</span> Ismene</td><td>1878, Sept. 22</td><td>Peters</td><td>Clinton<span class="pagenum">[Pg 21]</span></td></tr>
<tr><td><span class="ind">191.</span> Kolga</td><td>1878, Sept. 30</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">192.</span> Nausicaa</td><td>1879, Feb. 17</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">193.</span> Ambrosia</td><td>1879, Feb. 28</td><td>Coggia</td><td>Marseilles</td></tr>
<tr><td><span class="ind">194.</span> Procne</td><td>1879, Mar. 21</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">195.</span> Euryclea</td><td>1879, Apr. 22</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">196.</span> Philomela</td><td>1879, May 14</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">197.</span> Arete</td><td>1879, May 21</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">198.</span> Ampella</td><td>1879, June 13</td><td>Borelly</td><td>Marseilles</td></tr>
<tr><td><span class="ind">199.</span> Byblis</td><td>1879, July 9</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">200.</span> Dynamene</td><td>1879, July 27</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">201.</span> Penelope</td><td>1879, Aug. 7</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">202.</span> Chryseis</td><td>1879, Sept. 11</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">203.</span> Pompeia</td><td>1879, Sept. 25</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">204.</span> Callisto</td><td>1879, Oct. 8</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">205.</span> Martha</td><td>1879, Oct. 13</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">206.</span> Hersilia</td><td>1879, Oct. 13</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">207.</span> Hedda</td><td>1879, Oct. 17</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">208.</span> Lachrymosa</td><td>1879, Oct. 21</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">209.</span> Dido</td><td>1879, Oct. 22</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">210.</span> Isabella</td><td>1879, Nov. 12</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">211.</span> Isolda</td><td>1879, Dec. 10</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">212.</span> Medea</td><td>1880, Feb. 6</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">213.</span> Lilæa</td><td>1880, Feb. 16</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">214.</span> Aschera</td><td>1880, Feb. 26</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">215.</span> Œnone</td><td>1880, Apr. 7</td><td>Knorre</td><td>Berlin</td></tr>
<tr><td><span class="ind">216.</span> Cleopatra</td><td>1880, Apr. 10</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">217.</span> Eudora</td><td>1880, Aug. 30</td><td>Coggia</td><td>Marseilles</td></tr>
<tr><td><span class="ind">218.</span> Bianca</td><td>1880, Sept. 4</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">219.</span> Thusnelda</td><td>1880, Sept. 20</td><td>Palisa</td><td>Pola</td></tr>
<tr><td><span class="ind">220.</span> Stephania</td><td>1881, May 19</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">221.</span> Eos</td><td>1882, Jan. 18</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">222.</span> Lucia</td><td>1882, Feb. 9</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">223.</span> Rosa</td><td>1882, Mar. 9</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">224.</span> Oceana</td><td>1882, Mar. 30</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">225.</span> Henrietta</td><td>1882, Apr. 19</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">226.</span> Weringia</td><td>1882, July 19</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">227.</span> Philosophia</td><td>1882, Aug. 12</td><td>Paul Henry</td><td>Paris</td></tr>
<tr><td><span class="ind">228.</span> Agathe</td><td>1882, Aug. 19</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">229.</span> Adelinda</td><td>1882, Aug. 22</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">230.</span> Athamantis</td><td>1882, Sept. 3</td><td>De Ball</td><td>Bothcamp</td></tr>
<tr><td><span class="ind">231.</span> Vindobona</td><td>1882, Sept. 10</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">232.</span> Russia</td><td>1883, Jan. 31</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">233.</span> Asterope</td><td>1883, May 11</td><td>Borelly</td><td>Marseilles</td></tr>
<tr><td><span class="ind">234.</span> Barbara</td><td>1883, Aug. 13</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">235.</span> Caroline</td><td>1883, Nov. 29</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">236.</span> Honoria</td><td>1884, Apr. 26</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">237.</span> Cœlestina</td><td>1884, June 27</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">238.</span> Hypatia</td><td>1884, July 1</td><td>Knorre</td><td>Berlin</td></tr>
<tr><td><span class="ind">239.</span> Adrastea</td><td>1884, Aug. 18</td><td>Palisa</td><td>Vienna<span class="pagenum">[Pg 22]</span></td></tr>
<tr><td><span class="ind">240.</span> Vanadis</td><td>1884, Aug. 27</td><td>Borelly</td><td>Marseilles</td></tr>
<tr><td><span class="ind">241.</span> Germania</td><td>1884, Sept. 12</td><td>Luther</td><td>Dusseldorf</td></tr>
<tr><td><span class="ind">242.</span> Kriemhild</td><td>1884, Sept. 22</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">243.</span> Ida</td><td>1884, Sept. 29</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">244.</span> Sita</td><td>1884, Oct. 14</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">245.</span> Vera</td><td>1885, Feb. 6</td><td>Pogson</td><td>Madras</td></tr>
<tr><td><span class="ind">246.</span> Asporina</td><td>1885, Mar. 6</td><td>Borelly</td><td>Marseilles</td></tr>
<tr><td><span class="ind">247.</span> Eukrate</td><td>1885, Mar. 14</td><td>Luther</td><td>Dusseldorf</td></tr>
<tr><td><span class="ind">248.</span> Lameia</td><td>1885, June 5</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">249.</span> Ilse</td><td>1885, Aug. 17</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">250.</span> Bettina</td><td>1885, Sept. 3</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">251.</span> Sophia</td><td>1885, Oct. 4</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">252.</span> Clementina</td><td>1885, Oct. 27</td><td>Perrotin</td><td>Nice</td></tr>
<tr><td><span class="ind">253.</span> Mathilde</td><td>1885, Nov. 12</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">254.</span> Augusta</td><td>1886, Mar. 31</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">255.</span> Oppavia</td><td>1886, Mar. 31</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">256.</span> Walpurga</td><td>1886, Apr. 3</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">257.</span> Silesia</td><td>1886, Apr. 5</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">258.</span> Tyche</td><td>1886, May 4</td><td>Luther</td><td>Dusseldorf</td></tr>
<tr><td><span class="ind">259.</span> Aletheia</td><td>1886, June 28</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">260.</span> Huberta</td><td>1886, Oct. 3</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">261.</span> Prymno</td><td>1886, Oct. 31</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">262.</span> Valda</td><td>1886, Nov. 3</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">263.</span> Dresda</td><td>1886, Nov. 3</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">264.</span> Libussa</td><td>1886, Dec. 17</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">265.</span> Anna</td><td>1887, Feb. 25</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">266.</span> Aline</td><td>1887, May 17</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">267.</span> Tirza</td><td>1887, May 27</td><td>Charlois</td><td>Nice</td></tr>
<tr><td><span class="ind">268.</span></td><td>1887, June 9</td><td>Borelly</td><td>Marseilles</td></tr>
<tr><td><span class="ind">269.</span></td><td>1887, Sept. 21</td><td>Palisa</td><td>Vienna</td></tr>
<tr><td><span class="ind">270.</span></td><td>1887, Oct. 8</td><td>Peters</td><td>Clinton</td></tr>
<tr><td><span class="ind">271.</span></td><td>1887, Oct. 16</td><td>Knorre</td><td>Berlin</td></tr>
</table>
<p><span class="pagenum">[Pg 23]</span></p>
<h3><a id="Remarks_on_Table_I"></a>3. Remarks on Table I.</h3>
<p><a id="The_numbers_discovered_by_the_thirty-five_observers"></a>The numbers discovered by the thirty-five observers are respectively as
follows:</p>
<table summary="Discoverers">
<tr><td class="tdl">Palisa</td>
<td class="tdrb">60</td></tr>
<tr><td class="tdl">Peters</td>
<td class="tdrb">47</td></tr>
<tr><td class="tdl">Luther</td>
<td class="tdrb">23</td></tr>
<tr><td class="tdl">Watson</td>
<td class="tdrb">22</td></tr>
<tr><td class="tdl">Borelly</td>
<td class="tdrb">15</td></tr>
<tr><td class="tdl">Goldschmidt</td>
<td class="tdrb">14</td></tr>
<tr><td class="tdl">Hind</td>
<td class="tdrb">10</td></tr>
<tr><td class="tdl">De Gasparis</td>
<td class="tdrb">9</td></tr>
<tr><td class="tdl">Pogson</td>
<td class="tdrb">8</td></tr>
<tr><td class="tdl">Paul Henry</td>
<td class="tdrb">7</td></tr>
<tr><td class="tdl">Prosper Henry</td>
<td class="tdrb">7</td></tr>
<tr><td class="tdl">Chacornac</td>
<td class="tdrb">6</td></tr>
<tr><td class="tdl">Perrotin</td>
<td class="tdrb">6</td></tr>
<tr><td class="tdl">Coggia</td>
<td class="tdrb">5</td></tr>
<tr><td class="tdl">Knorre</td>
<td class="tdrb">4</td></tr>
<tr><td class="tdl">Tempel</td>
<td class="tdrb">4</td></tr>
<tr><td class="tdl">Ferguson</td>
<td class="tdrb">3</td></tr>
<tr><td class="tdl">Olbers</td>
<td class="tdrb">2</td></tr>
<tr><td class="tdl">Hencke</td>
<td class="tdrb">2</td></tr>
<tr><td class="tdl">Tuttle</td>
<td class="tdrb">2</td></tr>
<tr><td class="tdl">Foerster (with Lesser)</td>
<td class="tdrb">1</td></tr>
<tr><td class="tdl">Safford (with Peters)</td>
<td class="tdrb">1</td></tr>
<tr><td class="tdl hanging-indent">and Messrs. Charlois,
Cottenot,
D'Arrest,
De Ball,
Graham,
Harding,
Laurent,
Piazzi,
Schiaparelli,
Schulhof,
Stephan,
Searle,
and Tietjen, each</td>
<td class="tdrb">1</td></tr>
</table>
<p>Before arrangements had been made for the telegraphic transmission of
discoveries between Europe and America, or even between the
observatories of Europe, the same planet was sometimes independently
discovered by different observers. For example, Virginia was found by
Ferguson, at Washington, on October 4, 1857,<span class="pagenum">[Pg 24]</span> and by Luther, at Bilk,
fifteen days later. In all cases, however, credit has been given to the
first observer.</p>
<p>Hersilia, the two hundred and sixth of the group, was lost before
sufficient observations were obtained for determining its elements. It
was not rediscovered till December 14, 1884. Menippe, the one hundred
and eighty-eighth, was also lost soon after its discovery in 1878. It
has not been seen for more than nine years, and considerable uncertainty
attaches to its estimated elements.</p>
<p>Of the two hundred and seventy-one members now known (1887), one hundred
and ninety-one have been discovered in Europe, seventy-four in America,
and six in Asia. The years of most successful search, together with the
number discovered in each, were:</p>
<table class="all-center" summary="Asteroids by Year">
<tr><td> </td><td> Asteroids.</td></tr>
<tr><td>1879</td><td>20</td></tr>
<tr><td>1875</td><td>17</td></tr>
<tr><td>1868</td><td>12</td></tr>
<tr><td>1878</td><td>12</td></tr>
</table>
<p>And six has been the average yearly number since the commencement of
renewed effort in 1845. All the larger members of the group have,
doubtless, been discovered. It seems not improbable, however, that an
indefinite number of very small bodies belonging to the zone remain to
be found. The process of discovery is becoming more difficult as the
known number increases. The astronomer, for instance, who may discover
number two hundred and seventy-two must know the simultaneous positions
of the two hundred and seventy-one previously detected before he can
decide whether he has picked up a new planet or merely rediscovered an
old one. <a id="The_numbers_discovered_in_the_several_months"></a>The numbers discovered in the several months are as follows:</p>
<p><span class="pagenum">[Pg 25]</span></p>
<table summary="Asteroids by Month">
<tr><td class="tdl">January</td><td class="tdr"> 13</td></tr>
<tr><td class="tdl">February</td><td class="tdr"> 23</td></tr>
<tr><td class="tdl">March</td><td class="tdr"> 19</td></tr>
<tr><td class="tdl">April</td><td class="tdr"> 35</td></tr>
<tr><td class="tdl">May</td><td class="tdr"> 21</td></tr>
<tr><td class="tdl">June</td><td class="tdr"> 13</td></tr>
<tr><td class="tdl">July</td><td class="tdr"> 14</td></tr>
<tr><td class="tdl">August</td><td class="tdr"> 28</td></tr>
<tr><td class="tdl">September</td><td class="tdr"> 46</td></tr>
<tr><td class="tdl">October</td><td class="tdr"> 28</td></tr>
<tr><td class="tdl">November</td><td class="tdr"> 26</td></tr>
<tr><td class="tdl">December</td><td class="tdr"> 5</td></tr>
</table>
<p>This obvious disparity is readily explained. The weather is favorable
for night watching in April and September; the winter months are too
cold for continuous observations; and the small numbers in June and July
may be referred to the shortness of the nights.</p>
<h3><a id="Mode_of_Discovery"></a>4. Mode of Discovery.</h3>
<p>The astronomer who would undertake the search for new asteroids must
supply himself with star-charts extending some considerable distance on
each side of the ecliptic, and containing all telescopic stars down to
the thirteenth or fourteenth magnitude. The detection of a star not
found in the chart of a particular section will indicate its motion, and
hence its planetary character. The construction of such charts has been
a principal object in the labors of Dr. Peters, at Clinton, New York. In
fact, his discovery of minor planets has in most instances been merely
an incidental result of his larger and more important work.</p>
<h4><a id="NAMES_AND_SYMBOLS"></a>NAMES AND SYMBOLS.</h4>
<p>The fact that the names of female deities in the Greek and Roman
mythologies had been given to the first asteroids suggested a similar
course in the selection of names after the new epoch of discovery in
1845. While conformity to this rule has been the general aim<span class="pagenum">[Pg 26]</span> of
discoverers, the departures from it have been increasingly numerous. The
twelfth asteroid, discovered in London, was named Victoria, in honor of
the reigning sovereign; the twentieth and twenty-fifth, detected at
Marseilles,<a name="FNanchor_2" id="FNanchor_2"></a><a href="#Footnote_2" class="fnanchor">[2]</a> received names indicative of the place of their
discovery; Lutetia, the first found at Paris, received its name for a
similar purpose; the fifty-fourth was named Alexandra, for Alexander von
Humboldt; the sixty-seventh, found by Pogson at Madras, was named Asia,
to commemorate the fact that it was the first discovered on that
continent. We find, also, Julia, Bertha, Xantippe, Zelia, Maria,
Isabella, Martha, Dido, Cleopatra, Barbara, Ida, Augusta, and Anna. Why
these were selected we will not stop to inquire.</p>
<p>As the number of asteroids increased it was found inconvenient to
designate them individually by particular signs, as in the case of the
old planets. In 1849, Dr. B. A. Gould proposed to represent them by the
numbers expressing their order of discovery enclosed in a small circle.
This method was at once very generally adopted.</p>
<h3><a id="Magnitudes_of_the_Asteroids"></a>5. Magnitudes of the Asteroids.</h3>
<p>The apparent diameter of the largest is less than one-second of arc.
They are all too small, therefore, to be accurately measured by
astronomical instruments. From photometric observations, however,
Argelander,<a name="FNanchor_3" id="FNanchor_3"></a><a href="#Footnote_3" class="fnanchor">[3]</a> Stone,<a name="FNanchor_4" id="FNanchor_4"></a><a href="#Footnote_4" class="fnanchor">[4]</a> and Pickering<a name="FNanchor_5" id="FNanchor_5"></a><a href="#Footnote_5" class="fnanchor">[5]</a> have formed estimates of the
diameters,<span class="pagenum">[Pg 27]</span> the results giving probably close approximations to the true
magnitudes. According to these estimates the diameter of the largest,
Vesta, is about three hundred miles, that of Ceres about two hundred,
and those of Pallas and Juno between one and two hundred. The diameters
of about thirty are between fifty and one hundred miles, and those of
all others less than fifty; the estimates for Menippe and Eva giving
twelve and thirteen miles respectively. The diameter of the former is to
that of the earth as one to six hundred and sixty-four; and since
spheres are to each other as the cubes of their diameters, it would
require two hundred and ninety millions of such asteroids to form a
planet as large as our globe. In other words, if the earth be
represented by a sphere one foot in diameter, the magnitude of Menippe
on the same scale would be that of a sand particle whose diameter is one
fifty-fifth of an inch. Its surface contains about four hundred and
forty square miles,—an area equal to a county twenty-one miles square.
