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diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..d7b82bc --- /dev/null +++ b/.gitattributes @@ -0,0 +1,4 @@ +*.txt text eol=lf +*.htm text eol=lf +*.html text eol=lf +*.md text eol=lf diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 0000000..6312041 --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,11 @@ +This eBook, including all associated images, markup, improvements, +metadata, and any other content or labor, has been confirmed to be +in the PUBLIC DOMAIN IN THE UNITED STATES. + +Procedures for determining public domain status are described in +the "Copyright How-To" at https://www.gutenberg.org. + +No investigation has been made concerning possible copyrights in +jurisdictions other than the United States. Anyone seeking to utilize +this eBook outside of the United States should confirm copyright +status under the laws that apply to them. diff --git a/README.md b/README.md new file mode 100644 index 0000000..38869ee --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +Project Gutenberg (https://www.gutenberg.org) public repository for +eBook #54208 (https://www.gutenberg.org/ebooks/54208) diff --git a/old/54208-0.txt b/old/54208-0.txt deleted file mode 100644 index 8f7fd9f..0000000 --- a/old/54208-0.txt +++ /dev/null @@ -1,1199 +0,0 @@ -The Project Gutenberg EBook of Standard Measures of United States, Great -Britain and France, by Arthur S. C. Wurtele - -This eBook is for the use of anyone anywhere in the United States and most -other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms of -the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you'll have -to check the laws of the country where you are located before using this ebook. - -Title: Standard Measures of United States, Great Britain and France - History and actual comparisons with appendix on introduction - of the mètre - -Author: Arthur S. C. Wurtele - -Release Date: February 19, 2017 [EBook #54208] - -Language: English - -Character set encoding: UTF-8 - -*** START OF THIS PROJECT GUTENBERG EBOOK STANDARD MEASURES OF US, GB, FRANCE *** - - - - -Produced by Chris Curnow and the Online Distributed -Proofreading Team at http://www.pgdp.net (This file was -produced from images generously made available by The -Internet Archive) - - - - - - - - - - - STANDARD MEASURES - OF - UNITED STATES, - GREAT BRITAIN, AND FRANCE. - - HISTORY AND ACTUAL COMPARISONS. - - WITH - APPENDIX ON INTRODUCTION OF THE MÈTRE. - - BY - ARTHUR S. C. WURTELE, - ASS’T ENG., N. Y. C. & H. R. R. - - [Illustration] - - E. & F. N. SPON, - NEW YORK: 44 MURRAY STREET. - LONDON: 16 CHARING CROSS. - 1882. - - COPYRIGHT, 1882, BY ARTHUR S. C. WURTELE. - - - - -INTRODUCTION. - - -During the preparation of this investigation of Standard Measures a large -number of authorities were examined, including the following: Kelly’s -“Universal Cambist,” Maunder’s “Weights and Measures,” “Encyclopædia -Britannica,” “Chambers’ Encyclopædia,” Williams’ “Geodesy,” Hymer’s -works, “Smithsonian Reports,” “Coast Survey Reports,” Herschel’s -“Astronomy,” etc. The only concise and clear statement I found was J. E. -Hilgard’s report to the Coast Survey on standards in 1876, which I was -gratified to find coincides with my deductions. - - ARTHUR S. C. WURTELE. - -ALBANY, November 26, 1881. - - - - -STANDARD MEASURES. - - -A standard measure of length at first sight appears to be very -simple--merely a bar of metal of any length, according to the unit of any -country; and comparisons of different standards do not seem to present -any difficulty. But on looking further into the thing, we find that -standards are referred to some natural invariable length, and we are at -once confronted with a mass of scientific reductions giving different -values to the same thing, according to successively improved means of -observation. We find, also, that comparisons of one standard with another -differ, as given by reductions carried to great apparent exactness. - -Every author appears to assume the right of using his own judgment as to -what reduction is to be considered the most exact, and the result is a -very confusing difference in apparently exact figures, with nothing to -show how these differences arise. - -I have endeavored to indicate what may be the cause of this confusion by -giving the figures of actually observed comparisons and reductions; in a -manner, the roots of the figures used as statements of length. - -Sir Joseph Whitworth gives 1/40000 of an inch as the smallest length that -can be measured with certainty, with an ultimate possibility of 1/1000000 -of an inch; but imperceptible variations of temperature affect these -infinitesimal lengths to such an extent that he believes the limit can -only be reached at a standard temperature of 85° F., to avoid the effect -of heat of the body. - -It appears to me that comparisons should be made of double yards and -mètres with the old French toise, as the limit of exactness would be -thereby doubled. - -Another great defect in statements of relative values is the omission -of necessary facts--the material of which the bars or standards are -made, the temperature at which comparison was made, and the standard -temperatures used as to the final reduction, with the coefficient of -expansion adopted. - -Again, bars of different metals appear in time to sensibly change their -relative length. - - -ENGLISH STANDARDS OF LENGTH. - -The first establishment of a uniform standard appears to have been made -in 1101 by Henry I., who is said to have fixed the ulna (now the yard) -at the length of his arm; but nothing definite was done till 1736, when -the Royal Society took steps toward securing a general standard, and -in 1742 they had a standard yard made by Graham from a comparison of -various yards and ells of Henry VII. and Elizabeth, that were kept in the -Exchequer. - -Two copies of the Royal Society standard yard were made by Bird in -1758 for a committee of Parliament, one of which was marked “standard -of 1758,” and the other 1760. But no exact legal standard was yet -established, as shown by comparisons in 1802 of the various standard -measures in use which Pictet, of Geneva, made with an accurate scale by -Troughton, using means exact to the ten thousandth part of an inch, with -the following results at the temperature of 62° F.: - - Troughton Scale 36·00000 inches. - Parliamentary Standard (1758, Bird) 36·00023 “ - Royal Society “ (1760, “ ) 35·99955 “ - “ “ (Graham) 36·00130 “ - Exchequer “ 35·99330 “ - Tower “ 36·00400 “ - Gen. Roy “ (Trig. Survey) 36·00036 “ - -Parliament finally undertook to reform the measures of England, and -appointed a commission in 1818, under whose