The surface attractions of two planets having the same density are to
each other as their diameters. A body, therefore, weighing two hundred
pounds at the earth's surface would on the surface of the asteroid weigh
less than five ounces. At the earth's surface a weight falls sixteen
feet the first second, at the surface of Menippe it would fall about
one-fourth of an inch. A person might leap from its surface to a height
of several hundred feet, in which case he could not return in much less
than an hour. "But of such speculations," Sir John Herschel remarks,
"there is no end."</p>
<p>The number of these planetules between the orbits of Mars and Jupiter in
all probability can never be known. It was estimated by Leverrier that
the quantity of mat<span class="pagenum">[Pg 28]</span>ter contained in the group could not be greater than
one-fourth of the earth's mass. But this would be equal to five thousand
planets, each as large as Vesta, to seventy-two millions as large as
Menippe, or to four thousand millions of five miles in diameter. In
short, the existence of an indefinite number too small for detection by
the most powerful glasses is by no means improbable. The more we study
this wonderful section of the solar system, the more mystery seems to
envelop its origin and constitution.</p>
<h3><a id="The_Orbits_of_the_Asteroids"></a>6. The Orbits of the Asteroids.</h3>
<p>The form, magnitude, and position of a planet's orbit are determined by
the following elements:</p>
<p>1. The semi-axis major, or mean distance, denoted by the symbol <i>a</i>.</p>
<p>2. The eccentricity, <i>e</i>.</p>
<p>3. The longitude of the perihelion, <i>π</i>.</p>
<p>4. The longitude of the ascending node, ☊.</p>
<p>5. The inclination, or the angle contained between the plane of the
orbit and that of the ecliptic, <i>i</i>.</p>
<p>And in order to compute a planet's place in its orbit for any given time
we must also know</p>
<p>6. Its period, <i>P</i>, and</p>
<p>7. Its mean longitude, <i>l</i>, at a given epoch.</p>
<p>These elements, except the last, are given for all the asteroids, so far
as known, in Table II. In column first the number denoting the order of
discovery is attached to each name.</p>
<p><span class="pagenum">[Pg 29]</span></p>
<h3><a id="TABLE_II"></a>TABLE II.<br />
<span class="small"><i>Elements of the Asteroids.</i></span></h3>
<table class="ruled" summary="Elements of the Asteroids">
<tr><th>Name</th><th><i>a</i></th><th><i>P</i></th><th><i>e</i></th><th><i>π</i></th><th>☊</th><th><i>i</i></th></tr>
<tr><td><span class="ind">149.</span> Medusa</td><td>2.1327</td><td>1137.7d</td><td>0.1194</td>
<td><span class="ilb3">246</span><span class="ilb-deg">°</span><span class="ilb2">37</span>´</td>
<td><span class="ilb3">342</span><span class="ilb-deg">°</span><span class="ilb2">13</span>´</td>
<td><span class="ilb2">1</span><span class="ilb-deg">°</span><span class="ilb2">6</span>´</td></tr>
<tr><td><span class="ind">244.</span> Sita</td><td>2.1765</td><td>1172.8</td><td>0.1370</td>
<td><span class="ilb3">13</span><span class="ilb3">8</span></td>
<td><span class="ilb3">208</span><span class="ilb3">37</span></td>
<td><span class="ilb2">2</span><span class="ilb3">50</span></td></tr>
<tr><td><span class="ind">228.</span> Agathe</td><td>2.2009</td><td>1192.6</td><td>0.2405</td>
<td><span class="ilb3">329</span><span class="ilb3">23</span></td>
<td><span class="ilb3">313</span><span class="ilb3">18</span></td>
<td><span class="ilb2">2</span><span class="ilb3">33</span></td></tr>
<tr><td><span class="ind">8.</span> Flora</td><td>2.2014</td><td>1193.3</td><td>0.1567</td>
<td><span class="ilb3">32</span><span class="ilb3">54</span></td>
<td><span class="ilb3">110</span><span class="ilb3">18</span></td>
<td><span class="ilb2">5</span><span class="ilb3">53</span></td></tr>
<tr><td><span class="ind">43.</span> Ariadne</td><td>2.2033</td><td>1194.5</td><td>0.1671</td>
<td><span class="ilb3">277</span><span class="ilb3">58</span></td>
<td><span class="ilb3">264</span><span class="ilb3">35</span></td>
<td><span class="ilb2">3</span><span class="ilb3">28</span></td></tr>
<tr><td><span class="ind">254.</span> Augusta</td><td>2.2060</td><td>1196.8</td><td>0.1227</td>
<td><span class="ilb3">260</span><span class="ilb3">47</span></td>
<td><span class="ilb3">28</span><span class="ilb3">9</span></td>
<td><span class="ilb2">4</span><span class="ilb3">36</span></td></tr>
<tr><td><span class="ind">72.</span> Feronia</td><td>2.2661</td><td>1246.0</td><td>0.1198</td>
<td><span class="ilb3">307</span><span class="ilb3">58</span></td>
<td><span class="ilb3">207</span><span class="ilb3">49</span></td>
<td><span class="ilb2">5</span><span class="ilb3">24</span></td></tr>
<tr><td><span class="ind">40.</span> Harmonia</td><td>2.2673</td><td>1247.0</td><td>0.0466</td>
<td><span class="ilb3">0</span><span class="ilb3">54</span></td>
<td><span class="ilb3">93</span><span class="ilb3">35</span></td>
<td><span class="ilb2">4</span><span class="ilb3">16</span></td></tr>
<tr><td><span class="ind">207.</span> Hedda</td><td>2.2839</td><td>1260.7</td><td>0.0301</td>
<td><span class="ilb3">217</span><span class="ilb3">2</span></td>
<td><span class="ilb3">28</span><span class="ilb3">51</span></td>
<td><span class="ilb2">3</span><span class="ilb3">49</span></td></tr>
<tr><td><span class="ind">136.</span> Austria</td><td>2.2863</td><td>1262.7</td><td>0.0849</td>
<td><span class="ilb3">316</span><span class="ilb3">6</span></td>
<td><span class="ilb3">186</span><span class="ilb3">7</span></td>
<td><span class="ilb2">9</span><span class="ilb3">33</span></td></tr>
<tr><td><span class="ind">18.</span> Melpomene</td><td>2.2956</td><td>1270.4</td><td>0.2177</td>
<td><span class="ilb3">15</span><span class="ilb3">6</span></td>
<td><span class="ilb3">150</span><span class="ilb3">4</span></td>
<td><span class="ilb2">10</span><span class="ilb3">9</span></td></tr>
<tr><td><span class="ind">80.</span> Sappho</td><td>2.2962</td><td>1270.9</td><td>0.2001</td>
<td><span class="ilb3">355</span><span class="ilb3">18</span></td>
<td><span class="ilb3">218</span><span class="ilb3">44</span></td>
<td><span class="ilb2">8</span><span class="ilb3">37</span></td></tr>
<tr><td><span class="ind">261.</span> Prymno</td><td>2.3062</td><td>1278.4</td><td>0.0794</td>
<td><span class="ilb3">179</span><span class="ilb3">35</span></td>
<td><span class="ilb3">96</span><span class="ilb3">33</span></td>
<td><span class="ilb2">3</span><span class="ilb3">38</span></td></tr>
<tr><td><span class="ind">12.</span> Victoria</td><td>2.3342</td><td>1302.7</td><td>0.2189</td>
<td><span class="ilb3">301</span><span class="ilb3">39</span></td>
<td><span class="ilb3">235</span><span class="ilb3">35</span></td>
<td><span class="ilb2">8</span><span class="ilb3">23</span></td></tr>
<tr><td><span class="ind">27.</span> Euterpe</td><td>2.3472</td><td>1313.5</td><td>0.1739</td>
<td><span class="ilb3">87</span><span class="ilb3">59</span></td>
<td><span class="ilb3">93</span><span class="ilb3">51</span></td>
<td><span class="ilb2">1</span><span class="ilb3">36</span></td></tr>
<tr><td><span class="ind">219.</span> Thusnelda</td><td>2.3542</td><td>1319.4</td><td>0.2247</td>
<td><span class="ilb3">340</span><span class="ilb3">34</span></td>
<td><span class="ilb3">200</span><span class="ilb3">44</span></td>
<td><span class="ilb2">10</span><span class="ilb3">47</span></td></tr>
<tr><td><span class="ind">163.</span> Erigone</td><td>2.3560</td><td>1320.9</td><td>0.1567</td>
<td><span class="ilb3">93</span><span class="ilb3">46</span></td>
<td><span class="ilb3">159</span><span class="ilb3">2</span></td>
<td><span class="ilb2">4</span><span class="ilb3">42</span></td></tr>
<tr><td><span class="ind">169.</span> Zelia</td><td>2.3577</td><td>1322.3</td><td>0.1313</td>
<td><span class="ilb3">326</span><span class="ilb3">20</span></td>
<td><span class="ilb3">354</span><span class="ilb3">38</span></td>
<td><span class="ilb2">5</span><span class="ilb3">31</span></td></tr>
<tr><td><span class="ind">4.</span> Vesta</td><td>2.3616</td><td>1325.6</td><td>0.0884</td>
<td><span class="ilb3">250</span><span class="ilb3">57</span></td>
<td><span class="ilb3">103</span><span class="ilb3">29</span></td>
<td><span class="ilb2">7</span><span class="ilb3">8</span></td></tr>
<tr><td><span class="ind">186.</span> Celuta</td><td>2.3623</td><td>1326.2</td><td>0.1512</td>
<td><span class="ilb3">327</span><span class="ilb3">24</span></td>
<td><span class="ilb3">14</span><span class="ilb3">34</span></td>
<td><span class="ilb2">13</span><span class="ilb3">6</span></td></tr>
<tr><td><span class="ind">84.</span> Clio</td><td>2.3629</td><td>1326.7</td><td>0.2360</td>
<td><span class="ilb3">339</span><span class="ilb3">20</span></td>
<td><span class="ilb3">327</span><span class="ilb3">28</span></td>
<td><span class="ilb2">9</span><span class="ilb3">22</span></td></tr>
<tr><td><span class="ind">51.</span> Nemausa</td><td>2.3652</td><td>1328.6</td><td>0.0672</td>
<td><span class="ilb3">174</span><span class="ilb3">43</span></td>
<td><span class="ilb3">175</span><span class="ilb3">52</span></td>
<td><span class="ilb2">9</span><span class="ilb3">57</span></td></tr>
<tr><td><span class="ind">220.</span> Stephania</td><td>2.3666</td><td>1329.8</td><td>0.2653</td>
<td><span class="ilb3">332</span><span class="ilb3">53</span></td>
<td><span class="ilb3">258</span><span class="ilb3">24</span></td>
<td><span class="ilb2">7</span><span class="ilb3">35</span></td></tr>
<tr><td><span class="ind">30.</span> Urania</td><td>2.3667</td><td>1329.9</td><td>0.1266</td>
<td><span class="ilb3">31</span><span class="ilb3">46</span></td>
<td><span class="ilb3">308</span><span class="ilb3">12</span></td>
<td><span class="ilb2">2</span><span class="ilb3">6</span></td></tr>
<tr><td><span class="ind">105.</span> Artemis</td><td>2.3744</td><td>1336.4</td><td>0.1749</td>
<td><span class="ilb3">242</span><span class="ilb3">38</span></td>
<td><span class="ilb3">188</span><span class="ilb3">3</span></td>
<td><span class="ilb2">21</span><span class="ilb3">31</span></td></tr>
<tr><td><span class="ind">113.</span> Amalthea</td><td>2.3761</td><td>1337.8</td><td>0.0874</td>
<td><span class="ilb3">198</span><span class="ilb3">44</span></td>
<td><span class="ilb3">123</span><span class="ilb3">11</span></td>
<td><span class="ilb2">5</span><span class="ilb3">2</span></td></tr>
<tr><td><span class="ind">115.</span> Thyra</td><td>2.3791</td><td>1340.3</td><td>0.1939</td>
<td><span class="ilb3">43</span><span class="ilb3">2</span></td>
<td><span class="ilb3">309</span><span class="ilb3">5</span></td>
<td><span class="ilb2">11</span><span class="ilb3">35</span></td></tr>
<tr><td><span class="ind">161.</span> Athor</td><td>2.3792</td><td>1340.5</td><td>0.1389</td>
<td><span class="ilb3">310</span><span class="ilb3">40</span></td>
<td><span class="ilb3">18</span><span class="ilb3">27</span></td>
<td><span class="ilb2">9</span><span class="ilb3">3</span></td></tr>
<tr><td><span class="ind">172.</span> Baucis</td><td>2.3794</td><td>1340.6</td><td>0.1139</td>
<td><span class="ilb3">329</span><span class="ilb3">23</span></td>
<td><span class="ilb3">331</span><span class="ilb3">50</span></td>
<td><span class="ilb2">10</span><span class="ilb3">2</span></td></tr>
<tr><td><span class="ind">249.</span> Ilse</td><td>2.3795</td><td>1340.6</td><td>0.2195</td>
<td><span class="ilb3">14</span><span class="ilb3">17</span></td>
<td><span class="ilb3">334</span><span class="ilb3">49</span></td>
<td><span class="ilb2">9</span><span class="ilb3">40</span></td></tr>
<tr><td><span class="ind">230.</span> Athamantis</td><td>2.3842</td><td>1344.6</td><td>0.0615</td>
<td><span class="ilb3">17</span><span class="ilb3">31</span></td>
<td><span class="ilb3">239</span><span class="ilb3">33</span></td>
<td><span class="ilb2">9</span><span class="ilb3">26</span></td></tr>
<tr><td><span class="ind">7.</span> Iris</td><td>2.3862</td><td>1346.4</td><td>0.2308</td>
<td><span class="ilb3">41</span><span class="ilb3">23</span></td>
<td><span class="ilb3">259</span><span class="ilb3">48</span></td>
<td><span class="ilb2">5</span><span class="ilb3">28</span></td></tr>
<tr><td><span class="ind">9.</span> Metis</td><td>2.3866</td><td>1346.7</td><td>0.1233</td>
<td><span class="ilb3">71</span><span class="ilb3">4</span></td>
<td><span class="ilb3">68</span><span class="ilb3">32</span></td>
<td><span class="ilb2">5</span><span class="ilb3">36</span></td></tr>
<tr><td><span class="ind">234.</span> Barbara</td><td>2.3873</td><td>1347.3</td><td>0.2440</td>
<td><span class="ilb3">333</span><span class="ilb3">26</span></td>
<td><span class="ilb3">144</span><span class="ilb3">9</span></td>
<td><span class="ilb2">15</span><span class="ilb3">22</span></td></tr>
<tr><td><span class="ind">60.</span> Echo</td><td>2.3934</td><td>1352.4</td><td>0.1838</td>
<td><span class="ilb3">98</span><span class="ilb3">36</span></td>
<td><span class="ilb3">192</span><span class="ilb3">5</span></td>
<td><span class="ilb2">3</span><span class="ilb3">35</span></td></tr>
<tr><td><span class="ind">63.</span> Ausonia</td><td>2.3979</td><td>1356.3</td><td>0.1239</td>
<td><span class="ilb3">270</span><span class="ilb3">25</span></td>
<td><span class="ilb3">337</span><span class="ilb3">58</span></td>
<td><span class="ilb2">5</span><span class="ilb3">48</span></td></tr>
<tr><td><span class="ind">25.</span> Phocea</td><td>2.4005</td><td>1358.5</td><td>0.2553</td>
<td><span class="ilb3">302</span><span class="ilb3">48</span></td>
<td><span class="ilb3">208</span><span class="ilb3">27</span></td>
<td><span class="ilb2">21</span><span class="ilb3">35</span></td></tr>
<tr><td><span class="ind">192.</span> Nausicaa</td><td>2.4014</td><td>1359.3</td><td>0.2413</td>
<td><span class="ilb3">343</span><span class="ilb3">19</span></td>
<td><span class="ilb3">160</span><span class="ilb3">46</span></td>
<td><span class="ilb2">6</span><span class="ilb3">50</span></td></tr>
<tr><td><span class="ind">20.</span> Massalia</td><td>2.4024</td><td>1365.8</td><td>0.1429</td>
<td><span class="ilb3">99</span><span class="ilb3">7</span></td>
<td><span class="ilb3">206</span><span class="ilb3">36</span></td>
<td><span class="ilb2">0</span><span class="ilb3">41</span></td></tr>
<tr><td><span class="ind">265.</span> Anna</td><td>2.4096</td><td>1366.2</td><td>0.2628</td>
<td><span class="ilb3">226</span><span class="ilb3">18</span></td>
<td><span class="ilb3">335</span><span class="ilb3">26</span></td>
<td><span class="ilb2">25</span><span class="ilb3">24</span></td></tr>
<tr><td><span class="ind">182.</span> Elsa</td><td>2.4157</td><td>1371.4</td><td>0.1852</td>
<td><span class="ilb3">51</span><span class="ilb3">52</span></td>
<td><span class="ilb3">106</span><span class="ilb3">30</span></td>
<td><span class="ilb2">2</span><span class="ilb3">0</span></td></tr>
<tr><td><span class="ind">142.</span> Polana</td><td>2.4194</td><td>1374.5</td><td>0.1322</td>
<td><span class="ilb3">219</span><span class="ilb3">54</span></td>
<td><span class="ilb3">317</span><span class="ilb3">34</span></td>
<td><span class="ilb2">2</span><span class="ilb3">14</span></td></tr>
<tr><td><span class="ind">67.</span> Asia</td><td>2.4204</td><td>1375.4</td><td>0.1866</td>
<td><span class="ilb3">306</span><span class="ilb3">35</span></td>
<td><span class="ilb3">202</span><span class="ilb3">47</span></td>
<td><span class="ilb2">5</span><span class="ilb3">59</span></td></tr>
<tr><td><span class="ind">44.</span> Nysa</td><td>2.4223</td><td>1377.0</td><td>0.1507</td>
<td><span class="ilb3">111</span><span class="ilb3">57</span></td>
<td><span class="ilb3">131</span><span class="ilb3">11</span></td>
<td><span class="ilb2">3</span><span class="ilb3">42</span><span class="pagenum">[Pg 30]</span></td></tr>
<tr><td><span class="ind">6.</span> Hebe</td><td>2.4254</td><td>1379.3</td><td>0.2034</td>
<td><span class="ilb3">15</span><span class="ilb3">16</span></td>
<td><span class="ilb3">138</span><span class="ilb3">43</span></td>
<td><span class="ilb2">10</span><span class="ilb3">47</span></td></tr>
<tr><td><span class="ind">83.</span> Beatrix</td><td>2.4301</td><td>1383.6</td><td>0.0859</td>
<td><span class="ilb3">191</span><span class="ilb3">46</span></td>
<td><span class="ilb3">27</span><span class="ilb3">32</span></td>
<td><span class="ilb2">5</span><span class="ilb3">0</span></td></tr>
<tr><td><span class="ind">135.</span> Hertha</td><td>2.4303</td><td>1383.8</td><td>0.2037</td>
<td><span class="ilb3">320</span><span class="ilb3">11</span></td>
<td><span class="ilb3">344</span><span class="ilb3">3</span></td>
<td><span class="ilb2">2</span><span class="ilb3">19</span></td></tr>
<tr><td><span class="ind">131.</span> Vala</td><td>2.4318</td><td>1385.1</td><td>0.0683</td>
<td><span class="ilb3">222</span><span class="ilb3">50</span></td>
<td><span class="ilb3">65</span><span class="ilb3">15</span></td>
<td><span class="ilb2">4</span><span class="ilb3">58</span></td></tr>
<tr><td><span class="ind">112.</span> Iphigenia</td><td>2.4335</td><td>1386.6</td><td>0.1282</td>
<td><span class="ilb3">338</span><span class="ilb3">9</span></td>
<td><span class="ilb3">324</span><span class="ilb3">3</span></td>
<td><span class="ilb2">2</span><span class="ilb3">37</span></td></tr>
<tr><td><span class="ind">21.</span> Lutetia</td><td>2.4354</td><td>1388.2</td><td>0.1621</td>
<td><span class="ilb3">327</span><span class="ilb3">4</span></td>
<td><span class="ilb3">80</span><span class="ilb3">28</span></td>
<td><span class="ilb2">3</span><span class="ilb3">5</span></td></tr>
<tr><td><span class="ind">118.</span> Peitho</td><td>2.4384</td><td>1390.8</td><td>0.1608</td>
<td><span class="ilb3">77</span><span class="ilb3">36</span></td>
<td><span class="ilb3">47</span><span class="ilb3">30</span></td>
<td><span class="ilb2">7</span><span class="ilb3">48</span></td></tr>
<tr><td><span class="ind">126.</span> Velleda</td><td>2.4399</td><td>1392.1</td><td>0.1061</td>
<td><span class="ilb3">347</span><span class="ilb3">46</span></td>
<td><span class="ilb3">23</span><span class="ilb3">7</span></td>
<td><span class="ilb2">2</span><span class="ilb3">56</span></td></tr>
<tr><td><span class="ind">42.</span> Isis</td><td>2.4401</td><td>1392.2</td><td>0.2256</td>
<td><span class="ilb3">317</span><span class="ilb3">58</span></td>
<td><span class="ilb3">84</span><span class="ilb3">28</span></td>
<td><span class="ilb2">8</span><span class="ilb3">35</span></td></tr>
<tr><td><span class="ind">19.</span> Fortuna</td><td>2.4415</td><td>1394.4</td><td>0.1594</td>
<td><span class="ilb3">31</span><span class="ilb3">3</span></td>
<td><span class="ilb3">211</span><span class="ilb3">27</span></td>
<td><span class="ilb2">1</span><span class="ilb3">33</span></td></tr>
<tr><td><span class="ind">79.</span> Eurynome</td><td>2.4436</td><td>1395.2</td><td>0.1945</td>
<td><span class="ilb3">44</span><span class="ilb3">22</span></td>
<td><span class="ilb3">206</span><span class="ilb3">44</span></td>
<td><span class="ilb2">4</span><span class="ilb3">37</span></td></tr>
<tr><td><span class="ind">138.</span> Tolosa</td><td>2.4492</td><td>1400.0</td><td>0.1623</td>
<td><span class="ilb3">311</span><span class="ilb3">39</span></td>
<td><span class="ilb3">54</span><span class="ilb3">52</span></td>
<td><span class="ilb2">3</span><span class="ilb3">14</span></td></tr>
<tr><td><span class="ind">189.</span> Phthia</td><td>2.4505</td><td>1401.1</td><td>0.0356</td>
<td><span class="ilb3">6</span><span class="ilb3">50</span></td>
<td><span class="ilb3">203</span><span class="ilb3">22</span></td>
<td><span class="ilb2">5</span><span class="ilb3">10</span></td></tr>
<tr><td><span class="ind">11.</span> Parthenope</td><td>2.4529</td><td>1403.2</td><td>0.0994</td>
<td><span class="ilb3">318</span><span class="ilb3">2</span></td>
<td><span class="ilb3">125</span><span class="ilb3">11</span></td>
<td><span class="ilb2">4</span><span class="ilb3">37</span></td></tr>
<tr><td><span class="ind">178.</span> Belisana</td><td>2.4583</td><td>1407.8</td><td>0.1266</td>
<td><span class="ilb3">278</span><span class="ilb3">0</span></td>
<td><span class="ilb3">50</span><span class="ilb3">17</span></td>
<td><span class="ilb2">2</span><span class="ilb3">5</span></td></tr>
<tr><td><span class="ind">198.</span> Ampella</td><td>2.4595</td><td>1408.9</td><td>0.2266</td>
<td><span class="ilb3">354</span><span class="ilb3">46</span></td>
<td><span class="ilb3">268</span><span class="ilb3">45</span></td>
<td><span class="ilb2">9</span><span class="ilb3">20</span></td></tr>
<tr><td><span class="ind">248.</span> Lameia</td><td>2.4714</td><td>1419.1</td><td>0.0656</td>
<td><span class="ilb3">248</span><span class="ilb3">40</span></td>
<td><span class="ilb3">246</span><span class="ilb3">34</span></td>
<td><span class="ilb2">4</span><span class="ilb3">1</span></td></tr>
<tr><td><span class="ind">17.</span> Thetis</td><td>2.4726</td><td>1420.1</td><td>0.1293</td>
<td><span class="ilb3">261</span><span class="ilb3">37</span></td>
<td><span class="ilb3">125</span><span class="ilb3">24</span></td>
<td><span class="ilb2">5</span><span class="ilb3">36</span></td></tr>
<tr><td><span class="ind">46.</span> Hestia</td><td>2.5265</td><td>1466.8</td><td>0.1642</td>
<td><span class="ilb3">354</span><span class="ilb3">14</span></td>
<td><span class="ilb3">181</span><span class="ilb3">31</span></td>
<td><span class="ilb2">2</span><span class="ilb3">17</span></td></tr>
<tr><td><span class="ind">89.</span> Julia</td><td>2.5510</td><td>1488.2</td><td>0.1805</td>
<td><span class="ilb3">353</span><span class="ilb3">13</span></td>
<td><span class="ilb3">311</span><span class="ilb3">42</span></td>
<td><span class="ilb2">16</span><span class="ilb3">11</span></td></tr>
<tr><td><span class="ind">232.</span> Russia</td><td>2.5522</td><td>1489.3</td><td>0.1754</td>
<td><span class="ilb3">200</span><span class="ilb3">25</span></td>
<td><span class="ilb3">152</span><span class="ilb3">30</span></td>
<td><span class="ilb2">6</span><span class="ilb3">4</span></td></tr>
<tr><td><span class="ind">29.</span> Amphitrite</td><td>2.5545</td><td>1491.3</td><td>0.0742</td>
<td><span class="ilb3">56</span><span class="ilb3">23</span></td>
<td><span class="ilb3">356</span><span class="ilb3">41</span></td>
<td><span class="ilb2">6</span><span class="ilb3">7</span></td></tr>
<tr><td><span class="ind">170.</span> Maria</td><td>2.5549</td><td>1491.7</td><td>0.0639</td>
<td><span class="ilb3">95</span><span class="ilb3">47</span></td>
<td><span class="ilb3">301</span><span class="ilb3">20</span></td>
<td><span class="ilb2">14</span><span class="ilb3">23</span></td></tr>
<tr><td><span class="ind">262.</span> Valda</td><td>2.5635</td><td>1496.4</td><td>0.2172</td>
<td><span class="ilb3">61</span><span class="ilb3">42</span></td>
<td><span class="ilb3">38</span><span class="ilb3">40</span></td>
<td><span class="ilb2">7</span><span class="ilb3">46</span></td></tr>
<tr><td><span class="ind">258.</span> Tyche</td><td>2.5643</td><td>1499.8</td><td>0.1966</td>
<td><span class="ilb3">15</span><span class="ilb3">42</span></td>
<td><span class="ilb3">208</span><span class="ilb3">4</span></td>
<td><span class="ilb2">14</span><span class="ilb3">50</span></td></tr>
<tr><td><span class="ind">134.</span> Sophrosyne</td><td>2.5647</td><td>1500.3</td><td>0.1165</td>
<td><span class="ilb3">67</span><span class="ilb3">33</span></td>
<td><span class="ilb3">346</span><span class="ilb3">22</span></td>
<td><span class="ilb2">11</span><span class="ilb3">36</span></td></tr>
<tr><td><span class="ind">264.</span> Libussa</td><td>2.5672</td><td>1502.4</td><td>0.0925</td>
<td><span class="ilb3">0</span><span class="ilb3">7</span></td>
<td><span class="ilb3">50</span><span class="ilb3">23</span></td>
<td><span class="ilb2">10</span><span class="ilb3">29</span></td></tr>
<tr><td><span class="ind">193.</span> Ambrosia</td><td>2.5758</td><td>1510.0</td><td>0.2854</td>
<td><span class="ilb3">70</span><span class="ilb3">52</span></td>
<td><span class="ilb3">351</span><span class="ilb3">15</span></td>
<td><span class="ilb2">11</span><span class="ilb3">39</span></td></tr>
<tr><td><span class="ind">13.</span> Egeria</td><td>2.5765</td><td>1510.6</td><td>0.0871</td>
<td><span class="ilb3">120</span><span class="ilb3">10</span></td>
<td><span class="ilb3">43</span><span class="ilb3">12</span></td>
<td><span class="ilb2">16</span><span class="ilb3">32</span></td></tr>
<tr><td><span class="ind">5.</span> Astræa</td><td>2.5786</td><td>1512.4</td><td>0.1863</td>
<td><span class="ilb3">134</span><span class="ilb3">57</span></td>
<td><span class="ilb3">141</span><span class="ilb3">28</span></td>
<td><span class="ilb2">5</span><span class="ilb3">19</span></td></tr>
<tr><td><span class="ind">119.</span> Althea</td><td>2.5824</td><td>1515.7</td><td>0.0815</td>
<td><span class="ilb3">11</span><span class="ilb3">29</span></td>
<td><span class="ilb3">203</span><span class="ilb3">57</span></td>
<td><span class="ilb2">5</span><span class="ilb3">45</span></td></tr>
<tr><td><span class="ind">157.</span> Dejanira</td><td>2.5828</td><td>1516.1</td><td>0.2105</td>
<td><span class="ilb3">107</span><span class="ilb3">24</span></td>
<td><span class="ilb3">62</span><span class="ilb3">31</span></td>
<td><span class="ilb2">12</span><span class="ilb3">2</span></td></tr>
<tr><td><span class="ind">101.</span> Helena</td><td>2.5849</td><td>1518.0</td><td>0.1386</td>
<td><span class="ilb3">327</span><span class="ilb3">15</span></td>
<td><span class="ilb3">343</span><span class="ilb3">46</span></td>
<td><span class="ilb2">10</span><span class="ilb3">11</span></td></tr>
<tr><td><span class="ind">32.</span> Pomona</td><td>2.5873</td><td>1520.1</td><td>0.0830</td>
<td><span class="ilb3">193</span><span class="ilb3">22</span></td>
<td><span class="ilb3">220</span><span class="ilb3">43</span></td>
<td><span class="ilb2">5</span><span class="ilb3">29</span></td></tr>
<tr><td><span class="ind">91.</span> Ægina</td><td>2.5895</td><td>1522.1</td><td>0.1087</td>
<td><span class="ilb3">80</span><span class="ilb3">22</span></td>
<td><span class="ilb3">11</span><span class="ilb3">7</span></td>
<td><span class="ilb2">2</span><span class="ilb3">8</span></td></tr>
<tr><td><span class="ind">14.</span> Irene</td><td>2.5896</td><td>1522.1</td><td>0.1627</td>
<td><span class="ilb3">180</span><span class="ilb3">19</span></td>
<td><span class="ilb3">86</span><span class="ilb3">48</span></td>
<td><span class="ilb2">9</span><span class="ilb3">8</span></td></tr>
<tr><td><span class="ind">111.</span> Ate</td><td>2.5927</td><td>1524.8</td><td>0.1053</td>
<td><span class="ilb3">108</span><span class="ilb3">42</span></td>
<td><span class="ilb3">306</span><span class="ilb3">13</span></td>
<td><span class="ilb2">4</span><span class="ilb3">57</span></td></tr>
<tr><td><span class="ind">151.</span> Abundantia</td><td>2.5932</td><td>1525.3</td><td>0.0356</td>
<td><span class="ilb3">173</span><span class="ilb3">55</span></td>
<td><span class="ilb3">38</span><span class="ilb3">48</span></td>
<td><span class="ilb2">6</span><span class="ilb3">30</span></td></tr>
<tr><td><span class="ind">56.</span> Melete</td><td>2.6010</td><td>1532.2</td><td>0.2340</td>
<td><span class="ilb3">294</span><span class="ilb3">50</span></td>
<td><span class="ilb3">194</span><span class="ilb3">1</span></td>
<td><span class="ilb2">8</span><span class="ilb3">2</span></td></tr>
<tr><td><span class="ind">132.</span> Æthra</td><td>2.6025</td><td>1533.5</td><td>0.3799</td>
<td><span class="ilb3">152</span><span class="ilb3">24</span></td>
<td><span class="ilb3">260</span><span class="ilb3">2</span></td>
<td><span class="ilb2">25</span><span class="ilb3">0</span></td></tr>
<tr><td><span class="ind">214.</span> Aschera</td><td>2.6111</td><td>1541.1</td><td>0.0316</td>
<td><span class="ilb3">115</span><span class="ilb3">55</span></td>
<td><span class="ilb3">342</span><span class="ilb3">30</span></td>
<td><span class="ilb2">3</span><span class="ilb3">27</span></td></tr>
<tr><td><span class="ind">70.</span> Panopea</td><td>2.6139</td><td>1543.6</td><td>0.1826</td>
<td><span class="ilb3">299</span><span class="ilb3">49</span></td>
<td><span class="ilb3">48</span><span class="ilb3">18</span></td>
<td><span class="ilb2">11</span><span class="ilb3">38</span></td></tr>
<tr><td><span class="ind">194.</span> Procne</td><td>2.6159</td><td>1545.4</td><td>0.2383</td>
<td><span class="ilb3">319</span><span class="ilb3">33</span></td>
<td><span class="ilb3">159</span><span class="ilb3">19</span></td>
<td><span class="ilb2">18</span><span class="ilb3">24</span></td></tr>
<tr><td><span class="ind">53.</span> Calypso</td><td>2.6175</td><td>1546.8</td><td>0.2060</td>
<td><span class="ilb3">92</span><span class="ilb3">52</span></td>
<td><span class="ilb3">143</span><span class="ilb3">58</span></td>
<td><span class="ilb2">5</span><span class="ilb3">7</span></td></tr>
<tr><td><span class="ind">78.</span> Diana</td><td>2.6194</td><td>1548.5</td><td>0.2088</td>
<td><span class="ilb3">121</span><span class="ilb3">42</span></td>
<td><span class="ilb3">333</span><span class="ilb3">58</span></td>
<td><span class="ilb2">8</span><span class="ilb3">40</span></td></tr>
<tr><td><span class="ind">124.</span> Alceste</td><td>2.6297</td><td>1557.6</td><td>0.0784</td>
<td><span class="ilb3">245</span><span class="ilb3">42</span></td>
<td><span class="ilb3">188</span><span class="ilb3">26</span></td>
<td><span class="ilb2">2</span><span class="ilb3">56</span></td></tr>
<tr><td><span class="ind">23.</span> Thalia</td><td>2.6306</td><td>1558.4</td><td>0.2299</td>
<td><span class="ilb3">123</span><span class="ilb3">58</span></td>
<td><span class="ilb3">67</span><span class="ilb3">45</span></td>
<td><span class="ilb2">10</span><span class="ilb3">14</span></td></tr>
<tr><td><span class="ind">164.</span> Eva</td><td>2.6314</td><td>1559.1</td><td>0.3471</td>
<td><span class="ilb3">359</span><span class="ilb3">32</span></td>
<td><span class="ilb3">77</span><span class="ilb3">28</span></td>
<td><span class="ilb2">24</span><span class="ilb3">25</span></td></tr>
<tr><td><span class="ind">15.</span> Eunomia</td><td>2.6437</td><td>1570.0</td><td>0.1872</td>
<td><span class="ilb3">27</span><span class="ilb3">52</span></td>
<td><span class="ilb3">188</span><span class="ilb3">26</span></td>
<td><span class="ilb2">2</span><span class="ilb3">56</span></td></tr>
<tr><td><span class="ind">37.</span> Fides</td><td>2.6440</td><td>1570.3</td><td>0.1758</td>
<td><span class="ilb3">66</span><span class="ilb3">26</span></td>
<td><span class="ilb3">8</span><span class="ilb3">21</span></td>
<td><span class="ilb2">3</span><span class="ilb3">7</span><span class="pagenum">[Pg 31]</span></td></tr>
<tr><td><span class="ind">66.</span> Maia</td><td>2.6454</td><td>1571.6</td><td>0.1750</td>
<td><span class="ilb3">48</span><span class="ilb3">8</span></td>
<td><span class="ilb3">8</span><span class="ilb3">17</span></td>
<td><span class="ilb2">3</span><span class="ilb3">6</span></td></tr>
<tr><td><span class="ind">224.</span> Oceana</td><td>2.6465</td><td>1572.6</td><td>0.0455</td>
<td><span class="ilb3">270</span><span class="ilb3">51</span></td>
<td><span class="ilb3">353</span><span class="ilb3">18</span></td>
<td><span class="ilb2">5</span><span class="ilb3">52</span></td></tr>
<tr><td><span class="ind">253.</span> Mathilde</td><td>2.6469</td><td>1572.9</td><td>0.2620</td>
<td><span class="ilb3">333</span><span class="ilb3">39</span></td>
<td><span class="ilb3">180</span><span class="ilb3">3</span></td>
<td><span class="ilb2">6</span><span class="ilb3">37</span></td></tr>
<tr><td><span class="ind">50.</span> Virginia</td><td>2.6520</td><td>1577.4</td><td>0.2852</td>
<td><span class="ilb3">10</span><span class="ilb3">9</span></td>
<td><span class="ilb3">173</span><span class="ilb3">45</span></td>
<td><span class="ilb2">2</span><span class="ilb3">48</span></td></tr>
<tr><td><span class="ind">144.</span> Vibilia</td><td>2.6530</td><td>1578.4</td><td>0.2348</td>
<td><span class="ilb3">7</span><span class="ilb3">9</span></td>
<td><span class="ilb3">76</span><span class="ilb3">47</span></td>
<td><span class="ilb2">4</span><span class="ilb3">48</span></td></tr>
<tr><td><span class="ind">85.</span> Io</td><td>2.6539</td><td>1579.2</td><td>0.1911</td>
<td><span class="ilb3">322</span><span class="ilb3">35</span></td>
<td><span class="ilb3">203</span><span class="ilb3">56</span></td>
<td><span class="ilb2">11</span><span class="ilb3">53</span></td></tr>
<tr><td><span class="ind">26.</span> Proserpine</td><td>2.6561</td><td>1581.1</td><td>0.0873</td>
<td><span class="ilb3">236</span><span class="ilb3">25</span></td>
<td><span class="ilb3">45</span><span class="ilb3">55</span></td>
<td><span class="ilb2">3</span><span class="ilb3">36</span></td></tr>
<tr><td><span class="ind">233.</span> Asterope</td><td>2.6596</td><td>1584.3</td><td>0.1010</td>
<td><span class="ilb3">344</span><span class="ilb3">36</span></td>
<td><span class="ilb3">222</span><span class="ilb3">25</span></td>
<td><span class="ilb2">7</span><span class="ilb3">39</span></td></tr>
<tr><td><span class="ind">102.</span> Miriam</td><td>2.6619</td><td>1586.3</td><td>0.3035</td>
<td><span class="ilb3">354</span><span class="ilb3">39</span></td>
<td><span class="ilb3">211</span><span class="ilb3">58</span></td>
<td><span class="ilb2">5</span><span class="ilb3">4</span></td></tr>
<tr><td><span class="ind">240.</span> Vanadis</td><td>2.6638</td><td>1588.0</td><td>0.2056</td>
<td><span class="ilb3">51</span><span class="ilb3">53</span></td>
<td><span class="ilb3">114</span><span class="ilb3">54</span></td>
<td><span class="ilb2">2</span><span class="ilb3">6</span></td></tr>
<tr><td><span class="ind">73.</span> Clytie</td><td>2.6652</td><td>1589.3</td><td>0.0419</td>
<td><span class="ilb3">57</span><span class="ilb3">55</span></td>
<td><span class="ilb3">7</span><span class="ilb3">51</span></td>
<td><span class="ilb2">2</span><span class="ilb3">24</span></td></tr>
<tr><td><span class="ind">218.</span> Bianca</td><td>2.6653</td><td>1589.3</td><td>0.1155</td>
<td><span class="ilb3">230</span><span class="ilb3">14</span></td>
<td><span class="ilb3">170</span><span class="ilb3">50</span></td>
<td><span class="ilb2">15</span><span class="ilb3">13</span></td></tr>
<tr><td><span class="ind">141.</span> Lumen</td><td>2.6666</td><td>1590.5</td><td>0.2115</td>
<td><span class="ilb3">13</span><span class="ilb3">43</span></td>
<td><span class="ilb3">319</span><span class="ilb3">7</span></td>
<td><span class="ilb2">11</span><span class="ilb3">57</span></td></tr>
<tr><td><span class="ind">77.</span> Frigga</td><td>2.6680</td><td>1591.8</td><td>0.1318</td>
<td><span class="ilb3">58</span><span class="ilb3">47</span></td>
<td><span class="ilb3">2</span><span class="ilb3">0</span></td>
<td><span class="ilb2">2</span><span class="ilb3">28</span></td></tr>
<tr><td><span class="ind">3.</span> Juno</td><td>2.6683</td><td>1592.0</td><td>0.2579</td>
<td><span class="ilb3">54</span><span class="ilb3">50</span></td>
<td><span class="ilb3">170</span><span class="ilb3">53</span></td>
<td><span class="ilb2">13</span><span class="ilb3">1</span></td></tr>
<tr><td><span class="ind">97.</span> Clotho</td><td>2.6708</td><td>1594.3</td><td>0.2550</td>
<td><span class="ilb3">65</span><span class="ilb3">32</span></td>
<td><span class="ilb3">160</span><span class="ilb3">37</span></td>
<td><span class="ilb2">11</span><span class="ilb3">46</span></td></tr>
<tr><td><span class="ind">75.</span> Eurydice</td><td>2.6720</td><td>1595.3</td><td>0.3060</td>
<td><span class="ilb3">335</span><span class="ilb3">33</span></td>
<td><span class="ilb3">359</span><span class="ilb3">56</span></td>
<td><span class="ilb2">5</span><span class="ilb3">1</span></td></tr>
<tr><td><span class="ind">145.</span> Adeona</td><td>2.6724</td><td>1595.4</td><td>0.1406</td>
<td><span class="ilb3">117</span><span class="ilb3">53</span></td>
<td><span class="ilb3">77</span><span class="ilb3">41</span></td>
<td><span class="ilb2">12</span><span class="ilb3">38</span></td></tr>