authority Capt. Kater -compared the standard yards then in use with the following results, as -referred to the Indian Survey standard: - - Col. Lambton Standard (Indian Survey) 36·000000 inches. - Bird’s Standard (1760) 36·000659 “ - Sir Geo. Schuckburgh’s Standard 36·000642 “ - Ramsden’s Bar. Ordnance Survey 36·003147 “ - Gen. Roy’s Scale 36·001537 “ - Royal Society Standard 36·002007 “ - -The commission reported in favor of adopting Bird’s standard of 1760, as -it differed so slightly from Sir George Schuckburgh’s standard (which -had been used in deducing the value of the French mètre) that those -values could be assumed as correct. They also established the length of -the seconds pendulum at level of sea in London and in vacuo as 39·13929 -inches. The seconds pendulum had been previously fixed by Wollaston and -Playfair in 1814 as 39·13047 inches. - -On this report, an Act of Parliament in 1823 declared the only standard -measure of length for the United Kingdom to be the yard as given by the -distance at 32° F. between two points in gold studs on the brass bar, -made by Bird, and marked “Standard of 1760,” and in the keeping of the -Clerk of the House of Commons; also it referred this standard yard to the -natural standard of a pendulum vibrating seconds of mean solar time at -the level of the sea, in vacuo at London and temperature of 32° F., as -in the proportion of 36 to 39·13929; so that a pendulum 36 inches long -ought to make 90088·42 vibrations in 24 hours. - -The Royal Society had a copy of the legal standard made by Bailey in -1834; and in the same year the Parliamentary standard was destroyed by -fire at the burning of the Houses of Parliament, leaving the kingdom -again without a legal standard. - -All attempts made by a commission consisting of Airy, Bailey, Herschel, -Lubbock, and Sheepshanks, to restore the standard by means of the seconds -pendulum failed in exactness, on account of the many conditions of a -vibrating pendulum, and recourse was had to the Royal Society standard, -which had been carefully compared by Captain Kater in 1818, and from this -in 1838 Bailey and Sheepshanks made six bronze bars, one inch square, and -38 inches long, which in 1855 were legalized by Act of Parliament, and -the English standard of length defined as follows: - -“That the straight line on distance between the centres of the transverse -lines in the two gold plugs on the bronze bar deposited in the Exchequer -shall be the genuine standard yard at the temperature of 62° Fahrenheit; -and if lost, it shall be replaced by means of its copies.” - -The French metrical system was made legal permissively in 1864, at the -length established by Captain Kater, referred to in Act of Parliament of -1823, of 1 mètre equal to 39·37079 inches, or 3·28089916 feet. - -These are the standards now in use in the United Kingdom. - - -UNITED STATES. - -By the Constitution of the United States Congress is charged with fixing -the standard of measures (Art. 1, sec. 8); but as no enactment has been -made by Congress, the standard yard in England, which was legal previous -to 1776 in the Colonies, is the standard yard of the United States, and -does not differ with the English standard yard. - -Under resolution of Congress in 1830, Mr. Hassler was employed to examine -the standards in use. - -Considerable discrepancies were found, but the mean of all examined -corresponded very nearly with the English standard, and in 1832 the -recommendation of Mr. Hassler was adopted, and the standard yard defined -as the distance between the 27th and 63d inch marks, at the temperature -of 62° F., on the brass scale 82 inches long, being an exact copy of Sir -George Schuckburgh’s standard, made by Troughton, of London, for the -Coast Survey, and deposited in the Office of Weights and Measures at -Washington. - -In 1836 an Act of Congress ordered standards to be sent to each Governor -of a State, and the work was done under direction of Mr. Hassler. - -In 1856, two copies of the English standard yard, as restored after -destruction of the original standard by fire in 1834, No. 11 of bronze, -and No. 57 of Low Moor wrought iron, were presented to the United States -by Airy. - -The United States Troughton standard bar being compared with No. 11 -was found to be longer by 0·00085 inch, or in proportion of 1 to -1·0000237216, about 1½ inches in a mile, according to Report of Secretary -of Treasury in 1857. - -Later comparisons made by J. E. Hilgard, of the Coast Survey, at the -British Standards Office, between No. 11 and the standard imperial yard, -give No. 11 as 0·000088 inch shorter, or it would be of standard length -at temperature of 62·25° F. - -We may infer that the Troughton standard is too long by 0·000762 inch, or -would be standard length at temperature 59·77° F. instead of at 62° by -making expansion reduction with Airy’s coefficient for the bronze of the -imperial standards, 0·000342 inch per yard for 1° F. - -The mètre was made a legal standard permissively in 1866; the United -States mètre standard being one of the 12 iron mètre bars made and -verified for the French Government in 1799 on the adoption of the -metrical system, and brought to America by Mr. Hassler in 1800, the -relative value being fixed by Act of Congress at 39·37 inches. - -The relative value of 39·36850154 United States inches, as obtained by -Mr. Hassler, corrected to 62° F., was used by the Coast Survey till -1868, when it was found advisable to use the relative value of 39·3704 -as deduced by Clarke. Since 1800 several standard mètre bars were sent -to the United States by the French Government, and on comparison, there -appearing to be a slight discrepancy, the original iron standard mètre -bar was sent to Dr. F. A. P. Barnard in Paris, and in 1867 it was -compared with the French platinum standard, which is only used once in -ten years to verify other standards. - -A difference was found by this comparison of only ·00017 millimètre -or 1/160000 inch, which being only 1/100 of an inch in a mile is -inappreciable. - - -FRANCE. - -The standard of length of the système ancient was the toise of 6 pieds, -divided into 12 pouces of 12 lignes each. - -The origin of the toise is not known, but it was probably legally -established by Philip Le Bel, about 1300, as he first appears to have -taken steps toward a uniform system of measures in France. In the 13th -century the toise is mentioned by Ch. Le Rains. In the 14th century -Menongier writes that, in marching, the sight should strike the ground 4 -toises in front. In the fifteenth century Pereforest brings in the toise, -and in the sixteenth century the Contume de Berry says, “We use in this -country two