<tr><td><span class="ind">204.</span> Callisto</td><td>2.6732</td><td>1596.4</td><td>0.1752</td>
<td><span class="ilb3">257</span><span class="ilb3">45</span></td>
<td><span class="ilb3">205</span><span class="ilb3">40</span></td>
<td><span class="ilb2">8</span><span class="ilb3">19</span></td></tr>
<tr><td><span class="ind">114.</span> Cassandra</td><td>2.6758</td><td>1598.8</td><td>0.1401</td>
<td><span class="ilb3">153</span><span class="ilb3">6</span></td>
<td><span class="ilb3">164</span><span class="ilb3">24</span></td>
<td><span class="ilb2">4</span><span class="ilb3">55</span></td></tr>
<tr><td><span class="ind">201.</span> Penelope</td><td>2.6764</td><td>1599.3</td><td>0.1818</td>
<td><span class="ilb3">334</span><span class="ilb3">21</span></td>
<td><span class="ilb3">157</span><span class="ilb3">5</span></td>
<td><span class="ilb2">5</span><span class="ilb3">44</span></td></tr>
<tr><td><span class="ind">64.</span> Angelina</td><td>2.6816</td><td>1603.9</td><td>0.1271</td>
<td><span class="ilb3">125</span><span class="ilb3">36</span></td>
<td><span class="ilb3">311</span><span class="ilb3">4</span></td>
<td><span class="ilb2">1</span><span class="ilb3">19</span></td></tr>
<tr><td><span class="ind">98.</span> Ianthe</td><td>2.6847</td><td>1606.7</td><td>0.1920</td>
<td><span class="ilb3">148</span><span class="ilb3">52</span></td>
<td><span class="ilb3">354</span><span class="ilb3">7</span></td>
<td><span class="ilb2">15</span><span class="ilb3">32</span></td></tr>
<tr><td><span class="ind">34.</span> Circe</td><td>2.6864</td><td>1608.3</td><td>0.1073</td>
<td><span class="ilb3">148</span><span class="ilb3">41</span></td>
<td><span class="ilb3">184</span><span class="ilb3">46</span></td>
<td><span class="ilb2">5</span><span class="ilb3">27</span></td></tr>
<tr><td><span class="ind">123.</span> Brunhilda</td><td>2.6918</td><td>1613.2</td><td>0.1150</td>
<td><span class="ilb3">72</span><span class="ilb3">57</span></td>
<td><span class="ilb3">308</span><span class="ilb3">28</span></td>
<td><span class="ilb2">6</span><span class="ilb3">27</span></td></tr>
<tr><td><span class="ind">166.</span> Rhodope</td><td>2.6927</td><td>1613.9</td><td>0.2140</td>
<td><span class="ilb3">30</span><span class="ilb3">51</span></td>
<td><span class="ilb3">129</span><span class="ilb3">33</span></td>
<td><span class="ilb2">12</span><span class="ilb3">2</span></td></tr>
<tr><td><span class="ind">109.</span> Felicitas</td><td>2.6950</td><td>1616.0</td><td>0.3002</td>
<td><span class="ilb3">56</span><span class="ilb3">1</span></td>
<td><span class="ilb3">4</span><span class="ilb3">56</span></td>
<td><span class="ilb2">8</span><span class="ilb3">3</span></td></tr>
<tr><td><span class="ind">246.</span> Asporina</td><td>2.6994</td><td>1619.9</td><td>0.1065</td>
<td><span class="ilb3">255</span><span class="ilb3">54</span></td>
<td><span class="ilb3">162</span><span class="ilb3">35</span></td>
<td><span class="ilb2">15</span><span class="ilb3">39</span></td></tr>
<tr><td><span class="ind">58.</span> Concordia</td><td>2.7004</td><td>1620.8</td><td>0.0426</td>
<td><span class="ilb3">189</span><span class="ilb3">10</span></td>
<td><span class="ilb3">161</span><span class="ilb3">20</span></td>
<td><span class="ilb2">5</span><span class="ilb3">2</span></td></tr>
<tr><td><span class="ind">103.</span> Hera</td><td>2.7014</td><td>1621.8</td><td>0.0803</td>
<td><span class="ilb3">321</span><span class="ilb3">3</span></td>
<td><span class="ilb3">136</span><span class="ilb3">18</span></td>
<td><span class="ilb2">5</span><span class="ilb3">24</span></td></tr>
<tr><td><span class="ind">54.</span> Alexandra</td><td>2.7095</td><td>1629.1</td><td>0.2000</td>
<td><span class="ilb3">295</span><span class="ilb3">39</span></td>
<td><span class="ilb3">313</span><span class="ilb3">45</span></td>
<td><span class="ilb2">11</span><span class="ilb3">47</span></td></tr>
<tr><td><span class="ind">226.</span> Weringia</td><td>2.7118</td><td>1631.2</td><td>0.2048</td>
<td><span class="ilb3">284</span><span class="ilb3">46</span></td>
<td><span class="ilb3">135</span><span class="ilb3">18</span></td>
<td><span class="ilb2">15</span><span class="ilb3">50</span></td></tr>
<tr><td><span class="ind">59.</span> Olympia</td><td>2.7124</td><td>1631.7</td><td>0.1189</td>
<td><span class="ilb3">17</span><span class="ilb3">33</span></td>
<td><span class="ilb3">170</span><span class="ilb3">26</span></td>
<td><span class="ilb2">8</span><span class="ilb3">37</span></td></tr>
<tr><td><span class="ind">146.</span> Lucina</td><td>2.7189</td><td>1637.5</td><td>0.0655</td>
<td><span class="ilb3">227</span><span class="ilb3">34</span></td>
<td><span class="ilb3">84</span><span class="ilb3">16</span></td>
<td><span class="ilb2">13</span><span class="ilb3">6</span></td></tr>
<tr><td><span class="ind">45.</span> Eugenia</td><td>2.7205</td><td>1639.0</td><td>0.0811</td>
<td><span class="ilb3">232</span><span class="ilb3">5</span></td>
<td><span class="ilb3">147</span><span class="ilb3">57</span></td>
<td><span class="ilb2">6</span><span class="ilb3">35</span></td></tr>
<tr><td><span class="ind">210.</span> Isabella</td><td>2.7235</td><td>1641.7</td><td>0.1220</td>
<td><span class="ilb3">44</span><span class="ilb3">22</span></td>
<td><span class="ilb3">32</span><span class="ilb3">58</span></td>
<td><span class="ilb2">5</span><span class="ilb3">18</span></td></tr>
<tr><td><span class="ind">187.</span> Lamberta</td><td>2.7272</td><td>1645.0</td><td>0.2391</td>
<td><span class="ilb3">214</span><span class="ilb3">4</span></td>
<td><span class="ilb3">22</span><span class="ilb3">13</span></td>
<td><span class="ilb2">10</span><span class="ilb3">43</span></td></tr>
<tr><td><span class="ind">180.</span> Garumna</td><td>2.7286</td><td>1646.3</td><td>0.1722</td>
<td><span class="ilb3">125</span><span class="ilb3">56</span></td>
<td><span class="ilb3">314</span><span class="ilb3">42</span></td>
<td><span class="ilb2">0</span><span class="ilb3">54</span></td></tr>
<tr><td><span class="ind">160.</span> Una</td><td>2.7287</td><td>1646.4</td><td>0.0624</td>
<td><span class="ilb3">55</span><span class="ilb3">57</span></td>
<td><span class="ilb3">9</span><span class="ilb3">22</span></td>
<td><span class="ilb2">3</span><span class="ilb3">51</span></td></tr>
<tr><td><span class="ind">140.</span> Siwa</td><td>2.7316</td><td>1649.0</td><td>0.2160</td>
<td><span class="ilb3">300</span><span class="ilb3">33</span></td>
<td><span class="ilb3">107</span><span class="ilb3">2</span></td>
<td><span class="ilb2">3</span><span class="ilb3">12</span></td></tr>
<tr><td><span class="ind">110.</span> Lydia</td><td>2.7327</td><td>1650.0</td><td>0.0770</td>
<td><span class="ilb3">336</span><span class="ilb3">49</span></td>
<td><span class="ilb3">57</span><span class="ilb3">10</span></td>
<td><span class="ilb2">6</span><span class="ilb3">0</span></td></tr>
<tr><td><span class="ind">185.</span> Eunice</td><td>2.7372</td><td>1654.1</td><td>0.1292</td>
<td><span class="ilb3">16</span><span class="ilb3">32</span></td>
<td><span class="ilb3">153</span><span class="ilb3">50</span></td>
<td><span class="ilb2">23</span><span class="ilb3">17</span></td></tr>
<tr><td><span class="ind">203.</span> Pompeia</td><td>2.7376</td><td>1654.5</td><td>0.0588</td>
<td><span class="ilb3">42</span><span class="ilb3">51</span></td>
<td><span class="ilb3">348</span><span class="ilb3">37</span></td>
<td><span class="ilb2">3</span><span class="ilb3">13</span></td></tr>
<tr><td><span class="ind">200.</span> Dynamene</td><td>2.7378</td><td>1654.6</td><td>0.1335</td>
<td><span class="ilb3">46</span><span class="ilb3">38</span></td>
<td><span class="ilb3">325</span><span class="ilb3">26</span></td>
<td><span class="ilb2">6</span><span class="ilb3">56</span></td></tr>
<tr><td><span class="ind">197.</span> Arete</td><td>2.7390</td><td>1655.8</td><td>0.1621</td>
<td><span class="ilb3">324</span><span class="ilb3">51</span></td>
<td><span class="ilb3">82</span><span class="ilb3">6</span></td>
<td><span class="ilb2">8</span><span class="ilb3">48</span></td></tr>
<tr><td><span class="ind">206.</span> Hersilia</td><td>2.7399</td><td>1656.5</td><td>0.0389</td>
<td><span class="ilb3">95</span><span class="ilb3">44</span></td>
<td><span class="ilb3">145</span><span class="ilb3">16</span></td>
<td><span class="ilb2">3</span><span class="ilb3">46</span></td></tr>
<tr><td><span class="ind">255.</span> Oppavia</td><td>2.7402</td><td>1656.6</td><td>0.0728</td>
<td><span class="ilb3">169</span><span class="ilb3">15</span></td>
<td><span class="ilb3">14</span><span class="ilb3">6</span></td>
<td><span class="ilb2">9</span><span class="ilb3">33</span></td></tr>
<tr><td><span class="ind">247.</span> Eukrate</td><td>2.7412</td><td>1657.7</td><td>0.2387</td>
<td><span class="ilb3">53</span><span class="ilb3">44</span></td>
<td><span class="ilb3">0</span><span class="ilb3">20</span></td>
<td><span class="ilb2">25</span><span class="ilb3">7</span></td></tr>
<tr><td><span class="ind">38.</span> Leda</td><td>2.7432</td><td>1659.6</td><td>0.1531</td>
<td><span class="ilb3">101</span><span class="ilb3">20</span></td>
<td><span class="ilb3">296</span><span class="ilb3">27</span></td>
<td><span class="ilb2">6</span><span class="ilb3">57</span></td></tr>
<tr><td><span class="ind">125.</span> Liberatrix</td><td>2.7437</td><td>1660.0</td><td>0.0798</td>
<td><span class="ilb3">273</span><span class="ilb3">29</span></td>
<td><span class="ilb3">169</span><span class="ilb3">35</span></td>
<td><span class="ilb2">4</span><span class="ilb3">38</span><span class="pagenum">[Pg 32]</span></td></tr>
<tr><td><span class="ind">173.</span> Ino</td><td>2.7446</td><td>1660.8</td><td>0.2047</td>
<td><span class="ilb3">13</span><span class="ilb3">28</span></td>
<td><span class="ilb3">148</span><span class="ilb3">34</span></td>
<td><span class="ilb2">14</span><span class="ilb3">15</span></td></tr>
<tr><td><span class="ind">36.</span> Atalanta</td><td>2.7452</td><td>1661.3</td><td>0.3023</td>
<td><span class="ilb3">42</span><span class="ilb3">44</span></td>
<td><span class="ilb3">359</span><span class="ilb3">14</span></td>
<td><span class="ilb2">18</span><span class="ilb3">42</span></td></tr>
<tr><td><span class="ind">128.</span> Nemesis</td><td>2.7514</td><td>1666.9</td><td>0.1257</td>
<td><span class="ilb3">16</span><span class="ilb3">34</span></td>
<td><span class="ilb3">76</span><span class="ilb3">31</span></td>
<td><span class="ilb2">6</span><span class="ilb3">16</span></td></tr>
<tr><td><span class="ind">93.</span> Minerva</td><td>2.7537</td><td>1669.0</td><td>0.1405</td>
<td><span class="ilb3">274</span><span class="ilb3">44</span></td>
<td><span class="ilb3">5</span><span class="ilb3">4</span></td>
<td><span class="ilb2">8</span><span class="ilb3">37</span></td></tr>
<tr><td><span class="ind">127.</span> Johanna</td><td>2.7550</td><td>1670.3</td><td>0.0659</td>
<td><span class="ilb3">122</span><span class="ilb3">37</span></td>
<td><span class="ilb3">31</span><span class="ilb3">46</span></td>
<td><span class="ilb2">8</span><span class="ilb3">17</span></td></tr>
<tr><td><span class="ind">71.</span> Niobe</td><td>2.7558</td><td>1671.0</td><td>0.1732</td>
<td><span class="ilb3">221</span><span class="ilb3">17</span></td>
<td><span class="ilb3">316</span><span class="ilb3">30</span></td>
<td><span class="ilb2">23</span><span class="ilb3">19</span></td></tr>
<tr><td><span class="ind">213.</span> Lilæa</td><td>2.7563</td><td>1671.4</td><td>0.1437</td>
<td><span class="ilb3">281</span><span class="ilb3">4</span></td>
<td><span class="ilb3">122</span><span class="ilb3">17</span></td>
<td><span class="ilb2">6</span><span class="ilb3">47</span></td></tr>
<tr><td><span class="ind">55.</span> Pandora</td><td>2.7604</td><td>1675.1</td><td>0.1429</td>
<td><span class="ilb3">10</span><span class="ilb3">36</span></td>
<td><span class="ilb3">10</span><span class="ilb3">56</span></td>
<td><span class="ilb2">7</span><span class="ilb3">14</span></td></tr>
<tr><td><span class="ind">237.</span> Cœlestina</td><td>2.7607</td><td>1675.5</td><td>0.0738</td>
<td><span class="ilb3">282</span><span class="ilb3">49</span></td>
<td><span class="ilb3">84</span><span class="ilb3">33</span></td>
<td><span class="ilb2">9</span><span class="ilb3">46</span></td></tr>
<tr><td><span class="ind">143.</span> Adria</td><td>2.7619</td><td>1676.6</td><td>0.0729</td>
<td><span class="ilb3">222</span><span class="ilb3">27</span></td>
<td><span class="ilb3">333</span><span class="ilb3">42</span></td>
<td><span class="ilb2">11</span><span class="ilb3">30</span></td></tr>
<tr><td><span class="ind">82.</span> Alcmene</td><td>2.7620</td><td>1676.6</td><td>0.2228</td>
<td><span class="ilb3">131</span><span class="ilb3">45</span></td>
<td><span class="ilb3">26</span><span class="ilb3">57</span></td>
<td><span class="ilb2">2</span><span class="ilb3">51</span></td></tr>
<tr><td><span class="ind">116.</span> Sirona</td><td>2.7669</td><td>1681.1</td><td>0.1433</td>
<td><span class="ilb3">152</span><span class="ilb3">47</span></td>
<td><span class="ilb3">64</span><span class="ilb3">26</span></td>
<td><span class="ilb2">3</span><span class="ilb3">35</span></td></tr>
<tr><td><span class="ind">1.</span> Ceres</td><td>2.7673</td><td>1681.4</td><td>0.0763</td>
<td><span class="ilb3">149</span><span class="ilb3">38</span></td>
<td><span class="ilb3">80</span><span class="ilb3">47</span></td>
<td><span class="ilb2">10</span><span class="ilb3">37</span></td></tr>
<tr><td><span class="ind">88.</span> Thisbe</td><td>2.7673</td><td>1681.5</td><td>0.1632</td>
<td><span class="ilb3">308</span><span class="ilb3">34</span></td>
<td><span class="ilb3">277</span><span class="ilb3">54</span></td>
<td><span class="ilb2">16</span><span class="ilb3">11</span></td></tr>
<tr><td><span class="ind">215.</span> Œnone</td><td>2.7679</td><td>1682.0</td><td>0.0390</td>
<td><span class="ilb3">346</span><span class="ilb3">24</span></td>
<td><span class="ilb3">25</span><span class="ilb3">25</span></td>
<td><span class="ilb2">1</span><span class="ilb3">44</span></td></tr>
<tr><td><span class="ind">2.</span> Pallas</td><td>2.7680</td><td>1682.1</td><td>0.2408</td>
<td><span class="ilb3">122</span><span class="ilb3">12</span></td>
<td><span class="ilb3">172</span><span class="ilb3">45</span></td>
<td><span class="ilb2">34</span><span class="ilb3">44</span></td></tr>
<tr><td><span class="ind">39.</span> Lætitia</td><td>2.7680</td><td>1682.1</td><td>0.1142</td>
<td><span class="ilb3">3</span><span class="ilb3">8</span></td>
<td><span class="ilb3">157</span><span class="ilb3">15</span></td>
<td><span class="ilb2">10</span><span class="ilb3">22</span></td></tr>
<tr><td><span class="ind">41.</span> Daphne</td><td>2.7688</td><td>1682.8</td><td>0.2674</td>
<td><span class="ilb3">220</span><span class="ilb3">33</span></td>
<td><span class="ilb3">179</span><span class="ilb3">8</span></td>
<td><span class="ilb2">15</span><span class="ilb3">58</span></td></tr>
<tr><td><span class="ind">177.</span> Irma</td><td>2.7695</td><td>1683.5</td><td>0.2370</td>
<td><span class="ilb3">22</span><span class="ilb3">6</span></td>
<td><span class="ilb3">349</span><span class="ilb3">17</span></td>
<td><span class="ilb2">1</span><span class="ilb3">27</span></td></tr>
<tr><td><span class="ind">148.</span> Gallia</td><td>2.7710</td><td>1684.8</td><td>0.1855</td>
<td><span class="ilb3">36</span><span class="ilb3">7</span></td>
<td><span class="ilb3">145</span><span class="ilb3">13</span></td>
<td><span class="ilb2">25</span><span class="ilb3">21</span></td></tr>
<tr><td><span class="ind">267.</span> Tirza</td><td>2.7742</td><td>1687.6</td><td>0.0986</td>
<td><span class="ilb3">264</span><span class="ilb3">5</span></td>
<td><span class="ilb3">73</span><span class="ilb3">59</span></td>
<td><span class="ilb2">6</span><span class="ilb3">2</span></td></tr>
<tr><td><span class="ind">74.</span> Galatea</td><td>2.7770</td><td>1690.3</td><td>0.2392</td>
<td><span class="ilb3">8</span><span class="ilb3">18</span></td>
<td><span class="ilb3">197</span><span class="ilb3">51</span></td>
<td><span class="ilb2">4</span><span class="ilb3">0</span></td></tr>
<tr><td><span class="ind">205.</span> Martha</td><td>2.7771</td><td>1690.4</td><td>0.1752</td>
<td><span class="ilb3">21</span><span class="ilb3">54</span></td>
<td><span class="ilb3">212</span><span class="ilb3">12</span></td>
<td><span class="ilb2">10</span><span class="ilb3">40</span></td></tr>
<tr><td><span class="ind">139.</span> Juewa</td><td>2.7793</td><td>1692.4</td><td>0.1773</td>
<td><span class="ilb3">164</span><span class="ilb3">34</span></td>
<td><span class="ilb3">2</span><span class="ilb3">21</span></td>
<td><span class="ilb2">10</span><span class="ilb3">57</span></td></tr>
<tr><td><span class="ind">28.</span> Bellona</td><td>2.7797</td><td>1692.7</td><td>0.1491</td>
<td><span class="ilb3">124</span><span class="ilb3">1</span></td>
<td><span class="ilb3">144</span><span class="ilb3">37</span></td>
<td><span class="ilb2">9</span><span class="ilb3">22</span></td></tr>
<tr><td><span class="ind">68.</span> Leto</td><td>2.7805</td><td>1693.5</td><td>0.1883</td>
<td><span class="ilb3">345</span><span class="ilb3">14</span></td>
<td><span class="ilb3">45</span><span class="ilb3">1</span></td>
<td><span class="ilb2">7</span><span class="ilb3">58</span></td></tr>
<tr><td><span class="ind">216.</span> Cleopatra</td><td>2.7964</td><td>1708.0</td><td>0.2492</td>
<td><span class="ilb3">328</span><span class="ilb3">15</span></td>
<td><span class="ilb3">215</span><span class="ilb3">49</span></td>
<td><span class="ilb2">13</span><span class="ilb3">2</span></td></tr>
<tr><td><span class="ind">99.</span> Dike</td><td>2.7966</td><td>1708.3</td><td>0.2384</td>
<td><span class="ilb3">240</span><span class="ilb3">36</span></td>
<td><span class="ilb3">41</span><span class="ilb3">44</span></td>
<td><span class="ilb2">13</span><span class="ilb3">53</span></td></tr>
<tr><td><span class="ind">236.</span> Honoria</td><td>2.7993</td><td>1710.7</td><td>0.1893</td>
<td><span class="ilb3">356</span><span class="ilb3">59</span></td>
<td><span class="ilb3">186</span><span class="ilb3">27</span></td>
<td><span class="ilb2">7</span><span class="ilb3">37</span></td></tr>
<tr><td><span class="ind">183.</span> Istria</td><td>2.8024</td><td>1713.4</td><td>0.3530</td>
<td><span class="ilb3">45</span><span class="ilb3">0</span></td>
<td><span class="ilb3">142</span><span class="ilb3">46</span></td>
<td><span class="ilb2">26</span><span class="ilb3">33</span></td></tr>
<tr><td><span class="ind">266.</span> Aline</td><td>2.8078</td><td>1718.5</td><td>0.1573</td>
<td><span class="ilb3">23</span><span class="ilb3">52</span></td>
<td><span class="ilb3">236</span><span class="ilb3">18</span></td>
<td><span class="ilb2">13</span><span class="ilb3">20</span></td></tr>
<tr><td><span class="ind">188.</span> Menippe</td><td>2.8211</td><td>1730.7</td><td>0.2173</td>
<td><span class="ilb3">309</span><span class="ilb3">38</span></td>
<td><span class="ilb3">241</span><span class="ilb3">44</span></td>
<td><span class="ilb2">11</span><span class="ilb3">21</span></td></tr>
<tr><td><span class="ind">167.</span> Urda</td><td>2.8533</td><td>1760.4</td><td>0.0340</td>
<td><span class="ilb3">296</span><span class="ilb3">4</span></td>
<td><span class="ilb3">166</span><span class="ilb3">28</span></td>
<td><span class="ilb2">2</span><span class="ilb3">11</span></td></tr>
<tr><td><span class="ind">81.</span> Terpsichore</td><td>2.8580</td><td>1764.8</td><td>0.2080</td>
<td><span class="ilb3">49</span><span class="ilb3">1</span></td>
<td><span class="ilb3">2</span><span class="ilb3">25</span></td>
<td><span class="ilb2">7</span><span class="ilb3">55</span></td></tr>
<tr><td><span class="ind">174.</span> Phædra</td><td>2.8600</td><td>1766.6</td><td>0.1492</td>
<td><span class="ilb3">253</span><span class="ilb3">12</span></td>
<td><span class="ilb3">328</span><span class="ilb3">49</span></td>
<td><span class="ilb2">12</span><span class="ilb3">9</span></td></tr>
<tr><td><span class="ind">243.</span> Ida</td><td>2.8610</td><td>1767.5</td><td>0.0419</td>
<td><span class="ilb3">71</span><span class="ilb3">22</span></td>
<td><span class="ilb3">326</span><span class="ilb3">21</span></td>
<td><span class="ilb2">1</span><span class="ilb3">10</span></td></tr>
<tr><td><span class="ind">242.</span> Kriemhild</td><td>2.8623</td><td>1768.7</td><td>0.1219</td>
<td><span class="ilb3">123</span><span class="ilb3">1</span></td>
<td><span class="ilb3">207</span><span class="ilb3">57</span></td>
<td><span class="ilb2">11</span><span class="ilb3">17</span></td></tr>
<tr><td><span class="ind">129.</span> Antigone</td><td>2.8678</td><td>1773.9</td><td>0.2126</td>
<td><span class="ilb3">242</span><span class="ilb3">4</span></td>
<td><span class="ilb3">137</span><span class="ilb3">37</span></td>
<td><span class="ilb2">12</span><span class="ilb3">10</span></td></tr>
<tr><td><span class="ind">217.</span> Eudora</td><td>2.8690</td><td>1774.9</td><td>0.3068</td>
<td><span class="ilb3">314</span><span class="ilb3">41</span></td>
<td><span class="ilb3">164</span><span class="ilb3">10</span></td>
<td><span class="ilb2">10</span><span class="ilb3">19</span></td></tr>
<tr><td><span class="ind">158.</span> Coronis</td><td>2.8714</td><td>1777.2</td><td>0.0545</td>
<td><span class="ilb3">56</span><span class="ilb3">56</span></td>
<td><span class="ilb3">281</span><span class="ilb3">30</span></td>
<td><span class="ilb2">1</span><span class="ilb3">0</span></td></tr>
<tr><td><span class="ind">33.</span> Polyhymnia</td><td>2.8751</td><td>1780.7</td><td>0.3349</td>
<td><span class="ilb3">342</span><span class="ilb3">59</span></td>
<td><span class="ilb3">9</span><span class="ilb3">19</span></td>
<td><span class="ilb2">1</span><span class="ilb3">56</span></td></tr>
<tr><td><span class="ind">195.</span> Euryclea</td><td>2.8790</td><td>1784.2</td><td>0.0471</td>
<td><span class="ilb3">115</span><span class="ilb3">48</span></td>
<td><span class="ilb3">7</span><span class="ilb3">57</span></td>
<td><span class="ilb2">7</span><span class="ilb3">1</span></td></tr>
<tr><td><span class="ind">235.</span> Caroline</td><td>2.8795</td><td>1784.7</td><td>0.0595</td>
<td><span class="ilb3">268</span><span class="ilb3">29</span></td>
<td><span class="ilb3">66</span><span class="ilb3">35</span></td>
<td><span class="ilb2">9</span><span class="ilb3">4</span></td></tr>
<tr><td><span class="ind">47.</span> Aglaia</td><td>2.8819</td><td>1786.9</td><td>0.1317</td>
<td><span class="ilb3">312</span><span class="ilb3">40</span></td>
<td><span class="ilb3">40</span><span class="ilb3">20</span></td>
<td><span class="ilb2">5</span><span class="ilb3">1</span></td></tr>
<tr><td><span class="ind">208.</span> Lachrymosa</td><td>2.8926</td><td>1796.9</td><td>0.0149</td>
<td><span class="ilb3">127</span><span class="ilb3">52</span></td>
<td><span class="ilb3">5</span><span class="ilb3">43</span></td>
<td><span class="ilb2">1</span><span class="ilb3">48</span></td></tr>
<tr><td><span class="ind">191.</span> Kolga</td><td>2.8967</td><td>1800.8</td><td>0.0876</td>
<td><span class="ilb3">23</span><span class="ilb3">21</span></td>
<td><span class="ilb3">159</span><span class="ilb3">47</span></td>
<td><span class="ilb2">11</span><span class="ilb3">29</span></td></tr>
<tr><td><span class="ind">22.</span> Calliope</td><td>2.9090</td><td>1801.0</td><td>0.0193</td>
<td><span class="ilb3">62</span><span class="ilb3">43</span></td>
<td><span class="ilb3">4</span><span class="ilb3">47</span></td>
<td><span class="ilb2">1</span><span class="ilb3">45</span></td></tr>
<tr><td><span class="ind">155.</span> Scylla</td><td>2.9127</td><td>1815.7</td><td>0.2559</td>
<td><span class="ilb3">82</span><span class="ilb3">1</span></td>
<td><span class="ilb3">42</span><span class="ilb3">52</span></td>
<td><span class="ilb2">14</span><span class="ilb3">4</span></td></tr>
<tr><td><span class="ind">238.</span> Hypatia</td><td>2.9163</td><td>1819.0</td><td>0.0946</td>
<td><span class="ilb3">32</span><span class="ilb3">18</span></td>
<td><span class="ilb3">184</span><span class="ilb3">26</span></td>
<td><span class="ilb2">12</span><span class="ilb3">28</span></td></tr>
<tr><td><span class="ind">231.</span> Vindobona</td><td>2.9192</td><td>1821.7</td><td>0.1537</td>
<td><span class="ilb3">253</span><span class="ilb3">23</span></td>
<td><span class="ilb3">352</span><span class="ilb3">49</span></td>
<td><span class="ilb2">5</span><span class="ilb3">10</span><span class="pagenum">[Pg 33]</span></td></tr>
<tr><td><span class="ind">16.</span> Psyche</td><td>2.9210</td><td>1823.4</td><td>0.1392</td>
<td><span class="ilb3">15</span><span class="ilb3">9</span></td>
<td><span class="ilb3">150</span><span class="ilb3">36</span></td>
<td><span class="ilb2">3</span><span class="ilb3">4</span></td></tr>
<tr><td><span class="ind">179.</span> Clytemnestra</td><td>2.9711</td><td>1870.6</td><td>0.1133</td>
<td><span class="ilb3">355</span><span class="ilb3">39</span></td>
<td><span class="ilb3">253</span><span class="ilb3">13</span></td>
<td><span class="ilb2">7</span><span class="ilb3">47</span></td></tr>
<tr><td><span class="ind">239.</span> Adrastea</td><td>2.9736</td><td>1873.0</td><td>0.2279</td>
<td><span class="ilb3">26</span><span class="ilb3">1</span></td>
<td><span class="ilb3">181</span><span class="ilb3">34</span></td>
<td><span class="ilb2">6</span><span class="ilb3">4</span></td></tr>
<tr><td><span class="ind">69.</span> Hesperia</td><td>2.9779</td><td>1877.0</td><td>0.1712</td>
<td><span class="ilb3">108</span><span class="ilb3">19</span></td>
<td><span class="ilb3">187</span><span class="ilb3">12</span></td>
<td><span class="ilb2">8</span><span class="ilb3">28</span></td></tr>
<tr><td><span class="ind">150.</span> Nuwa</td><td>2.9785</td><td>1877.5</td><td>0.1307</td>
<td><span class="ilb3">355</span><span class="ilb3">27</span></td>
<td><span class="ilb3">207</span><span class="ilb3">35</span></td>
<td><span class="ilb2">2</span><span class="ilb3">9</span></td></tr>
<tr><td><span class="ind">61.</span> Danaë</td><td>2.9855</td><td>1884.2</td><td>0.1615</td>
<td><span class="ilb3">344</span><span class="ilb3">4</span></td>
<td><span class="ilb3">334</span><span class="ilb3">11</span></td>
<td><span class="ilb2">18</span><span class="ilb3">14</span></td></tr>
<tr><td><span class="ind">117.</span> Lomia</td><td>2.9907</td><td>1889.1</td><td>0.0229</td>
<td><span class="ilb3">48</span><span class="ilb3">46</span></td>
<td><span class="ilb3">349</span><span class="ilb3">39</span></td>
<td><span class="ilb2">14</span><span class="ilb3">58</span></td></tr>
<tr><td><span class="ind">35.</span> Leucothea</td><td>2.9923</td><td>1890.6</td><td>0.2237</td>
<td><span class="ilb3">202</span><span class="ilb3">25</span></td>
<td><span class="ilb3">355</span><span class="ilb3">49</span></td>
<td><span class="ilb2">8</span><span class="ilb3">12</span></td></tr>
<tr><td><span class="ind">263.</span> Dresda</td><td>3.0120</td><td>1909.3</td><td>0.3051</td>
<td><span class="ilb3">308</span><span class="ilb3">49</span></td>
<td><span class="ilb3">217</span><span class="ilb3">56</span></td>
<td><span class="ilb2">1</span><span class="ilb3">27</span></td></tr>
<tr><td><span class="ind">221.</span> Eos</td><td>3.0134</td><td>1910.7</td><td>0.1028</td>
<td><span class="ilb3">330</span><span class="ilb3">58</span></td>
<td><span class="ilb3">142</span><span class="ilb3">35</span></td>
<td><span class="ilb2">10</span><span class="ilb3">51</span></td></tr>
<tr><td><span class="ind">162.</span> Laurentia</td><td>3.0241</td><td>1920.8</td><td>0.1726</td>
<td><span class="ilb3">145</span><span class="ilb3">52</span></td>
<td><span class="ilb3">38</span><span class="ilb3">15</span></td>
<td><span class="ilb2">6</span><span class="ilb3">4</span></td></tr>
<tr><td><span class="ind">156.</span> Xantippe</td><td>3.0375</td><td>1933.7</td><td>0.2637</td>
<td><span class="ilb3">155</span><span class="ilb3">58</span></td>
<td><span class="ilb3">246</span><span class="ilb3">11</span></td>
<td><span class="ilb2">7</span><span class="ilb3">29</span></td></tr>
<tr><td><span class="ind">241.</span> Germania</td><td>3.0381</td><td>1934.0</td><td>0.1013</td>
<td><span class="ilb3">340</span><span class="ilb3">7</span></td>
<td><span class="ilb3">272</span><span class="ilb3">28</span></td>
<td><span class="ilb2">5</span><span class="ilb3">30</span></td></tr>
<tr><td><span class="ind">256.</span> Walpurga</td><td>3.0450</td><td>1940.8</td><td>0.1180</td>
<td><span class="ilb3">240</span><span class="ilb3">17</span></td>
<td><span class="ilb3">183</span><span class="ilb3">35</span></td>
<td><span class="ilb2">12</span><span class="ilb3">44</span></td></tr>
<tr><td><span class="ind">211.</span> Isolda</td><td>3.0464</td><td>1942.2</td><td>0.1541</td>
<td><span class="ilb3">74</span><span class="ilb3">12</span></td>
<td><span class="ilb3">265</span><span class="ilb3">29</span></td>
<td><span class="ilb2">3</span><span class="ilb3">51</span></td></tr>
<tr><td><span class="ind">96.</span> Ægle</td><td>3.0497</td><td>1945.3</td><td>0.1405</td>
<td><span class="ilb3">163</span><span class="ilb3">10</span></td>
<td><span class="ilb3">322</span><span class="ilb3">50</span></td>
<td><span class="ilb2">16</span><span class="ilb3">7</span></td></tr>
<tr><td><span class="ind">257.</span> Silesia</td><td>3.0572</td><td>1952.5</td><td>0.2555</td>
<td><span class="ilb3">54</span><span class="ilb3">16</span></td>
<td><span class="ilb3">34</span><span class="ilb3">31</span></td>
<td><span class="ilb2">4</span><span class="ilb3">41</span></td></tr>
<tr><td><span class="ind">133.</span> Cyrene</td><td>3.0578</td><td>1953.0</td><td>0.1398</td>
<td><span class="ilb3">247</span><span class="ilb3">13</span></td>
<td><span class="ilb3">321</span><span class="ilb3">8</span></td>
<td><span class="ilb2">7</span><span class="ilb3">14</span></td></tr>
<tr><td><span class="ind">95.</span> Arethusa</td><td>3.0712</td><td>1965.9</td><td>0.1447</td>
<td><span class="ilb3">32</span><span class="ilb3">58</span></td>
<td><span class="ilb3">244</span><span class="ilb3">17</span></td>
<td><span class="ilb2">12</span><span class="ilb3">54</span></td></tr>
<tr><td><span class="ind">202.</span> Chryseis</td><td>3.0777</td><td>1972.1</td><td>0.0959</td>
<td><span class="ilb3">129</span><span class="ilb3">46</span></td>
<td><span class="ilb3">137</span><span class="ilb3">47</span></td>
<td><span class="ilb2">8</span><span class="ilb3">48</span></td></tr>
<tr><td><span class="ind">268.</span> ——</td><td>3.0852</td><td>1973.9</td><td>0.1285</td>
<td><span class="ilb3">184</span><span class="ilb3">48</span></td>
<td><span class="ilb3">121</span><span class="ilb3">53</span></td>
<td><span class="ilb2">2</span><span class="ilb3">25</span></td></tr>
<tr><td><span class="ind">100.</span> Hecate</td><td>3.0904</td><td>1984.3</td><td>0.1639</td>
<td><span class="ilb3">308</span><span class="ilb3">3</span></td>
<td><span class="ilb3">128</span><span class="ilb3">12</span></td>
<td><span class="ilb2">6</span><span class="ilb3">23</span></td></tr>
<tr><td><span class="ind">49.</span> Pales</td><td>3.0908</td><td>1984.7</td><td>0.2330</td>
<td><span class="ilb3">31</span><span class="ilb3">15</span></td>
<td><span class="ilb3">290</span><span class="ilb3">40</span></td>
<td><span class="ilb2">3</span><span class="ilb3">8</span></td></tr>
<tr><td><span class="ind">223.</span> Rosa</td><td>3.0940</td><td>1987.9</td><td>0.1186</td>
<td><span class="ilb3">102</span><span class="ilb3">48</span></td>
<td><span class="ilb3">49</span><span class="ilb3">0</span></td>
<td><span class="ilb2">1</span><span class="ilb3">59</span></td></tr>
<tr><td><span class="ind">52.</span> Europa</td><td>3.0955</td><td>1988.0</td><td>0.1098</td>
<td><span class="ilb3">106</span><span class="ilb3">57</span></td>
<td><span class="ilb3">129</span><span class="ilb3">40</span></td>
<td><span class="ilb2">7</span><span class="ilb3">27</span></td></tr>
<tr><td><span class="ind">245.</span> Vera</td><td>3.0985</td><td>1992.1</td><td>0.1950</td>
<td><span class="ilb3">25</span><span class="ilb3">29</span></td>
<td><span class="ilb3">62</span><span class="ilb3">37</span></td>
<td><span class="ilb2">5</span><span class="ilb3">10</span></td></tr>
<tr><td><span class="ind">86.</span> Semele</td><td>3.1015</td><td>1995.1</td><td>0.2193</td>
<td><span class="ilb3">29</span><span class="ilb3">10</span></td>
<td><span class="ilb3">87</span><span class="ilb3">45</span></td>
<td><span class="ilb2">4</span><span class="ilb3">47</span></td></tr>
<tr><td><span class="ind">159.</span> Æmilia</td><td>3.1089</td><td>2002.2</td><td>0.1034</td>
<td><span class="ilb3">101</span><span class="ilb3">22</span></td>
<td><span class="ilb3">135</span><span class="ilb3">9</span></td>
<td><span class="ilb2">6</span><span class="ilb3">4</span></td></tr>
<tr><td><span class="ind">48.</span> Doris</td><td>3.1127</td><td>2005.9</td><td>0.0649</td>
<td><span class="ilb3">70</span><span class="ilb3">33</span></td>
<td><span class="ilb3">184</span><span class="ilb3">55</span></td>
<td><span class="ilb2">6</span><span class="ilb3">31</span></td></tr>
<tr><td><span class="ind">196.</span> Philomela</td><td>3.1137</td><td>2006.8</td><td>0.0118</td>
<td><span class="ilb3">309</span><span class="ilb3">19</span></td>
<td><span class="ilb3">73</span><span class="ilb3">24</span></td>
<td><span class="ilb2">7</span><span class="ilb3">16</span></td></tr>
<tr><td><span class="ind">130.</span> Electra</td><td>3.1145</td><td>2007.7</td><td>0.2132</td>
<td><span class="ilb3">20</span><span class="ilb3">34</span></td>
<td><span class="ilb3">146</span><span class="ilb3">6</span></td>
<td><span class="ilb2">22</span><span class="ilb3">57</span></td></tr>
<tr><td><span class="ind">212.</span> Medea</td><td>3.1157</td><td>2008.8</td><td>0.1013</td>
<td><span class="ilb3">56</span><span class="ilb3">18</span></td>
<td><span class="ilb3">315</span><span class="ilb3">16</span></td>
<td><span class="ilb2">4</span><span class="ilb3">16</span></td></tr>
<tr><td><span class="ind">120.</span> Lachesis</td><td>3.1211</td><td>2014.0</td><td>0.0475</td>
<td><span class="ilb3">214</span><span class="ilb3">0</span></td>
<td><span class="ilb3">342</span><span class="ilb3">51</span></td>
<td><span class="ilb2">7</span><span class="ilb3">1</span></td></tr>
<tr><td><span class="ind">181.</span> Eucharis</td><td>3.1226</td><td>2015.4</td><td>0.2205</td>
<td><span class="ilb3">95</span><span class="ilb3">25</span></td>
<td><span class="ilb3">144</span><span class="ilb3">45</span></td>
<td><span class="ilb2">18</span><span class="ilb3">38</span></td></tr>
<tr><td><span class="ind">62.</span> Erato</td><td>3.1241</td><td>2016.9</td><td>0.1756</td>
<td><span class="ilb3">39</span><span class="ilb3">0</span></td>
<td><span class="ilb3">125</span><span class="ilb3">46</span></td>
<td><span class="ilb2">2</span><span class="ilb3">12</span></td></tr>
<tr><td><span class="ind">222.</span> Lucia</td><td>3.1263</td><td>2019.0</td><td>0.1453</td>
<td><span class="ilb3">258</span><span class="ilb3">2</span></td>
<td><span class="ilb3">80</span><span class="ilb3">11</span></td>
<td><span class="ilb2">2</span><span class="ilb3">11</span></td></tr>
<tr><td><span class="ind">137.</span> Melibœa</td><td>3.1264</td><td>2019.1</td><td>0.2074</td>
<td><span class="ilb3">307</span><span class="ilb3">58</span></td>
<td><span class="ilb3">204</span><span class="ilb3">22</span></td>
<td><span class="ilb2">13</span><span class="ilb3">22</span></td></tr>
<tr><td><span class="ind">165.</span> Loreley</td><td>3.1269</td><td>2019.6</td><td>0.0734</td>
<td><span class="ilb3">223</span><span class="ilb3">50</span></td>
<td><span class="ilb3">304</span><span class="ilb3">6</span></td>
<td><span class="ilb2">10</span><span class="ilb3">12</span></td></tr>
<tr><td><span class="ind">251.</span> Sophia</td><td>3.1315</td><td>2024.1</td><td>0.1243</td>
<td><span class="ilb3">77</span><span class="ilb3">7</span></td>