toises; one for carpenters of 5 pieds and a half, the other -for masons of 6 pieds.” - -Picard used the toise in his measurement of an arc of meridian from -Malvoisin to London in 1669. - -The meridians measured by the Academy in 1735 to settle the question of -the figure of the earth were made by means of two standard toises, known -as the “Toise du Nord,” and the “Toise du Sud.” - -The first, used by Maupertuis, Clairault, and Le Monnier, in Lapland, was -destroyed by immersion in sea-water, when their ship was wrecked on the -return voyage. - -The second, with which La Condamine, Bourgner, and Godin operated in -Peru, was the original of the toise Canivet made in 1768, and of the -standards used in determining the mètre. - -The commencement of the move for a scientific standard of length in -France which resulted in the mètre was in 1790, when the revolutionary -government proposed to England the formation of a commission of equal -numbers from the English Royal Society and the French Academy, for the -purpose of fixing the length of the seconds pendulum at latitude 45° as -the basis of a new system of measures. This proposal was not favorably -received, and the Academy, at the request of government, appointed as -a commission Borda, Lagrange, Laplace, Monge, and Condorcet, to decide -whether the seconds pendulum, the quarter of the equator, or the quarter -of a meridian, should be used as the natural standard for the new system -of measures. They settled on the last as best for the purpose, and -resolved that the ten millionth of the meridian quadrant, or distance -from equator to pole, measured at sea level, be taken for basis of the -new system, and be called a mètre. - -Delambre and Mechin were at once charged with re-measurement of the -meridian surveyed in 1739 by La Caille and Cassini, from Dunkirk to -Perpignan, and its extension to Barcelona. - -Operations were commenced in 1792, and carried on with great accuracy -to completion in 1799; Delambre working between Dunkirk and Paris, and -Mechin between Paris and Barcelona. - -The distance measured from Dunkirk to Barcelona was 9° 40´ 24·24´´ of -arc, or 1,075,059 mètres, as reduced to the new standard. - -The “toise de Peru” was the standard used in the work at a temperature of -13° R. - -Two base-lines were measured with Borda’s compensating bars of brass and -platinum; one at Melun, near Paris, 6076 toises long, and the second at -Perpignan, 6028 toises long, and though over 900,000 mètres apart, the -calculated length differed by only 10 pouces. - -This meridian was afterward, in 1806, extended by Gen. Roy to Greenwich, -on the north, and by Biot and Arago to Formentera, on the south. The -results, as given by Laplace in centesimal degrees and mètres, are as -follows: - - Greenwich 57·19753° ·0 mètres. - Pantheon, Paris 54·27431° 292,719·3 “ - Formentera 42·96178° 1,423,636·1 “ - -The middle of the arc being 50·079655° Cent., or 45° 4´ 18·0822´´ Sexa., -and the middle degree centesimal being very nearly 100,000 mètres. - -The determination of the final result of these geodetic measurements was -referred to a committee of 20 members; 9 named by the French Government, -and the others by the governments of Holland, Savoy, Denmark, Spain, -Tuscany, and of the Cisalpine, Ligurian, and Swiss republics, on the -invitation of France. - -This committee established the meridian quadrant at 5,130,740 toises; -making the mètre 0·513074 of the toise, or 36·9413 pouces, or 443·296 -lignes, and the toise 1·94903659 mètres. - -Iron standard mètre bars, 12 in number were made by Borda, also 2 of -platinum and 4 standard toise bars. - -The 12 standard iron mètre bars were sent to different countries, after -being verified by the French Government, and on the 2d of November, 1801, -the mètrical système was legalized by France, and the standard unit of -length declared to be the ten millionth part of a meridian quadrant of -the earth, as defined by the distance at a temperature of 0° Centigrade -(32° F.) between two points on a platinum bar in the keeping of the -Academy of Science at Paris. This standard bar is used only once every -ten years for exact comparisons, as stated by Dr. F. A. P. Barnard. - -About 1837 Bessel, by a combination of 11 measured arcs of meridian, -deduced the quadrant of meridian as 5,131,179·81 toises instead -of 5,130,740 toises, as fixed by law. This would make to quadrant -10,000,565·278 legal mètres, or would increase the mètre length from -443·296 lignes to 443·334 lignes, agreeing very nearly with result -obtained by Airy in 1830, from a combination of 13 measured arcs. - -The following are the measured arcs used by Bessel and Airy; the -combinations being indicated by initial letters, A and B. - - _Measurer._ _Mid. Lat._ _Arc._ _Length._ - B.--Svanberg, Sweden +66° 20´ 10·0´´ 1° 37´ 19·6´´ 593,277 feet - A.--Maupertuis, Sweden +66° 19´ 37·0´´ 0° 57´ 30·4´´ 351,832 “ - A.--Struve, Russia +58° 17´ 37·0´´ 3° 35´ 5·2´´ 1,309,742 “ - B.--Struve and Tenner, - Russia +56° 3´ 55·5´´ 8° 2´ 28·9´´ 2,937,439 “ - B.--Bessel and Bayer, - Prussia +54° 58´ 26·0´´ 1° 30´ 29·0´´ 551,073 “ - B.--Schumacher, Denmark +54° 8´ 13·7´´ 1° 31´ 53·3´´ 559,121 “ - A, B.--Ganss, Hanover +52° 32´ 16·6´´ 2° 0´ 57·4´´ 736,425 “ - A.--Roy and Kater, England +52° 35´ 45·0´´ 3° 57´ 13·1´´ 1,442,953 “ - B.-- “ “ “ +52° 2´ 19·0´´ 2° 50´ 23·5´´ 1,036,409 “ - A.--Lacaille and Cassini, - France +46° 52´ 2·0´´ 8° 20´ 0·3´´ 3,040,605 “ - A, B.--Delambre and Mechin, - France +44° 51´ 2·5´´ 12° 22´ 12·7´´ 4,509,832 “ - A.--Boscovich, Rome +42° 59´ ·0´´ 2° 9´ 47·0´´ 787,919 “ - A.--Mason and Dixon, - America +39° 12´ ·0´´ 1° 28´ 45·0´´ 538,100 “ - A, B.--Lambton, India +16° 8´ 21·5´´ 15° 57´ 40·7´´ 5,794,598 “ - A, B.--Lambton and Everest, - India +12° 32´ 20·8´´ 1° 34´ 56·4´´ 574,318 “ - A, B.--Lacondamine, Peru - 1° 31´ 0·4´´ 3° 7´ 3·5´´ 1,131,050 “ - A.--Lacaille, Cape Good - Hope -33° 18´ 30·0´´ 1° 13´ 17·5´´ 445,506 “ - B.--Maclear, “ “ -35° 43´ 20·0´´ 3° 34´ 34·7´´ 1,301,993 “ - A.