<td><span class="ilb3">157</span><span class="ilb3">6</span></td>
<td><span class="ilb2">10</span><span class="ilb3">20</span></td></tr>
<tr><td><span class="ind">24.</span> Themis</td><td>3.1357</td><td>2028.1</td><td>0.1242</td>
<td><span class="ilb3">144</span><span class="ilb3">8</span></td>
<td><span class="ilb3">35</span><span class="ilb3">49</span></td>
<td><span class="ilb2">0</span><span class="ilb3">49</span></td></tr>
<tr><td><span class="ind">152.</span> Atala</td><td>3.1362</td><td>2028.6</td><td>0.0862</td>
<td><span class="ilb3">84</span><span class="ilb3">23</span></td>
<td><span class="ilb3">41</span><span class="ilb3">29</span></td>
<td><span class="ilb2">12</span><span class="ilb3">12</span></td></tr>
<tr><td><span class="ind">10.</span> Hygeia</td><td>3.1366</td><td>2029.1</td><td>0.1156</td>
<td><span class="ilb3">237</span><span class="ilb3">2</span></td>
<td><span class="ilb3">285</span><span class="ilb3">38</span></td>
<td><span class="ilb2">3</span><span class="ilb3">49</span></td></tr>
<tr><td><span class="ind">259.</span> Aletheia</td><td>3.1369</td><td>2029.3</td><td>0.1176</td>
<td><span class="ilb3">241</span><span class="ilb3">45</span></td>
<td><span class="ilb3">88</span><span class="ilb3">32</span></td>
<td><span class="ilb2">10</span><span class="ilb3">40</span></td></tr>
<tr><td><span class="ind">227.</span> Philosophia</td><td>3.1393</td><td>2031.6</td><td>0.2131</td>
<td><span class="ilb3">226</span><span class="ilb3">23</span></td>
<td><span class="ilb3">330</span><span class="ilb3">52</span></td>
<td><span class="ilb2">9</span><span class="ilb3">16</span></td></tr>
<tr><td><span class="ind">147.</span> Protogenea</td><td>3.1393</td><td>2031.6</td><td>0.0247</td>
<td><span class="ilb3">25</span><span class="ilb3">38</span></td>
<td><span class="ilb3">251</span><span class="ilb3">16</span></td>
<td><span class="ilb2">1</span><span class="ilb3">54</span></td></tr>
<tr><td><span class="ind">171.</span> Ophelia</td><td>3.1432</td><td>2035.4</td><td>0.1168</td>
<td><span class="ilb3">143</span><span class="ilb3">59</span></td>
<td><span class="ilb3">101</span><span class="ilb3">10</span></td>
<td><span class="ilb2">2</span><span class="ilb3">34</span></td></tr>
<tr><td><span class="ind">209.</span> Dido</td><td>3.1436</td><td>2035.9</td><td>0.0637</td>
<td><span class="ilb3">257</span><span class="ilb3">33</span></td>
<td><span class="ilb3">2</span><span class="ilb3">0</span></td>
<td><span class="ilb2">7</span><span class="ilb3">15</span></td></tr>
<tr><td><span class="ind">31.</span> Euphrosyne</td><td>3.1468</td><td>2039.0</td><td>0.2228</td>
<td><span class="ilb3">93</span><span class="ilb3">26</span></td>
<td><span class="ilb3">31</span><span class="ilb3">31</span></td>
<td><span class="ilb2">26</span><span class="ilb3">27</span></td></tr>
<tr><td><span class="ind">90.</span> Antiope</td><td>3.1475</td><td>2039.7</td><td>0.1645</td>
<td><span class="ilb3">301</span><span class="ilb3">15</span></td>
<td><span class="ilb3">71</span><span class="ilb3">29</span></td>
<td><span class="ilb2">2</span><span class="ilb3">17</span></td></tr>
<tr><td><span class="ind">104.</span> Clymene</td><td>3.1507</td><td>2042.7</td><td>0.1579</td>
<td><span class="ilb3">59</span><span class="ilb3">32</span></td>
<td><span class="ilb3">43</span><span class="ilb3">32</span></td>
<td><span class="ilb2">2</span><span class="ilb3">54</span><span class="pagenum">[Pg 34]</span></td></tr>
<tr><td><span class="ind">57.</span> Mnemosyne</td><td>3.1510</td><td>2043.0</td><td>0.1145</td>
<td><span class="ilb3">53</span><span class="ilb3">25</span></td>
<td><span class="ilb3">200</span><span class="ilb3">2</span></td>
<td><span class="ilb2">15</span><span class="ilb3">12</span></td></tr>
<tr><td><span class="ind">250.</span> Bettina</td><td>3.1524</td><td>2044.3</td><td>0.1302</td>
<td><span class="ilb3">87</span><span class="ilb3">28</span></td>
<td><span class="ilb3">26</span><span class="ilb3">12</span></td>
<td><span class="ilb2">12</span><span class="ilb3">54</span></td></tr>
<tr><td><span class="ind">252.</span> Clementina</td><td>3.1552</td><td>2047.1</td><td>0.0837</td>
<td><span class="ilb3">355</span><span class="ilb3">8</span></td>
<td><span class="ilb3">208</span><span class="ilb3">19</span></td>
<td><span class="ilb2">10</span><span class="ilb3">2</span></td></tr>
<tr><td><span class="ind">94.</span> Aurora</td><td>3.1602</td><td>2052.0</td><td>0.0827</td>
<td><span class="ilb3">48</span><span class="ilb3">46</span></td>
<td><span class="ilb3">4</span><span class="ilb3">9</span></td>
<td><span class="ilb2">8</span><span class="ilb3">4</span></td></tr>
<tr><td><span class="ind">106.</span> Dione</td><td>3.1670</td><td>2058.6</td><td>0.1788</td>
<td><span class="ilb3">25</span><span class="ilb3">57</span></td>
<td><span class="ilb3">63</span><span class="ilb3">14</span></td>
<td><span class="ilb2">4</span><span class="ilb3">38</span></td></tr>
<tr><td><span class="ind">199.</span> Byblis</td><td>3.1777</td><td>2069.0</td><td>0.1687</td>
<td><span class="ilb3">261</span><span class="ilb3">20</span></td>
<td><span class="ilb3">89</span><span class="ilb3">52</span></td>
<td><span class="ilb2">15</span><span class="ilb3">22</span></td></tr>
<tr><td><span class="ind">92.</span> Undina</td><td>3.1851</td><td>2076.3</td><td>0.1024</td>
<td><span class="ilb3">331</span><span class="ilb3">27</span></td>
<td><span class="ilb3">102</span><span class="ilb3">52</span></td>
<td><span class="ilb2">9</span><span class="ilb3">57</span></td></tr>
<tr><td><span class="ind">184.</span> Deiopea</td><td>3.1883</td><td>2079.4</td><td>0.0725</td>
<td><span class="ilb3">169</span><span class="ilb3">22</span></td>
<td><span class="ilb3">336</span><span class="ilb3">18</span></td>
<td><span class="ilb2">1</span><span class="ilb3">12</span></td></tr>
<tr><td><span class="ind">176.</span> Idunna</td><td>3.1906</td><td>2081.6</td><td>0.1641</td>
<td><span class="ilb3">20</span><span class="ilb3">34</span></td>
<td><span class="ilb3">201</span><span class="ilb3">13</span></td>
<td><span class="ilb2">22</span><span class="ilb3">31</span></td></tr>
<tr><td><span class="ind">154.</span> Bertha</td><td>3.1976</td><td>2088.5</td><td>0.0788</td>
<td><span class="ilb3">190</span><span class="ilb3">47</span></td>
<td><span class="ilb3">37</span><span class="ilb3">35</span></td>
<td><span class="ilb2">20</span><span class="ilb3">59</span></td></tr>
<tr><td><span class="ind">108.</span> Hecuba</td><td>3.2113</td><td>2101.0</td><td>0.1005</td>
<td><span class="ilb3">173</span><span class="ilb3">49</span></td>
<td><span class="ilb3">352</span><span class="ilb3">17</span></td>
<td><span class="ilb2">4</span><span class="ilb3">24</span></td></tr>
<tr><td><span class="ind">122.</span> Gerda</td><td>3.2177</td><td>2108.2</td><td>0.0415</td>
<td><span class="ilb3">203</span><span class="ilb3">45</span></td>
<td><span class="ilb3">178</span><span class="ilb3">43</span></td>
<td><span class="ilb2">1</span><span class="ilb3">36</span></td></tr>
<tr><td><span class="ind">168.</span> Sibylla</td><td>3.3765</td><td>2266.2</td><td>0.0707</td>
<td><span class="ilb3">11</span><span class="ilb3">26</span></td>
<td><span class="ilb3">209</span><span class="ilb3">47</span></td>
<td><span class="ilb2">4</span><span class="ilb3">33</span></td></tr>
<tr><td><span class="ind">225.</span> Henrietta</td><td>3.4007</td><td>2277.8</td><td>0.2661</td>
<td><span class="ilb3">299</span><span class="ilb3">13</span></td>
<td><span class="ilb3">200</span><span class="ilb3">45</span></td>
<td><span class="ilb2">20</span><span class="ilb3">45</span></td></tr>
<tr><td><span class="ind">229.</span> Adelinda</td><td>3.4129</td><td>2302.9</td><td>0.1562</td>
<td><span class="ilb3">332</span><span class="ilb3">7</span></td>
<td><span class="ilb3">30</span><span class="ilb3">49</span></td>
<td><span class="ilb2">2</span><span class="ilb3">11</span></td></tr>
<tr><td><span class="ind">76.</span> Freia</td><td>3.4140</td><td>2304.1</td><td>0.1700</td>
<td><span class="ilb3">90</span><span class="ilb3">49</span></td>
<td><span class="ilb3">212</span><span class="ilb3">5</span></td>
<td><span class="ilb2">2</span><span class="ilb3">3</span></td></tr>
<tr><td><span class="ind">260.</span> Huberta</td><td>3.4212</td><td>2311.5</td><td>0.1113</td>
<td><span class="ilb3">313</span><span class="ilb3">22</span></td>
<td><span class="ilb3">168</span><span class="ilb3">48</span></td>
<td><span class="ilb2">6</span><span class="ilb3">18</span></td></tr>
<tr><td><span class="ind">65.</span> Maximiliana</td><td>3.4270</td><td>2317.2</td><td>0.1097</td>
<td><span class="ilb3">260</span><span class="ilb3">36</span></td>
<td><span class="ilb3">158</span><span class="ilb3">50</span></td>
<td><span class="ilb2">3</span><span class="ilb3">29</span></td></tr>
<tr><td><span class="ind">121.</span> Hermione</td><td>3.4535</td><td>2344.2</td><td>0.1255</td>
<td><span class="ilb3">357</span><span class="ilb3">50</span></td>
<td><span class="ilb3">76</span><span class="ilb3">46</span></td>
<td><span class="ilb2">7</span><span class="ilb3">36</span></td></tr>
<tr><td><span class="ind">87.</span> Sylvia</td><td>3.4833</td><td>2374.5</td><td>0.0922</td>
<td><span class="ilb3">333</span><span class="ilb3">48</span></td>
<td><span class="ilb3">75</span><span class="ilb3">49</span></td>
<td><span class="ilb2">10</span><span class="ilb3">55</span></td></tr>
<tr><td><span class="ind">107.</span> Camilla</td><td>3.4847</td><td>2376.0</td><td>0.0756</td>
<td><span class="ilb3">115</span><span class="ilb3">53</span></td>
<td><span class="ilb3">176</span><span class="ilb3">18</span></td>
<td><span class="ilb2">9</span><span class="ilb3">54</span></td></tr>
<tr><td><span class="ind">175.</span> Andromache</td><td>3.5071</td><td>2399.0</td><td>0.3476</td>
<td><span class="ilb3">293</span><span class="ilb3">0</span></td>
<td><span class="ilb3">23</span><span class="ilb3">35</span></td>
<td><span class="ilb2">3</span><span class="ilb3">46</span></td></tr>
<tr><td><span class="ind">190.</span> Ismene</td><td>3.9471</td><td>2864.3</td><td>0.1634</td>
<td><span class="ilb3">105</span><span class="ilb3">39</span></td>
<td><span class="ilb3">177</span><span class="ilb3">0</span></td>
<td><span class="ilb2">6</span><span class="ilb3">7</span></td></tr>
<tr><td><span class="ind">153.</span> Hilda</td><td>3.9523</td><td>2869.9</td><td>0.1721</td>
<td><span class="ilb3">285</span><span class="ilb3">47</span></td>
<td><span class="ilb3">228</span><span class="ilb3">20</span></td>
<td><span class="ilb2">7</span><span class="ilb3">55</span></td></tr>
</table>
<hr class="chap" />
<p><span class="pagenum">[Pg 35]<br />[Pg 36]</span></p>
<h2><a name="PART_II" id="PART_II">PART II.</a></h2>
<p><span class="pagenum">[Pg 37]</span></p>
<h2><a name="DISCUSSION_OF_THE_FACTS_IN_TABLE_II" id="DISCUSSION_OF_THE_FACTS_IN_TABLE_II">DISCUSSION OF THE FACTS IN TABLE II.</a></h2>
<h3><a id="Extent_of_the_Zone"></a>1. Extent of the Zone.</h3>
<p>In Table II. the unit of column <i>a</i> is the earth's mean distance from
the sun, or ninety-three million miles. On this scale the breadth of the
zone is 1.8196. Or, if we estimate the breadth from the perihelion of
Æthra (1.612) to the aphelion of Andromache (4.726), it is 3.114,—more
than three times the radius of the earth's orbit. A very remarkable
characteristic of the group is the interlacing or intertwining of
orbits. "One fact," says D'Arrest, "seems above all to confirm the idea
of an intimate relation between all the minor planets; it is, that if
their orbits are figured under the form of material rings, these rings
will be found so entangled that it would be possible, by means of one
among them taken at hazard, to lift up all the rest."<a name="FNanchor_6" id="FNanchor_6"></a><a href="#Footnote_6" class="fnanchor">[6]</a> Our present
knowledge of this wide and complicated cluster is the result of a vast
amount, not only of observations, but also of mathematical labor. In
view, however, of the perturbations of these bodies by the larger
planets, and especially by Jupiter, it is easy to see that the
discussion<span class="pagenum">[Pg 38]</span> of their motions must present a field of investigation
practically boundless.</p>
<p>While the known minor planets were but few in number the <a id="theory_of_Olbers"></a>theory of
Olbers in regard to their origin seemed highly probable; it has,
however, been completely disproved by more recent discoveries. The
breadth of the zone being now greater than the distance of Mars from the
sun, it is no more probable that the asteroids were produced by the
disruption of a single planet than that Mercury, Venus, the earth, and
Mars originated in a similar manner.</p>
<h3><a id="The_Small_Mass_of_the_Asteroids"></a>2. The Small Mass of the Asteroids.</h3>
<p>In taking a general view of the solar system we cannot fail to be struck
by the remarkable fact that Jupiter, whose mass is much greater than
that of all other planets united, should be immediately succeeded by a
region so nearly destitute of matter as the zone of asteroids. Leverrier
inferred from the motion of Mars's perihelion that the mass of Jupiter
is at least twelve hundred times greater than that of all the planets in
the asteroid ring. The fact is suggestive of Jupiter's dominating energy
in the evolution of the asteroid system. We find also something
analogous among the satellites of Jupiter, Saturn, and Uranus. Jupiter's
third satellite, the largest of the number, is nearly four times greater
than the second. Immediately within the orbit of Titan, the largest
satellite of Saturn, occurs a wide hiatus, and the volume of the next
interior satellite is to that of Titan in the ratio of one to
twenty-one. In the Uranian system the widest interval between adjacent
orbits is just within the orbit of the bright satellite, Titania.</p>
<p><span class="pagenum">[Pg 39]</span></p>
<p>The foregoing facts suggest the inquiry, What effect would be produced
by a large planet on interior masses abandoned by a central spheroid? As
the phenomena in all instances would be of the same nature, we will
consider a single case,—that of Jupiter and the asteroids.</p>
<p>The powerful mass of the exterior body would produce great perturbations
of the neighboring small planets abandoned at the solar equator. The
disturbed orbits, in some cases, would thus attain considerable
eccentricity, so that the matter moving in them would, in perihelion, be
brought in contact with the equatorial parts of the central body, and
thus become reunited with it.<a name="FNanchor_7" id="FNanchor_7"></a><a href="#Footnote_7" class="fnanchor">[7]</a> The extreme rarity of the zone between
Mars and Jupiter, regarded as a single ring, is thus accounted for in
accordance with known dynamical laws.</p>
<h3><a id="The_Limits_of_Perihelion_Distance"></a>3. The Limits of Perihelion Distance.</h3>
<p>It is sufficiently obvious that whenever the perihelion distance of a
planet or comet is less than the sun's radius, a collision must occur as
the moving body approaches the focus of its path. The great comet of
1843 passed so near the sun as almost to graze its surface. With a
perihelion distance but very slightly less, it would have been
precipitated into the sun and incorporated with its mass. In former
epochs, when the dimensions of the sun were much greater than at
present, this falling of comets into the central orb of the system must
have been a comparatively frequent occurrence. Again, if Mercury's orbit
had its present eccentricity when the radius<span class="pagenum">[Pg 40]</span> of the solar spheroid was
twenty-nine million miles, the planet at its nearest approach to the
centre of its motion must have passed through the outer strata of the
central body. In such case a lessening of the planet's mean distance
would be a necessary consequence. We thus see that in the formation of
the solar system the eccentricity of an asteroidal orbit could not
increase beyond a moderate limit without the planet's return to the
solar mass. The bearing of these views on the arrangement of the minor
planets will appear in what follows.</p>
<h3><a id="Was_the_Asteroid_Zone_originally_Stable_Distribution_of_the_Members_in_Space"></a>4. Was the Asteroid Zone originally Stable?—Distribution of the Members
in Space.</h3>
<p>One of the most interesting discoveries of the eighteenth century was
Lagrange's law securing the stability of the solar system. This
celebrated theorem, however, is not to be understood in an absolute or
unlimited sense. It makes no provision against the effect of a resisting
medium, or against the entrance of cosmic matter from without. It does
not secure the stability of all periodic comets nor of the meteor
streams revolving about the sun. In the early stages of the system's
development the matter moving in unstable orbits may have been, and
probably was, much more abundant than at present. But even now, are we
justified in concluding that all known asteroids have stable orbits? For
the major planets the secular variations of eccentricity have been
calculated, but for the orbits between Mars and Jupiter these limits are
unknown. With an eccentricity of 0.252 (less than that of many
asteroids), the distance of Hilda's aphelion would be greater than that
of Jupiter's perihelion. It seems possible, therefore, that certain<span class="pagenum">[Pg 41]</span>
minor planets may have their orbits much changed by Jupiter's disturbing
influence.<a name="FNanchor_8" id="FNanchor_8"></a><a href="#Footnote_8" class="fnanchor">[8]</a></p>
<p>Whoever looks at a table of asteroids arranged in their order of
discovery will find only a perplexing mass of figures. Whether we regard
their distances, their inclinations, or the forms of their orbits, the
elements of the members are without any obvious connection. Nor is the
confusion lessened when the orbits are drawn and presented to the eye.
In fact, the crossing and recrossing of so many ellipses of various
forms merely increase the entanglement. But can no order be traced in
all this complexity? Are there no breaks or vacant spaces within the
zone's extreme limits? Has Jupiter's influence been effective in fixing
the position and arrangement of the cluster? Such are some of the
questions demanding our attention. If "the universe is a book written
for man's reading," patient study may resolve the problem contained in
these mysterious leaves.</p>
<p>Simultaneously with the discovery of new members in the cluster of minor
planets, near the middle of the century, occurred the resolution of the
great nebula in Orion. This startling achievement by Lord Rosse's
telescope was the signal for the abandonment of the nebular hypothesis
by many of its former advocates. To the present writer, however, the
partial resolution of a single nebula seemed hardly a sufficient reason
for its summary rejection. The question then arose whether any probable
test of Laplace's theory could be found in<span class="pagenum">[Pg 42]</span> the solar system itself. The
train of thought was somewhat as follows: Several new members have been
found in the zone of asteroids; its dimensions have been greatly
extended, so that we can now assign no definite limits either to the
ring itself or to the number of its planets; if the nebular hypothesis
be true, the sun, after Jupiter's separation, extended successively to
the various decreasing distances of the several asteroids; the
eccentricities of these bodies are generally greater than those of the
old planets; this difference is probably due to the disturbing force of
Jupiter; the zone includes several distances at which the periods of
asteroids would be commensurable with that of Jupiter; in such case the
conjunctions of the minor with the major planet would occur in the same
parts of its path, the disturbing effects would accumulate, and the
eccentricity would become very marked; such bodies in perihelion would
return to the sun, and hence blanks or chasms would be formed in
particular parts of the zone. On the other hand, if the nebular
hypothesis was not true, the occurrence of these gaps was not to be
expected. Having thus pointed out a prospective test of the theory, it
was announced with some hesitation that <i>those parts of the asteroid
zone in which a simple relation of commensurability would obtain between
the period of a minor planet and that of Jupiter are distinguished as
gaps or chasms similar to the interval in Saturn's ring</i>.</p>
<p><a id="The_existence_of_these_blanks_was_thus_predicted"></a>The existence of these blanks was thus predicted in theory before it was
established as a fact of observation. When the law was first publicly
stated in 1866, but ten asteroids had been found with distances greater
than three times that of the earth. The number of such now known is
sixty-five. For more than a score of<span class="pagenum">[Pg 43]</span> years the progress of discovery
has been watched with lively interest, and the one hundred and eighty
new members of the group have been found moving in harmony with this law
of distribution.<a name="FNanchor_9" id="FNanchor_9"></a><a href="#Footnote_9" class="fnanchor">[9]</a></p>
<h4><a id="COMMENSURABILITY_OF_PERIODS"></a>COMMENSURABILITY OF PERIODS.</h4>
<p>When we say that an asteroid's period is commensurable with that of
Jupiter, we mean that a certain whole number of the former is equal to
another whole number of the latter. For instance, if a minor planet
completes two revolutions to Jupiter's one, or five to Jupiter's two,
the periods are commensurable. It must be remarked, however, that
Jupiter's effectiveness in disturbing the motion of a minor planet
depends on the <i>order</i> of commensurability. Thus, if the ratio of the
less to the greater period is expressed by the fraction <sup>1</sup>⁄<sub>2</sub>, where the
difference between the numerator and the denominator is one, the
commensurability is of the first order; <sup>1</sup>⁄<sub>3</sub> is of the second; <sup>2</sup>⁄<sub>5</sub>, of
the third, etc. The difference between the terms of the ratio indicates
the frequency of conjunctions while Jupiter is completing the number of
revolutions expressed by the numerator. The distance 3.277,
corresponding to the ratio <sup>1</sup>⁄<sub>2</sub>, is the only case of the first order in
the entire ring; those of the second order, answering to <sup>1</sup>⁄<sub>3</sub> and <sup>3</sup>⁄<sub>5</sub>,
are 2.50 and 3.70. These orders of commensurability may be thus arranged
in a tabular form, the radius of the earth's orbit being the unit of
distance:</p>
<p><span class="pagenum">[Pg 44]</span></p>
<table class="ruled vm" summary="Orders of Commensurability">
<tr><th>Order.</th><th>Ratio.</th><th>Distance.</th></tr>
<tr><td>First</td><td class="tdc"><sup>1</sup>⁄<sub>2</sub></td><td class="tdc">3.277</td></tr>
<tr><td>Second</td><td class="tdc"><sup>1</sup>⁄<sub>3</sub>, <sup>3</sup>⁄<sub>5</sub></td>
<td class="tdc"><span class="ilb">⎧<br />⎨<br />⎩</span><span class="ilb">2.50<br />3.70</span></td></tr>
<tr><td>Third</td><td class="tdc"><sup>2</sup>⁄<sub>5</sub>, <sup>4</sup>⁄<sub>7</sub>, <sup>5</sup>⁄<sub>8</sub></td>
<td class="tdc"><span class="ilb">⎧<br />⎨<br />⎩</span><span class="ilb">2.82<br />3.58<br />3.80</span></td></tr>
<tr><td>Fourth</td><td class="tdc"><sup>3</sup>⁄<sub>7</sub>, <sup>5</sup>⁄<sub>9</sub>, <sup>7</sup>⁄<sub>11</sub></td>
<td class="tdc"><span class="ilb">⎧<br />⎨<br />⎩</span><span class="ilb">2.95<br />3.51<br />3.85</span></td></tr>
</table>
<p><a id="Do_these_parts_of_the_ring_present_discontinuities"></a>Do these parts of the ring present discontinuities? and, if so, can they
be ascribed to a chance distribution? Let us consider them in order.</p>
<h5>I.—The Distance 3.277.</h5>
<p>At this distance an asteroid's conjunctions with Jupiter would all occur
at the same place, and its perturbations would be there repeated at
intervals equal to Jupiter's period (11.86 y.). Now, when the asteroids
are arranged in the order of their mean distances (as in Table II.) this
part of the zone presents a wide chasm. The space between 3.218 and
3.376 remains, hitherto a perfect blank, while the adjacent portions of
equal breadth, interior and exterior, contain fifty-four minor planets.
The probability that this distribution is not the result of chance is
more than three hundred billions to one.</p>
<p>The breadth of this chasm is one-twentieth part of its distance from the
sun, or one-eleventh part of the breadth of the entire zone.</p>
<h5>II.—The Second Order of Commensurability.—The Distances 2.50 and 3.70.</h5>
<p>At the former of these distances an asteroid's period would be one-third
of Jupiter's, and at the latter, three-<span class="pagenum">[Pg 45]</span>fifths. That part of the zone
included between the distances 2.30 and 2.70 contains one hundred and
ten intervals, exclusive of the maximum at the critical distance 2.50.
This gap—between Thetis and Hestia—is not only much greater than any
other of this number, but is more than sixteen times greater than their
average. The distance 3.70 falls in the wide hiatus interior to the
orbit of Ismene.</p>
<h5>III.—Chasms corresponding to the Third Order.—The Distances 2.82,
3.58, and 3.80.</h5>
<p>As the order of commensurability becomes less simple, the corresponding
breaks in the zone are less distinctly marked. In the present case
conjunctions with Jupiter would occur at angular intervals of 120°. The
gaps, however, are still easily perceptible. Between the distances 2.765
and 2.808 we find twenty minor planets. In the next exterior space of
equal breadth, containing the distance 2.82, there is but one. This is
No. 188, Menippe, whose elements are still somewhat uncertain. The space
between 2.851 and 2.894—that is, the part of equal extent immediately
beyond the gap—contains thirteen asteroids. The distances 3.58 and 3.80
are in the chasm between Andromache and Ismene.</p>
<h5>IV.—The Distances 2.95, 3.51,<a name="FNanchor_10" id="FNanchor_10"></a><a href="#Footnote_10" class="fnanchor">[10]</a> and 3.85, corresponding to the Fourth
Order of Commensurability.</h5>
<p>The first of these distances is in the interval between Psyche and
Clytemnestra; the second and third, in that exterior to Andromache.</p>
<p><span class="pagenum">[Pg 46]</span></p>
<p>The nine cases considered are the only ones in which the conjunctions
with Jupiter would occur at less than five points of an asteroid's
orbit. Higher orders of commensurability may perhaps be neglected. It
will be seen, however, that the distances 2.25, 2.70, 3.03, and 3.23,
corresponding to the ratios of the fifth order, <sup>2</sup>⁄<sub>7</sub>, <sup>3</sup>⁄<sub>8</sub>, <sup>4</sup>⁄<sub>9</sub>, and 6/11,
still afford traces of Jupiter's influence. The first is in the interval
between Augusta and Feronia; the last falls in the same gap with 3.277;
and the second and third are in breaks less distinctly marked. It may
also be worthy of notice that the rather wide interval between Prymno
and Victoria is where ten periods of a minor planet would be equal to
three of Jupiter. The distance of Medusa is somewhat uncertain.</p>
<p>The <span class="smcap lowercase">FACT</span> of the existence of well-defined gaps in the designated parts
of the ring has been clearly established. But the theory of probability
applied in a single instance gives, as we have seen, but one chance in
300,000,000,000 that the distribution is accidental. This improbability
is increased many millions of times when we include all the gaps
corresponding to simple cases of commensurability. We conclude,
therefore, that those discontinuities cannot be referred to a chance
arrangement. <a id="What_then_was_their_physical_cause"></a>What, then, was their physical cause? and what has become
of the eliminated asteroids?</p>
<p><span class="pagenum">[Pg 47]</span></p>
<p>What was said in regard to the limits of perihelion distance may suggest
a possible answer to these interesting questions. The doctrine of the
sun's gradual contraction is now accepted by a majority of astronomers.
According to this theory the solar radius at an epoch not relatively
remote was twice what it is at present. At anterior stages it was 0.4,
1.0, 2.0,<a name="FNanchor_11" id="FNanchor_11"></a><a href="#Footnote_11" class="fnanchor">[11]</a> etc. At the first mentioned the comets of 1843 and 1668,
as well as several others, could not have been moving in their present
orbits, since in perihelion they must have plunged into the sun. At the
second, Encke's comet and all others with perihelia within Mercury's
orbit would have shared a similar fate. At the last named all asteroids
with perihelion distances less than two would have been re-incorporated
with the central mass. As the least distance of Æthra is but 1.587, its
orbit could not have had its present form and dimensions when the radius
of the solar nebula was equal to the aphelion distance of Mars (1.665).</p>
<p>It is easy to see, therefore, that in those parts of the ring where
Jupiter would produce extraordinary disturbance the formation of chasms
would be very highly probable.</p>
<h3><a id="Relations_between_certain_Adjacent_Orbits"></a>5. Relations between certain Adjacent Orbits.</h3>
<p>The distances, periods, inclinations, and eccentricities of Hilda and
Ismene, the outermost pair of the group, are very nearly identical. It
is a remarkable fact, however, that the longitudes of their perihelia
differ by almost exactly 180°. Did they separate at nearly the<span class="pagenum">[Pg 48]</span> same
time from opposite sides of the solar nebula? Other adjacent pairs
having a striking similarity between their orbital elements are Sirona
and Ceres, Fides and Maia, Fortuna and Eurynome, and perhaps a few
others. Such coincidences can hardly be accidental. Original asteroids,
soon after their detachment from the central body, may have been
separated by the sun's unequal attraction on their parts. Such divisions
have occurred in the world of comets, why not also in the cluster of
minor planets?</p>
<h3><a id="The_Eccentricities"></a>6. The Eccentricities.</h3>
<p>The least eccentric orbit in the group is that of Philomela (196); the
most eccentric that of Æthra (132). Comparing these with the orbit of
the second comet of 1867 we have</p>
<table summary="Eccentricities">
<tr><td>The</td><td> eccentricity </td><td>of</td><td class="tdr"> Philomela = 0.01</td></tr>
<tr><td class="tdc">"</td><td class="tdc">"</td><td class="tdc">"</td><td class="tdr"> Æthra = 0.38</td></tr>
<tr><td class="tdc">"</td><td class="tdc">"</td><td class="tdc">"</td><td class="tdr"> Comet II. 1867 (ret. in 1885) = 0.41</td></tr>
</table>
<p>The orbit of Æthra, it is seen, more nearly resembles the last than the
first. It might perhaps be called the connecting-link between planetary
and cometary orbits.</p>
<p>The average eccentricity of the two hundred and sixty-eight asteroids
whose orbits have been calculated is 0.1569. As with the orbits of the
old planets, the eccentricities vary within moderate limits, some
increasing, others diminishing. The average, however, will probably
remain very nearly the same. An inspection of the table shows that while
but one orbit is less eccentric than the earth's, sixty-nine depart more
from<span class="pagenum">[Pg 49]</span> the circular form than the orbit of Mercury. These eccentricities
seem to indicate that the forms of the asteroidal orbits were influenced
by special causes. It may be worthy of remark that the eccentricity does
not appear to vary with the distance from the sun, being nearly the same
for the interior members of the zone as for the exterior.</p>
<h3><a id="The_Inclinations"></a>7. The Inclinations.</h3>
<p>The inclinations in Table II. are thus distributed:</p>
<table summary="Inclinations">
<tr><td>From</td><td class="tdr"> 0° to</td><td class="tdr"> 4°</td><td class="tdcount">70</td></tr>
<tr><td class="tdc">"</td><td class="tdr"> 4° to</td><td class="tdr"> 8°</td><td class="tdcount">83</td></tr>
<tr><td class="tdc">"</td><td class="tdr"> 8° to</td><td class="tdr"> 12°</td><td class="tdcount">59</td></tr>
<tr><td class="tdc">"</td><td class="tdr"> 12° to</td><td class="tdr"> 16°</td><td class="tdcount">32</td></tr>
<tr><td class="tdc">"</td><td class="tdr"> 16° to</td><td class="tdr"> 20°</td><td class="tdcount">8</td></tr>
<tr><td class="tdc">"</td><td class="tdr"> 20° to</td><td class="tdr"> 24°</td><td class="tdcount">8</td></tr>
<tr><td class="tdc">"</td><td class="tdr"> 24° to</td><td class="tdr"> 28°</td><td class="tdcount">7</td></tr>
<tr><td class="tdc">"</td><td class="tdr"> 28° to</td><td class="tdr"> 32°</td><td class="tdcount">0</td></tr>
<tr><td colspan="3">above 32°</td><td class="tdcount">1</td></tr>
</table>
<p>One hundred and fifty-four, considerably more than half, have
inclinations between 3° and 11°, and the mean of the whole number is
about 8°,—slightly greater than the inclination of Mercury, or that of
the plane of the sun's equator. The smallest inclination, that of
Massalia, is 0° 41´, and the largest, that of Pallas, is about 35°.
Sixteen minor planets, or six per cent. of the whole number, have
inclinations exceeding 20°. Does any relation obtain between high
inclinations and great eccentricities? These elements in the cases named
above are as follows:</p>
<p><span class="pagenum">[Pg 50]</span></p>
<table class="ruled" summary="Inclination and Eccentricity">
<tr><th>Asteroid.</th><th>Inclination.</th><th>Eccentricity.</th></tr>
<tr><td>Pallas</td>
<td><span class="ilb2">34</span><span class="ilb-deg">°</span><span class="ilb2">42</span>´</td>
<td class="tdc">0.238</td></tr>
<tr><td>Istria</td>
<td><span class="ilb2">26</span><span class="ilb3">30</span></td>
<td class="tdc">0.353</td></tr>
<tr><td>Euphrosyne</td>
<td><span class="ilb2">26</span><span class="ilb3">29</span></td>
<td class="tdc">0.228</td></tr>
<tr><td>Anna</td>
<td><span class="ilb2">25</span><span class="ilb3">24</span></td>
<td class="tdc">0.263</td></tr>
<tr><td>Gallia</td>
<td><span class="ilb2">25</span><span class="ilb3">21</span></td>
<td class="tdc">0.185</td></tr>
<tr><td>Æthra</td>
<td><span class="ilb2">25</span><span class="ilb3">0</span></td>
<td class="tdc">0.380</td></tr>
<tr><td>Eukrate</td>
<td><span class="ilb2">24</span><span class="ilb3">57</span></td>
<td class="tdc">0.236</td></tr>
<tr><td>Eva</td>
<td><span class="ilb2">24</span><span class="ilb3">25</span></td>
<td class="tdc">0.347</td></tr>
<tr><td>Niobe</td>
<td><span class="ilb2">23</span><span class="ilb3">19</span></td>
<td class="tdc">0.173</td></tr>
<tr><td>Eunice</td>
<td><span class="ilb2">23</span><span class="ilb3">17</span></td>
<td class="tdc">0.129</td></tr>
<tr><td>Electra</td>
<td><span class="ilb2">22</span><span class="ilb3">55</span></td>
<td class="tdc">0.208</td></tr>
<tr><td>Idunna</td>
<td><span class="ilb2">22</span><span class="ilb3">31</span></td>
<td class="tdc">0.164</td></tr>
<tr><td>Phocea</td>
<td><span class="ilb2">21</span><span class="ilb3">35</span></td>
<td class="tdc">0.255</td></tr>
<tr><td>Artemis</td>
<td><span class="ilb2">21</span><span class="ilb3">31</span></td>
<td class="tdc">0.175</td></tr>
<tr><td>Bertha</td>
<td><span class="ilb2">20</span><span class="ilb3">59</span></td>
<td class="tdc">0.085</td></tr>
<tr><td>Henrietta</td>
<td><span class="ilb2">20</span><span class="ilb3">47</span></td>
<td class="tdc">0.260</td></tr>
</table>
<p>This comparison shows the most inclined orbits to be also very
eccentric; Bertha and Eunice being the only exceptions in the foregoing
list. On the other hand, however, we find over fifty asteroids with
eccentricities exceeding 0.20 whose inclinations are not extraordinary.