--Plana and Cartessi, - Piedmont -------------- 1° 7´ 31·1´´ ------------ - -The following different lengths of the mètre have been obtained: - - As adopted by France, 1801 443·296 lignes. - According to Delambre 443·264 “ - “ Bessel 443·33394 “ - “ Airy 443·32387 “ - “ Clarke 443·36146 “ - From Peru Meridian 443·440 “ - -The length of a pendulum vibrating 100,000 times in a mean solar day was -determined in numerous careful experiments by Biot, Arago, and Mathieu, -in mètres of 443·296 lignes, as follows: - - Dunkirk 56·67 lat. Cent. 0 above sea 0·7419076 mètres. - Paris 54·26 “ 65 “ 0·7418870 “ - “ by Borda 54·26 “ 0 “ 0·7416274 “ - Bordeau 49·82 “ 0 “ 0·7412615 “ - Formentera 42·96 “ 196 “ 0·7412061 “ - -Borda also determined the length of the seconds pendulum at Paris, in -vacuo: - - First result 440·5595 lignes = 0·9938267 mètre. - Second result “ “ = 0·9938460 “ - As given by Ganot “ “ = 0·9935 “ - -In 1812 the système usuelle was established, of which the unit was one -third of the mètre, with the old name of pied, and duodecimally divided -into pouces and lignes. - -This system continued in use till 1840, when it was abolished by law, and -the names of pied, pouce, and ligne forbidden under penalties. So the -mètre, decimally divided, remains the only legal measure of length in -France. - - -COMPARISONS OF UNITED STATES AND ENGLISH STANDARDS. - -In 1832, under resolution of Congress, Mr. Hassler compared the different -standard yards in America, with the following results, using the yard -between the twenty-seventh and sixty-third inches on the scale made of -bronze by Troughton, of London, for the United States Coast Survey, as -the reference, that being identical with Sir George Schuckburg’s standard: - - Troughton Scale, mid. yard 36·0000000 inches. - “ “ between platinum points 35·9989758 “ - Jones yard in State Department 35·9990285 “ - Iron yard in Engineer Department 35·9987760 “ - Brass yard, Albany, Sec. of State 36·0002465 “ - Gilbert yard, University of Virginia 35·9952318 “ - -In 1856 the Troughton standard bronze scale was compared with the bronze -standard yard No. 11, which was sent over by Airy as a copy of the -English imperial standard, as restored after destruction of the original -standard by fire in 1834, and the United States standard was found to be -longer by 0·00085 inch. - -Later comparisons by J. E. Hilgard, of the Coast Survey, of the bronze -standard No. 11 with the imperial standard yard, at the British Standards -Office, gave No. 11 as 0·000088 shorter than the imperial standard. - -Hassler’s reduction of the mètre, as deduced by Beach at 62° F., -39·36850154, compared with the English reduction of the mètre, 39·37079 -inches, gives an excess to the United States Standard of 0·002029 inch. - -The following reductions have been given for the United States yard in -English inches: - - Report of Sec. of Treas., 1857 36·00087 = 1·00002416 - Chambers’ Encyclopædia, 1872 36·00087 - “ “ “ 36·0020892 = 1·0000580334 - Trautwine 36·0020894 = 1·000058038 - Mathewson, U. S. surveyor 36·00208944 = 1·00005804 - Hassler and Beach 36·002092 = 1·00005811 - J. E. Hilgard, Coast Survey 36·00076 = 1·000021 - -To Mr. Hassler’s reduction the name of United States inch has been -applied; but his reduction is not correct, as he used a rate of expansion -for brass deduced by himself of 0·0003783 inch in one yard for 1° F., -and later experiments show that the smaller rate of 0·000342, deduced by -Airy, is more correct. - -By correcting Hassler’s reduction with the later rate of expansion, J. E. -Hilgard shows that the difference would be very small, or only 36·0002286 -= 1·00000635, or about ⅖ of an inch in a mile. - -In Coast Survey report for 1876, J. E. Hilgard calls attention to another -difficulty in the matter of extreme accuracy, in the uncertainty with -regard to the permanence in the length of a bar, and states that the -bronze standard bar No. 11 and the Low Moor iron standard bar No. 57, -presented to the United States by Great Britain, are found to have -changed their relative length by 0·00025 inch in 25 years; the bronze bar -being now relatively shorter by that amount. This subject, he states, is -undergoing further investigation. - - -COMPARISON OF UNITED STATES AND FRENCH STANDARDS. - -In 1817 Mr. Hassler examined the French standards in America, for the -Coast Survey, using the Troughton bronze standard scale, which is -identical with Sir George Schuckburg’s standard, as the reference, with -the following results, all being reduced to temperature of 32° F. - - Original Iron Mètre, 1799 39·381022708 inches. - Lenoir Iron Mètre, Coast Survey 39·37972015 “ - “ Brass “ “ 39·380247972 “ - “ “ “ Eng. Dept. 39·38052739 “ - Canivet Iron Toise, 1768 76·74334472 “ - Lenoir “ “ 76·74192710 “ - -In 1814 Troughton had compared with his own scale in London two of the -above. - - Lenoir Iron Mètre, C. S. 39·3802506 inches. - “ Brass “ “ 39·3803333 “ - -In 1832, under resolution of Congress, Hassler again compared the French -standards in the United States, using as before the Troughton scale, and -reducing all to temperature of 32° F. as follows: - - Original Iron Mètre, 1799 39·3808643 inches. - Lenoir “ “ C. S. 39·3799120 “ - “ Brass Mètre C. S. 39·380447 “ - “ “ Eng. Dept. 39·3801714 “ - “ “ “ in 1829 39·3807095 “ - Fortin “ State Dept. 39·3796084 “ - “ Treas. “ 39·3795983 “ - Iron Mètre “ “ 39·3807827 “ - Gilbert “ Univ. of Virg. 39·365408 “ - Platinum Mètre 39·3803278 “ - “ (Nicollet) 39·380511 “ - Canivet Iron Toise, 1768 76·74290511 “ - Lenoir “ 1799 76·74047599 “ - -From the mean of his comparisons between the United States brass -Troughton standard yard and the authentic French standard mètres used by -the Coast Survey, Hassler, in 1832, deduced the value of the mètre at -39·3809172 inches, at 32° F., and by correction for expansion to United -States standard temperature of 62° F., he made the mètre at 32° equal to -39·36850154 inches at 62° F. - -The British imperial standard and the United States Troughton standard -differ by only 0·000762 inch, which applied to the English reduction -of 39·37079, would give 39·36996 as the relative value according to -Troughton standard. - -The difference between these reductions is probably to be attributed -to the use of different rates of expansion, in correcting for standard -temperatures, which vary considerably, according to high authority as -follows for brass at 1° F. - - Whitworth, 1876 0·00000956 = 0·00034416 in. per yard. - Borda, 1799 0·000009913 = 0·00035687 “ - Smeaton, 1750 0·000010417 = 0·00037501 “ - Hassler 0·000010508 = 0·0003783 “ - Ramsden, 1760 0·000010516 = 0·0003786 “ - Faraday, 1830 0·00001059 = 0·00038124 “ - -And for the bronze of which the British imperial standards are made: - - Airy and Sheepshanks 0·0000095 = 0·000342 in. per yard. - Fizeau 0·00000975 = 0·000351 “ - -The correction at Ramsden’s rate is nearly identical with Hassler’s, -and gives 39·3684933; at Whitworth’s rate it would give 39·36962, very -nearly the same as deduced from the difference between the British -Imperial standard and the United States Troughton standard. The results -of Sir Joseph Whitworth were obtained by use of all late improvements for -scientific precision, and they must be accepted as most reliable. - -It would appear preferable to give comparisons at the same temperature in -connection with the corrected result, so that international comparisons -of scientific measurements may not be vitiated by accidental variations. - - -COMPARISON OF ENGLISH AND FRENCH STANDARDS. - -When the mètre standard was established in France, 1799, it was compared -with Sir George Schuckburg’s standard yard by Captain Kater. The -quadrant of 10,000,000 mètres, or 5,130,740 toises, was determined to -be 32,808,992 English feet, giving the mètre equal to 3·2808992 English -feet, or 39·37079 inches, and the toise equal to 6·3945925921 English -feet. - -In 1814 Wollaston and Playfair, by comparison with the platinum mètre -standard at 55° F., deduced the mètre as equal to 39·3828 English inches. - -During the geodetic operations of General Roy in 1802, who used 60° F. -as standard temperature, Pictet’s comparisons, using means capable of -measuring the 10,000th part of an inch, gave the mètre standard, which is -used at 32° F. as standard temperature, at 39·3828 English inches; this -corrected for temperature by Dr. Young, gave 39·371 English inches at 62° -F.; which result was confirmed by Bird, Maskelyne and Laudale. - -In 1823, by Act of Parliament on report of committee, the mètre is fixed -as 39·37079 English inches. - -In 1800 the Royal Society, by comparison with two toise standards sent by -Lalande to Maskelyne, deduced the mètre as 39·3702 English inches. - -Later comparisons by Clarke in the Ordnance Survey Office at Southampton, -in 1866, give the mètre as 39·37043 inches. - -The French Academy of Sciences by comparison with Sir George Schuckburg’s -standard at temperature of 32° F., deduced the mètre as 39·3824 English -inches, which reduced to standard temperature of 62° F., would be -39·3711, or slightly in excess of the value deduced by Dr. Young from -Pictet’s comparisons. - -The legal value in England is one mètre equal to 39·37079, and the latest -reduction is 39·37043 inches by Clarke in 1866, which is probably the -most exact reduction. - -DIFFERENT REDUCTIONS OF THE FRENCH TOISE INTO ENGLISH FEET. - - Captain Kater, 1799 6·3945925921 feet. - Hassler, 1832 6·3951409 “ - Chambers’ Encyclopædia 6·39456 “ - “ Mathematics 6·394662 “ - Wallace 6·39462 “ - Nystrom 6·39625 “ - Alexander 6·39435 “ - Dana 6·3946 “ - -The following table of reductions as used shows clearly how great a -confusion exists in the matter of comparisons: - -MÈTRE IN INCHES. - - Phœnixville Hand-book 39·368 inches. - Hassler 39·36850154 “ - “ 39·370788 “ - “ 39·3809172 “ - Trautwine 39·368505 “ - “ 39·37079 “ - Silliman 39·368505 “ - “ 39·37079 “ - Chambers’ Encyclopædia 39·36850535 “ - “ “ 39·3707904 “ - Act of United States Congress, 1866 39·37 “ - Smithsonian Report 39·37 “ - Youmans 39·37 “ - Davies 39·37 “ - Homan’s Encyclopædia 39·37008 “ - Weale 39·3702 “ - Ordnance Survey (England, 1866) 39·37043 “ - Clerk Maxwell 39·37043 “ - Capt. Clarke 39·3704316 “ - J. M. Rankine (1870) 39·3704316 “ - “ (1866) 39·3707904 “ - Alexander (weights and measures) 39·37068 “ - Ganot 39·370788 “ - Vose 39·370788 “ - Act of British Parliament, 1823 39·37079 “ - Encyclopædia Britannica 39·37079 “ - Hymer 39·37079 “ - Davies and Peck 39·37079 “ - J. W. Clarke 39·37079 “ - Dana 39·37079 “ - Whittaker 39·37079 “ - Sommerville 39·3707904 “ - Chambers’ Mathematics 39·3707904 “ - Gwilt’s Encyclopædia 39·3707904 “ - Gillespie 39·3707904 “ - Capt. Kater 39·3708 “ - Appleton’s Encyclopædia 39·37079 “ - Van Nostrand 39·3708 “ - D’Aubuisson 39·3708 “ - Johnson (draftsman) 39·3708 “ - Encyclopædia Americana 39·371 “ - Jameson’s Dictionary 39·371 “ - Herbert’s Encyclopædia 39·371 “ - Popular “ 39·371 “ - Molesworth 39·371 “ - Dr. Young (1802) 39·371 “ - Wallace (engineer) 39·371 “ - Nystrom 39·38091 “ - Hencke 39·3809172 “ - Act of Canadian Parliament, 1873 39·3819 “ - Paris Academy 39·3824 “ - -LENGTH OF THE SECONDS PENDULUM AS GIVEN BY DIFFERENT WRITERS. - - NEW YORK.--Hencke 39·1012 inches. - Bartlet 39·11256 “ - Nystrom 39·1017 “ - Ganot 39·1012 “ - Byrne 39·10153 “ - Wallace 39·10153 “ - - LONDON.--Hencke 39·13908 “ - Gillespie 39·13929 “ - Chambers’ Encyclopædia 39·13929 “ - Williams’ Geodesy 39·13929 “ - Act of Parliament, 1823 39·13929 “ - Wallace (engineer) 39·1393 “ - Chambers’ Mathematics 39·1393 “ - Hymer Astronomy 39·13734 “ - Bartlet 39·13908 “ - Vose 39·1393 “ - Sommerville 39·1393 “ - Nystrom 39·1393 “ - Davies and Peck 39·13908 “ - Ganot 39·1398 “ - Wollaston (1814) 39·13047 “ - Galbraith 39·139 “ - Byrne 39·1393 “ - Capt. Kater 39·13829 “ - - PARIS.--Hencke 39·12843 “ - Ganot 39·1285 “ - Galbraith 39·128 “ - Byrne 39·12843 “ - Wallace 39·12843 “ - - - - -APPENDIX. - - -Having shown in the preceding pages that in the point of view of -scientific accuracy the yard, mètre, and toise standards are on a -common level, and that in the matter of comparisons there is no extreme -accuracy, I will now refer to the proposed change of our standard from -the yard to the mètre. - -Theoretically the mètre is the 10,000,000th part of the earth’s quadrant, -and the yard the 36/39·13929th part of a seconds pendulum at London. -Practically, neither the mètre nor yard could be recovered with exactness -from their natural basis. The legal French mètre differs from the -latest reduction enough to give an excess of over three miles to the -circumference of the earth. In fact, the mètre and yard are only the -lengths of bars of metal kept in certain offices, from which copies are -made. Decimally considered, it is as easy to divide one as the other into -tenths, hundredths, etc., and the yard standard is often so divided. - -As to nomenclature, the metrical system is overloaded with Greek and -Latin prefixes, which are in no way so easy and convenient in expression -as the short, sharp Anglo-Saxon words yard, foot, inch. - -In all sciences Latin and Greek names are given for easier purposes -of classification; but the different peoples invariably keep their -own household names for daily purposes, leaving prefix and affix to -specialists, probably with advantage to both parties. - -The units used for different purposes are entirely distinct from the -base of any system, and though always referable to such base, are not -practically so referred. It therefore seems useless to burden the people -with long scientific names in the ordinary transactions of daily life. - -For long distances the units in the yard and metrical systems are -respectively the mile and the kilomètre. - -The mile has a definite meaning in our minds, being associated, from the -days of youth, with the measured distances in race-courses, speed in -walking, railway and steamer travel, length of surveyed lots--the same -being in use among about 100,000,000 people. - -For mechanical structures, the units are respectively