The dependence of the phenomena on a common cause can, therefore, hardly
be admitted. At least, the forces which produced the great eccentricity
failed in a majority of cases to cause high inclinations.</p>
<h3><a id="Longitudes_of_the_Perihelia"></a>8. Longitudes of the Perihelia.</h3>
<p>The perihelia of the asteroidal orbits are very unequally distributed;
one hundred and thirty-six—a majority of the whole number
determined—being within the 120° from longitude 290° 50´ to 59° 50´.
The maximum occurs between 30° and 60°, where thirty-five perihelia are
found in 30° of longitude.</p>
<p><span class="pagenum">[Pg 51]</span></p>
<h3><a id="Distribution_of_the_Ascending_Nodes"></a>9. Distribution of the Ascending Nodes.</h3>
<p>An inspection of the column containing the longitudes of the ascending
nodes, in Table II., indicates two well-marked maxima, each extending
about sixty degrees, in opposite parts of the heavens.</p>
<table summary="Ascending Nodes">
<tr><td class="tdr">I. </td>
<td>From</td><td> 310° to </td><td class="tdr">10°,</td><td> containing </td><td class="tdr">61</td>
<td> ascending </td><td>nodes.</td></tr>
<tr><td class="tdr">II. </td>
<td class="tdc">"</td><td> 120° to </td><td class="tdr">180°,</td><td class="tdc">"</td><td class="tdr">59</td>
<td class="tdc">"</td><td class="tdc">"</td></tr>
<tr><td class="tdr"> </td>
<td colspan="4" class="tdl">Making in 120°</td><td class="tdr bt">120</td>
<td class="tdc">"</td><td class="tdc">"</td></tr>
</table>
<p>A uniform distribution would give 89. An arc of 84°—from 46° to
130°—contains the ascending nodes of all the old planets. This arc, it
will be noticed, is not coincident with either of the maxima found for
the asteroids.</p>
<h3><a id="The_Periods"></a>10. The Periods.</h3>
<p>Since, according to Kepler's third law, the periods of planets depend
upon their mean distances, the clustering tendency found in the latter
must obtain also in the former. This marked irregularity in the order of
periods is seen below.</p>
<table summary="Periods">
<tr><td>Between</td><td> 1100 </td><td class="tdc">and</td><td> 1200 </td><td>days</td><td class="tdr"> 6 </td><td>periods.</td></tr>
<tr><td class="tdc">"</td><td> 1200 </td><td class="tdc">"</td><td> 1300 </td><td class="tdc">"</td><td class="tdr"> 7 </td><td class="tdc">"</td></tr>
<tr><td class="tdc">"</td><td> 1300 </td><td class="tdc">"</td><td> 1400 </td><td class="tdc">"</td><td class="tdr"> 43 </td><td class="tdc">"</td></tr>
<tr><td class="tdc">"</td><td> 1400 </td><td class="tdc">"</td><td> 1500 </td><td class="tdc">"</td><td class="tdr"> 13 </td><td class="tdc">"</td></tr>
<tr><td class="tdc">"</td><td> 1500 </td><td class="tdc">"</td><td> 1600 </td><td class="tdc">"</td><td class="tdr"> 46 </td><td class="tdc">"</td></tr>
<tr><td class="tdc">"</td><td> 1600 </td><td class="tdc">"</td><td> 1700 </td><td class="tdc">"</td><td class="tdr"> 54 </td><td class="tdc">"</td></tr>
<tr><td class="tdc">"</td><td> 1700 </td><td class="tdc">"</td><td> 1800 </td><td class="tdc">"</td><td class="tdr"> 20 </td><td class="tdc">"</td></tr>
<tr><td class="tdc">"</td><td> 1800 </td><td class="tdc">"</td><td> 1900 </td><td class="tdc">"</td><td class="tdr"> 13 </td><td class="tdc">"</td></tr>
<tr><td class="tdc">"</td><td> 1900 </td><td class="tdc">"</td><td> 2000 </td><td class="tdc">"</td><td class="tdr"> 19 </td><td class="tdc">"</td></tr>
<tr><td class="tdc">"</td><td> 2000 </td><td class="tdc">"</td><td> 2100 </td><td class="tdc">"</td><td class="tdr"> 33 </td><td class="tdc">"</td></tr>
<tr><td class="tdc">"</td><td> 2100 </td><td class="tdc">"</td><td> 2200 </td><td class="tdc">"</td><td class="tdr"> 2 </td><td class="tdc">"</td></tr>
<tr><td class="tdc">"</td><td> 2200 </td><td class="tdc">"</td><td> 2300 </td><td class="tdc">"</td><td class="tdr"> 2 </td><td class="tdc">"</td></tr>
<tr><td class="tdc">"</td><td> 2300 </td><td class="tdc">"</td><td> 2400 </td><td class="tdc">"</td><td class="tdr"> 8 </td><td class="tdc">"</td></tr>
<tr><td class="tdc">"</td><td> 2400 </td><td class="tdc">"</td><td> 2800 </td><td class="tdc">"</td><td class="tdr"> 0 </td><td class="tdc">"</td></tr>
<tr><td class="tdc">"</td><td> 2800 </td><td class="tdc">"</td><td> 2900 </td><td class="tdc">"</td><td class="tdr"> 2 </td><td class="tdc">"</td></tr>
</table>
<p><span class="pagenum">[Pg 52]</span>
The period of Hilda (153) is more than two and a half times that of
Medusa (149). This is greater than the ratio of Saturn's period to that
of Jupiter. The maximum observed between 2000 and 2100 days corresponds
to the space immediately interior to chasm I. on a previous page, that
between 1300 and 1400 to the space interior to the second, and that
between 1500 and 1700 to the part of the zone within the fourth gap. The
table presents quite numerous instances of approximate equality; in
forty-three cases the periods differing less than twenty-four hours. It
is impossible to say, however, whether any two of these periods are
<i>exactly</i> equal. In cases of a very close approach two asteroids,
notwithstanding their small mass, may exert upon each other quite
sensible perturbations.</p>
<h3><a id="Origin_of_the_Asteroids"></a>11. Origin of the Asteroids.</h3>
<p>But four minor planets had been discovered when Laplace issued his last
edition of the "Système du Monde." The author, in his celebrated seventh
note in the second volume of that work, explained the origin of these
bodies by assuming that the primitive ring from which they were formed,
instead of collecting into a single sphere, as in the case of the major
planets, broke up into four distinct masses. But the form and extent of
the cluster as now known, as well as the observed facts bearing on the
constitution of Saturn's ring, seem to require a modification of
Laplace's theory. Throughout the greater part of the interval between
Mars and Jupiter an almost continuous succession of small planetary
masses—not nebulous rings—appears to have been abandoned at the solar
equator. The entire cluster,<span class="pagenum">[Pg 53]</span> distributed throughout a space whose outer
radius exceeds the inner by more than two hundred millions of miles,
could not have originated, as supposed by Laplace, in a single nebulous
zone the different parts of which revolved with the same angular
velocity. The following considerations may furnish a suggestion in
regard to the mode in which these bodies were separated from the equator
of the solar nebula.</p>
<p>(<i>a</i>) The perihelion distance of Jupiter is 4.950, while the aphelion
distance of Hilda is 4.623. If, therefore, the sun once extended to the
latter, the central attraction of its mass on an equatorial particle was
but five times greater than Jupiter's perihelion influence on the same.
It is easy to see, then, that this "giant planet" would produce enormous
tidal elevations in the solar mass.</p>
<p>(<i>b</i>) The centrifugal force would be greatest at the crest of this tidal
wave.</p>
<p>(<i>c</i>) Three periods of solar revolution were then about equal to two
periods of Jupiter. The disturbing influence of the planet would
therefore be increased at each conjunction with this protuberance. The
ultimate separation (not of a ring but) of a planetary mass would be the
probable result of these combined and accumulating forces.</p>
<h3><a id="Variability_of_Certain_Asteroids"></a>12. Variability of Certain Asteroids.</h3>
<p>Observations of some minor planets have indicated a variation of their
apparent magnitudes. Frigga, discovered by Dr. Peters in 1862, was
observed at the next opposition in 1864; but after this it could not be<span class="pagenum">[Pg 54]</span>
found till 1868, when it was picked up by Professor Tietjen. From the
latter date its light seems again to have diminished, as all efforts to
re-observe it were unsuccessful till 1879. According to Dr. Peters, the
change in brightness during the period of observation in that year was
greater than that due to its varying distance. No explanation of such
changes has yet been offered. It has been justly remarked, however, that
"the length of the period of the fluctuation does not allow of our
connecting it with the rotation of the planet."</p>
<h3><a id="The_Average_Asteroid_Orbit"></a>13. The Average Asteroid Orbit.</h3>
<p>At the meeting of the American Association for the Advancement of
Science in 1884, Professor Mark W. Harrington, of Ann Arbor, Michigan,
presented a paper in which the elements of the asteroid system were
considered on the principle of averages. Two hundred and thirty orbits,
all that had then been determined, were employed in the discussion.
Professor Harrington supposes two planes to intersect the ecliptic at
right angles; one passing through the equinoxes and the other through
the solstices. These planes will intersect the asteroidal orbits, each
in four points, and "the mean intersection at each solstice and equinox
may be considered a point in the average orbit."</p>
<p>In 1883 the Royal Academy of Denmark offered its gold medal for a
statistical examination of the orbits of the small planets considered as
parts of a ring around the sun. The prize was awarded in 1885 to M.
Svedstrup, of Copenhagen. The results obtained by these astronomers
severally are as follows:</p>
<p><span class="pagenum">[Pg 55]</span></p>
<table class="ruled" summary="Averages">
<tr><th> </th><th>Harrington.</th><th>Svedstrup.</th></tr>
<tr><td>Longitude of perihelion</td>
<td><span class="ilb3">14</span><span class="ilb-deg">°</span><span class="ilb2">39</span>´</td>
<td><span class="ilb3">101</span><span class="ilb-deg">°</span><span class="ilb2">48</span>´</td></tr>
<tr><td>Longitude of ascending node</td>
<td><span class="ilb3">113</span><span class="ilb3">56</span></td>
<td><span class="ilb3">133</span><span class="ilb3">27</span></td></tr>
<tr><td>Inclination</td>
<td><span class="ilb3">1</span><span class="ilb3">0</span></td>
<td><span class="ilb3">6</span><span class="ilb3">6</span></td></tr>
<tr><td>Eccentricity</td>
<td class="tdc">0.0448</td>
<td class="tdc">0.0281</td></tr>
<tr><td>Mean distance</td>
<td class="tdc">2.7010</td>
<td class="tdc">2.6435</td></tr>
</table>
<p>These elements, with the exception of the first, are in reasonable
harmony.</p>
<h3><a id="The_Relation_of_Short-Period_Comets_to_the_Zone_of_Asteroids"></a>14. The Relation of Short-Period Comets to the Zone of Asteroids.</h3>
<p>Did comets originate within the solar system, or do they enter it from
without? Laplace assigned them an extraneous origin, and his view is
adopted by many eminent astronomers. With all due respect to the
authority of great names, the present writer has not wholly abandoned
the theory that some comets of short period are specially related to the
minor planets. According to M. Lehmann-Filhès, the eccentricity of the
third comet of 1884, before its last close approach to Jupiter, was only
0.2787.<a name="FNanchor_12" id="FNanchor_12"></a><a href="#Footnote_12" class="fnanchor">[12]</a> This is exceeded by that of twelve known minor planets. Its
mean distance before this great perturbation was about 4.61, and six of
its periods were nearly equal to five of Jupiter's,—a commensurability
of the first order. According to Hind and Krueger, the great
transformation of its orbit by Jupiter's influence occurred in May,
1875. It had previously<span class="pagenum">[Pg 56]</span> been an asteroid too remote to be seen even in
perihelion. This body was discovered by M. Wolf, at Heidelberg,
September 17, 1884. Its present period is about six and one-half years.</p>
<p>The perihelion distance of the comet 1867 II. at its return in 1885 was
2.073; its aphelion is 4.897; so that its entire path, like those of the
asteroids, is included between the orbits of Mars and Jupiter. Its
eccentricity, as we have seen, is little greater than that of Æthra, and
its period, inclination, and longitude of the ascending node are
approximately the same with those of Sylvia, the eighty-seventh minor
planet. In short, this comet may be regarded as an asteroid whose
elements have been considerably modified by perturbation.</p>
<p>It has been stated that the gap at the distance 3.277 is the only one
corresponding to the first order of commensurability. The distance
3.9683, where an asteroid's period would be two-thirds of Jupiter's, is
immediately beyond the outer limit of the cluster as at present known;
the mean distance of Hilda being 3.9523. The discovery of new members
beyond this limit is by no means improbable. Should a minor planet at
the mean distance 3.9683 attain an eccentricity of 0.3—and this is less
than that of eleven now known—its aphelion would be more remote than
the perihelion of Jupiter. Such an orbit might not be stable. Its form
and extent might be greatly changed after the manner of Lexell's comet.
Two well-known comets, Faye's and Denning's, have periods approximately
equal to two-thirds of Jupiter's. In like manner the periods of
D'Arrest's and Biela's comets correspond to the hiatus at 3.51, and that
of 1867 II. to that at 3.277.</p>
<p>Of the thirteen telescopic comets whose periods cor<span class="pagenum">[Pg 57]</span>respond to mean
distances within the asteroid zone, all have direct motion; all have
inclinations similar to those of the minor planets; and their
eccentricities are generally less than those of other known comets. Have
these facts any significance in regard to their origin?</p>
<hr class="chap" />
<p><span class="pagenum">[Pg 58]<br />[Pg 59]</span></p>
<h2><a name="APPENDIX" id="APPENDIX">APPENDIX.</a></h2>
<h3>NOTE A.<br />
<span class="small">THE POSSIBLE EXISTENCE OF ASTEROIDS IN UNDISCOVERED RINGS.</span></h3>
<p>If Jupiter's influence was a factor in the separation of planetules at
the sun's equator, may not similar clusters exist in other parts of our
system? The hypothesis is certainly by no means improbable. For anything
we know to the contrary a group may circulate between Jupiter and
Saturn; such bodies, however, could not be discovered—at least not by
ordinary telescopes—on account of their distance. The Zodiacal Light,
it has been suggested, may be produced by a cloud of indefinitely small
particles related to the planets between the sun and Mars. The rings of
Saturn are merely a dense asteroidal cluster; and, finally, the
phenomena of luminous meteors indicate the existence of small masses of
matter moving with different velocities in interstellar space.</p>
<h3>NOTE B.<br />
<span class="small">THE ORIGIN AND STRUCTURE OF COSMICAL RINGS.</span></h3>
<p>The general theory of cosmical rings and of their arrangement in
sections or clusters with intervening chasms may be briefly stated in
the following propositions:</p>
<p><span class="pagenum">[Pg 60]</span></p>
<h4>I.</h4>
<p>Whenever the separating force of a primary body on a secondary or
satellite is greater than the central attraction of the latter on its
superficial stratum, the satellite, if either gaseous or liquid, will be
transformed into a ring.</p>
<p><span class="smcap">Examples.</span>—Saturn's ring, and the meteoric rings of April 20, August 10,
November 14, and November 27.</p>
<p>See Payne's <i>Sidereal Messenger</i>, April, 1885.</p>
<h4>II.</h4>
<p>When a cosmical body is surrounded by a ring of considerable breadth,
and has also exterior satellites at such distances that a simple
relation of commensurability would obtain between the periods of these
satellites and those of certain particles of the ring, the disturbing
influence of the former will produce gaps or intervals in the ring so
disturbed.</p>
<p>See "Meteoric Astronomy," Chapter XII.; also the <i>Proceedings of the
American Philosophical Society</i>, October 6, 1871; and the <i>Sidereal
Messenger</i> for February, 1884; where the papers referred to assign a
physical cause for the gaps in Saturn's ring.</p>
<h3>THE END.</h3>
<div class="footnotes"><h3>FOOTNOTES:</h3>
<div class="footnote">
<p><a name="Footnote_1" id="Footnote_1"></a><a href="#FNanchor_1"><span class="label">[1]</span></a> The discoverer, Piazzi, was not, as has been so often
affirmed, one of the astronomers to whom the search had been especially
committed.</p></div>
<div class="footnote">
<p><a name="Footnote_2" id="Footnote_2"></a><a href="#FNanchor_2"><span class="label">[2]</span></a> Massalia was discovered by De Gasparis, at Naples, Sept.
19, 1852, and independently, the next night, by Chacornac, at
Marseilles. The name was given by the latter.</p></div>
<div class="footnote">
<p><a name="Footnote_3" id="Footnote_3"></a><a href="#FNanchor_3"><span class="label">[3]</span></a> Astr. Nach., No. 932.</p></div>
<div class="footnote">
<p><a name="Footnote_4" id="Footnote_4"></a><a href="#FNanchor_4"><span class="label">[4]</span></a> Monthly Notices, vol. xxvii.</p></div>
<div class="footnote">
<p><a name="Footnote_5" id="Footnote_5"></a><a href="#FNanchor_5"><span class="label">[5]</span></a> Annals of the Obs. of Harv. Coll., 1879.</p></div>
<div class="footnote">
<p><a name="Footnote_6" id="Footnote_6"></a><a href="#FNanchor_6"><span class="label">[6]</span></a> This ingenious idea may be readily extended. The least
distance of Æthra is less than the present aphelion distance of Mars;
and the maximum aphelion distance of the latter exceeds the perihelion
distance of several known asteroids. Moreover, if we represent the
orbits of the major planets, and also those of the comets of known
periods, by material rings, it is easy to see that the major as well as
the minor planets are all linked together in the manner suggested by
D'Arrest.</p></div>
<div class="footnote">
<p><a name="Footnote_7" id="Footnote_7"></a><a href="#FNanchor_7"><span class="label">[7]</span></a> The effects of Jupiter's disturbing influence will again be
resumed.</p></div>
<div class="footnote">
<p><a name="Footnote_8" id="Footnote_8"></a><a href="#FNanchor_8"><span class="label">[8]</span></a> Not only nebulæ are probably unstable, but also many of the
sidereal systems. The Milky Way itself was so regarded by Sir William
Herschel.</p></div>
<div class="footnote">
<p><a name="Footnote_9" id="Footnote_9"></a><a href="#FNanchor_9"><span class="label">[9]</span></a> Menippe, No. 188, is placed in one of the gaps by its
calculated elements; but the fact that it has not been seen since the
year of its discovery, 1878, indicates a probable error in its
elements.</p></div>
<div class="footnote">
<p><a name="Footnote_10" id="Footnote_10"></a><a href="#FNanchor_10"><span class="label">[10]</span></a> The minor planet Andromache, immediately interior to the
critical distance 3.51, has elements somewhat remarkable. With two
exceptions, Æthra (132) and Istria (183), it has the greatest
eccentricity (0.3571),—nearly equal to that of the comet 1867 II. at
its last return. Its perihelion distance is 2.2880, its aphelion 4.7262;
hence the distance from the perihelion to the aphelion of its orbit is
greater than its least distance from the sun, and it crosses the orbits
of all members of the group so far as known; its least distance from the
sun being considerably less than the aphelion of Medusa, and its
greatest exceeding the aphelion of Hilda.</p></div>
<div class="footnote">
<p><a name="Footnote_11" id="Footnote_11"></a><a href="#FNanchor_11"><span class="label">[11]</span></a> The unit being the sun's distance from the earth.</p></div>
<div class="footnote">
<p><a name="Footnote_12" id="Footnote_12"></a><a href="#FNanchor_12"><span class="label">[12]</span></a> Annuaire, 1886.</p></div></div>
<p> </p>
<p> </p>
<div>*** END OF THE PROJECT GUTENBERG EBOOK 41570 ***</div>
</body>
</html>
|