the foot and the -mètre. The foot is used instead of the yard, as being the most convenient -in practice, and is fixed in the minds of the people by constant -association with length of foot-rules, size of buildings, doors, windows, -etc., all of which are always before us. - -For commercial purposes the units are respectively the yard and the -mètre. The yard is associated with length of yard-sticks, distance -between brass nails on counters, so many finger-lengths by ladies. -Probably three fourths of the business of the world is conducted on the -yard standard. - -For machine and shop work the English unit is the inch and fractions, -and countries having the metrical standard have universally adopted the -millimètre. - -The inch is well fixed in the minds of all mechanics by constant use, and -the ease with which the fractions are had by halving only renders the -system very convenient. - -As more figures must be used to indicate a size by millimètres than by -inches and fractions, it appears that the metrical system cannot shorten -the work of arithmetical computation in shop work, and is therefore of no -advantage to the mechanic or draftsman, but rather the reverse. This is -the opinion of Coleman Sellers, the distinguished Philadelphia engineer -and manufacturer, who, after a trial of the millimètre in his shops for -some years, returned to the use of the inch, and writes in _Engineering -News_: “The loss from the use of a small unit requiring many figures -to express what is needed, takes away from the other advantages of the -system when considered from a labor-saving point of view.” - -In France itself the metrical system is not wholly decimal in actual -practice, as we find the following measures in use in addition to the -decimal divisions: double decamètre, demi-decamètre, double mètre, -demi-mètre, and double decimètre. - -The metrical system has been adopted in the following countries: France -and colonies, Holland and colonies, Belgium, Spain and colonies, -Portugal, Italy, Germany, Greece, Roumania, British India, Mexico, -New Granada, Ecuador, Peru, Brazil, Uruguay, Argentine Confederacy, -Chili, Venezuela; and partially in Wurtemburg, Bavaria, Baden, Hesse, -Switzerland, Denmark, Austria, and Turkey. - -In the past centuries all the work and records of English-speaking -peoples--now numbering about 100,000,000, and increasing and progressing -faster than all other nationalities, as well as being closely connected -by descent and business--have been done and recorded under the yard -standard, and any change now would inevitably render necessary continual -reductions, to the great detriment and inconvenience of the mass of our -people, and with little or no practical benefit, except perhaps to a -small class of scientific and pseudo-scientific men, who can and do amuse -themselves with the fancied uniformity of the mètre. - -All our numerous text-books and tables, mechanical and scientific, would -be rendered entirely useless by the change, and this is a serious final -consideration. - - - - - -End of the Project Gutenberg EBook of Standard Measures of United States, -Great Britain and France, by Arthur S. 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C. Wurtele - -This eBook is for the use of anyone anywhere in the United States and most -other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms of -the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you'll have -to check the laws of the country where you are located before using this ebook. - -Title: Standard Measures of United States, Great Britain and France - History and actual comparisons with appendix on introduction - of the mètre - -Author: Arthur S. C. Wurtele - -Release Date: February 19, 2017 [EBook #54208] - -Language: English - -Character set encoding: UTF-8 - -*** START OF THIS PROJECT GUTENBERG EBOOK STANDARD MEASURES OF US, GB, FRANCE *** - - - - -Produced by Chris Curnow and the Online Distributed -Proofreading Team at http://www.pgdp.net (This file was -produced from images generously made available by The -Internet Archive) - - - - - - -</pre> - - -<h1><span class="smcap">Standard Measures</span><br /> -<span class="smaller">OF</span><br /> -UNITED STATES,<br /> -GREAT BRITAIN, AND FRANCE.</h1> - -<p class="titlepage">HISTORY AND ACTUAL COMPARISONS.</p> - -<p class="titlepage"><span class="smaller">WITH</span><br /> -APPENDIX ON INTRODUCTION OF THE MÈTRE.</p> - -<p class="titlepage">BY<br /> -<span class="larger">ARTHUR S. C. WURTELE,</span><br /> -ASS’T ENG., N. Y. C. & H. R. R.</p> - -<div class="figcenter"> -<img src="images/spon.jpg" width="80" height="80" alt="E. & F. N. Spon publisher’s mark" /> -</div> - -<p class="titlepage smaller">E. & F. N. SPON,<br /> -NEW YORK: 44 MURRAY STREET.<br /> -LONDON: 16 CHARING CROSS.<br /> -1882.</p> - -<p class="titlepage"><span class="smcap">Copyright, 1882, by Arthur S. C. Wurtele.</span></p> - -<hr /> - -<p><span class="pagenum"><a name="Page_1" id="Page_1">[1]</a></span></p> - -<h2>INTRODUCTION.</h2> - -<p>During the preparation of this investigation of Standard -Measures a large number of authorities were examined, -including the following: Kelly’s “Universal -Cambist,” Maunder’s “Weights and Measures,” “Encyclopædia -Britannica,” “Chambers’ Encyclopædia,” Williams’ -“Geodesy,” Hymer’s works, “Smithsonian Reports,” “Coast -Survey Reports,” Herschel’s “Astronomy,” etc. The only -concise and clear statement I found was J. E. Hilgard’s -report to the Coast Survey on standards in 1876, which I -was gratified to find coincides with my deductions.</p> - -<p class="right"><span class="smcap">Arthur S. C. Wurtele.</span></p> - -<p class="smaller"><span class="smcap">Albany</span>, November 26, 1881.</p> - -<p><span class="pagenum"><a name="Page_2" id="Page_2">[2]</a></span></p> - -<hr /> - -<p><span class="pagenum"><a name="Page_3" id="Page_3">[3]</a></span></p> - -<h2>STANDARD MEASURES.</h2> - -<p>A standard measure of length at first sight appears to -be very simple—merely a bar of metal of any length, according -to the unit of any country; and comparisons of -different standards do not seem to present any difficulty. -But on looking further into the thing, we find that standards -are referred to some natural invariable length, and -we are at once confronted with a mass of scientific reductions -giving different values to the same thing, according -to successively improved means of observation. We find, -also, that comparisons of one standard with another differ, -as given by reductions carried to great apparent exactness.</p> - -<p>Every author appears to assume the right of using his -own judgment as to what reduction is to be considered -the most exact, and the result is a very confusing difference -in apparently exact figures, with nothing to show -how these differences arise.</p> - -<p>I have endeavored to indicate what may be the cause -of this confusion by giving the figures of actually observed -comparisons and reductions; in a manner, the roots -of the figures used as statements of length.</p> - -<p>Sir Joseph Whitworth gives 1/40000 of an inch as the -smallest length that can be measured with certainty, with -an ultimate possibility of 1/1000000 of an inch; but imperceptible -variations of temperature affect these infinitesimal<span class="pagenum"><a name="Page_4" id="Page_4">[4]</a></span> -lengths to such an extent that he believes the limit -can only be reached at a standard temperature of 85° F., -to avoid the effect of heat of the body.</p> - -<p>It appears to me that comparisons should be made of -double yards and mètres with the old French toise, as the -limit of exactness would be thereby doubled.</p> - -<p>Another great defect in statements of relative values is -the omission of necessary facts—the material of which -the bars or standards are made, the temperature at which -comparison was made, and the standard temperatures used -as to the final reduction, with the coefficient of expansion -adopted.</p> - -<p>Again, bars of different metals appear in time to sensibly -change their relative length.</p> - -<h3>ENGLISH STANDARDS OF LENGTH.</h3> - -<p>The first establishment of a uniform standard appears -to have been made in 1101 by Henry I., who is said to -have fixed the ulna (now the yard) at the length of his -arm; but nothing definite was done till 1736, when the -Royal Society took steps toward securing a general standard, -and in 1742 they had a standard yard made by -Graham from a comparison of various yards and ells of -Henry VII. and Elizabeth, that were kept in the Exchequer.</p> - -<p>Two copies of the Royal Society standard yard were -made by Bird in 1758 for a committee of Parliament, one -of which was marked “standard of 1758,” and the other -1760. But no exact legal standard was yet established, -as shown by comparisons in 1802 of the various standard -measures in use which Pictet, of Geneva, made with an -accurate scale by Troughton, using means exact to the -ten thousandth part of an inch, with the following results -at the temperature of 62° F.:</p> - -<p><span class="pagenum"><a name="Page_5" id="Page_5">[5]</a></span></p> - -<table summary="Comparative lengths of the “standard” yard measures, taken at 62° F."> - <tr> - <td colspan="2">Troughton Scale</td> - <td></td> - <td class="right">36·00000</td> - <td>inches.</td> - </tr> - <tr> - <td>Parliamentary</td> - <td>Standard</td> - <td>(1758, Bird)</td> - <td class="right">36·00023</td> - <td class="center">“</td> - </tr> - <tr> - <td>Royal Society</td> - <td class="center">“</td> - <td>(1760, “ )</td> - <td class="right">35·99955</td> - <td class="center">“</td> - </tr> - <tr> - <td class="center">“</td> - <td class="center">“</td> - <td>(Graham)</td> - <td class="right">36·00130</td> - <td class="center">“</td> - </tr> - <tr> - <td>Exchequer</td> - <td class="center">“</td> - <td></td> - <td class="right">35·99330</td> - <td class="center">“</td> - </tr> - <tr> - <td>Tower</td> - <td class="center">“</td> - <td></td> - <td class="right">36·00400</td> - <td class="center">“</td> - </tr> - <tr> - <td>Gen. Roy</td> - <td class="center">“</td> - <td>(Trig. Survey)</td> - <td class="right">36·00036</td> - <td class="center">“</td> - </tr> -</table> - -<p>Parliament finally undertook to reform the measures of -England, and appointed a commission in 1818, under -whose authority Capt. Kater compared the standard yards -then in use with the following results, as referred to the -Indian Survey standard:</p> - -<table summary="Comparative lengths of various “standard” yard measures"> - <tr> - <td>Col. Lambton Standard (Indian Survey)</td> - <td class="right">36·000000</td> - <td>inches.</td> - </tr> - <tr> - <td>Bird’s Standard (1760)</td> - <td class="right">36·000659</td> - <td class="center">“</td> - </tr> - <tr> - <td>Sir Geo. Schuckburgh’s Standard</td> - <td class="right">36·000642</td> - <td class="center">“</td> - </tr> - <tr> - <td>Ramsden’s Bar. Ordnance Survey</td> - <td class="right">36·003147</td> - <td class="center">“</td> - </tr> - <tr> - <td>Gen. Roy’s Scale</td> - <td class="right">36·001537</td> - <td class="center">“</td> - </tr> - <tr> - <td>Royal Society Standard</td> - <td class="right">36·002007</td> - <td class="center">“</td> - </tr> -</table> - -<p>The commission reported in favor of adopting Bird’s -standard of 1760, as it differed so slightly from Sir George -Schuckburgh’s standard (which had been used in deducing -the value of the French mètre) that those values could -be assumed as correct. They also established the length -of the seconds pendulum at level of sea in London and in -vacuo as 39·13929 inches. The seconds pendulum had -been previously fixed by Wollaston and Playfair in 1814 -as 39·13047 inches.</p> - -<p>On this report, an Act of Parliament in 1823 declared -the only standard measure of length for the United Kingdom -to be the yard as given by the distance at 32° F. -between two points in gold studs on the brass bar, made -by Bird, and marked “Standard of 1760,” and in the -keeping of the Clerk of the House of Commons; also it -referred this standard yard to the natural standard of a -pendulum vibrating seconds of mean solar time at the<span class="pagenum"><a name="Page_6" id="Page_6">[6]</a></span> -level of the sea, in vacuo at London and temperature of 32° -F., as in the proportion of 36 to 39·13929; so that a pendulum -36 inches long ought to make 90088·42 vibrations -in 24 hours.</p> - -<p>The Royal Society had a copy of the legal standard -made by Bailey in 1834; and in the same year the Parliamentary -standard was destroyed by fire at the burning -of the Houses of Parliament, leaving the kingdom again -without a legal standard.</p> - -<p>All attempts made by a commission consisting of Airy, -Bailey, Herschel, Lubbock, and Sheepshanks, to restore the -standard by means of the seconds pendulum failed in -exactness, on account of the many conditions of a vibrating -pendulum, and recourse was had to the Royal Society -standard, which had been carefully compared by Captain -Kater in 1818, and from this in 1838 Bailey and Sheepshanks -made six bronze bars, one inch square, and 38 inches -long, which in 1855 were legalized by Act of Parliament, -and the English standard of length defined as follows:</p> - -<p>“That the straight line on distance between the centres -of the transverse lines in the two gold plugs on the -bronze bar deposited in the Exchequer shall be the -genuine standard yard at the temperature of 62° Fahrenheit; -and if lost, it shall be replaced by means of its copies.”</p> - -<p>The French metrical system was made legal permissively -in 1864, at the length established by Captain Kater, referred -to in Act of Parliament of 1823, of 1 mètre equal to -39·37079 inches, or 3·28089916 feet.</p> - -<p>These are the standards now in use in the United -Kingdom.</p> - -<h3>UNITED STATES.</h3> - -<p>By the Constitution of the United States Congress is -charged with fixing the standard of measures (Art. 1,<span class="pagenum"><a name="Page_7" id="Page_7">[7]</a></span> -sec. 8); but as no enactment has been made by Congress, -the standard yard in England, which was legal previous to -1776 in the Colonies, is the standard yard of the United -States, and does not differ with the English standard -yard.</p> - -<p>Under resolution of Congress in 1830, Mr. Hassler was -employed to examine the standards in use.</p> - -<p>Considerable discrepancies were found, but the mean of -all examined corresponded very nearly with the English -standard, and in 1832 the recommendation of Mr. Hassler -was adopted, and the standard yard defined as the -distance between the 27th and 63d inch marks, at the -temperature of 62° F., on the brass scale 82 inches long, -being an exact copy of Sir George Schuckburgh’s standard, -made by Troughton, of London, for the Coast Survey, and -deposited in the Office of Weights and Measures at Washington.</p> - -<p>In 1836 an Act of Congress ordered standards to be -sent to each Governor of a State, and the work was done -under direction of Mr. Hassler.</p> - -<p>In 1856, two copies of the English standard yard, as -restored after destruction of the original standard by fire -in 1834, No. 11 of bronze, and No. 57 of Low Moor wrought -iron, were presented to the United States by Airy.</p> - -<p>The United States Troughton standard bar being compared -with No. 11 was found to be longer by 0·00085 -inch, or in proportion of 1 to 1·0000237216, about -1½ inches in a mile, according to Report of Secretary of -Treasury in 1857.</p> - -<p>Later comparisons made by J. E. Hilgard, of the Coast -Survey, at the British Standards Office, between No. 11 and -the standard imperial yard, give No. 11 as 0·000088 inch -shorter, or it would be of standard length at temperature -of 62·25° F.</p> - -<p><span class="pagenum"><a name="Page_8" id="Page_8">[8]</a></span></p> - -<p>We may infer that the Troughton standard is too long -by 0·000762 inch, or would be standard length at temperature -59·77° F. instead of at 62° by making expansion -reduction with Airy’s coefficient for the bronze of the -imperial standards, 0·000342 inch per yard for 1° F.</p> - -<p>The mètre was made a legal standard permissively in -1866; the United States mètre standard being one of the -12 iron mètre bars made and verified for the French Government -in 1799 on the adoption of the metrical system, -and brought to America by Mr. Hassler in 1800, the -relative value being fixed by Act of Congress at 39·37 -inches.</p> - -<p>The relative value of 39·36850154 United States inches, -as obtained by Mr. Hassler, corrected to 62° F., was used -by the Coast Survey till 1868, when it was found advisable -to use the relative value of 39·3704 as deduced by Clarke. -Since 1800 several standard mètre bars were sent to the -United States by the French Government, and on comparison, -there appearing to be a slight discrepancy, the -original iron standard mètre bar was sent to Dr. F. A. P. -Barnard in Paris, and in 1867 it was compared with the -French platinum standard, which is only used once in ten -years to verify other standards.</p> - -<p>A difference was found by this comparison of only -·00017 millimètre or 1/160000 inch, which being only 1/100 of -an inch in a mile is inappreciable.</p> - -<h3>FRANCE.</h3> - -<p>The standard of length of the système ancient was the -toise of 6 pieds, divided into 12 pouces of 12 lignes -each.</p> - -<p>The origin of the toise is not known, but it was probably -legally established by Philip Le Bel, about 1300, as he -first appears to have taken steps toward a uniform system<span class="pagenum"><a name="Page_9" id="Page_9">[9]</a></span> -of measures in France. In the 13th century the -toise is mentioned by Ch. Le Rains. In the 14th century -Menongier writes that, in marching, the sight should strike -the ground 4 toises in front. In the fifteenth century Pereforest -brings in the toise, and in the sixteenth century the -Contume de Berry says, “We use in this country two toises; -one for carpenters of 5 pieds and a half, the other for masons -of 6 pieds.”</p> - -<p>Picard used the toise in his measurement of an arc of -meridian from Malvoisin to London in 1669.</p> - -<p>The meridians measured by the Academy in 1735 to settle -the question of the figure of the earth were made by means -of two standard toises, known as the “Toise du Nord,” and -the “Toise du Sud.”</p> - -<p>The first, used by Maupertuis, Clairault, and Le Monnier, -in Lapland, was destroyed by immersion in sea-water, -when their ship was wrecked on the return voyage.</p> - -<p>The second, with which La Condamine, Bourgner, and -Godin operated in Peru, was the original of the toise Canivet -made in 1768, and of the standards used in determining -the mètre.</p> - -<p>The commencement of the move for a scientific standard -of length in France which resulted in the mètre was in -1790, when the revolutionary government proposed to -England the formation of a commission of equal numbers -from the English Royal Society and the French Academy, -for the purpose of fixing the length of the seconds pendulum -at latitude 45° as the basis of a new system of measures. -This proposal was not favorably received, and the -Academy, at the request of government, appointed as a -commission Borda, Lagrange, Laplace, Monge, and Condorcet, -to decide whether the seconds pendulum, the quarter -of the equator, or the quarter of a meridian, should be used -as the natural standard for the new system of measures.<span class="pagenum"><a name="Page_10" id="Page_10">[10]</a></span> -They settled on the last as best for the purpose, and resolved -that the ten millionth of the meridian quadrant, or distance -from equator to pole, measured at sea level, be taken for -basis of the new system, and be called a mètre.</p> - -<p>Delambre and Mechin were at once charged with re-measurement -of the meridian surveyed in 1739 by La Caille -and Cassini, from Dunkirk to Perpignan, and its extension -to Barcelona.</p> - -<p>Operations were commenced in 1792, and carried on -with great accuracy to completion in 1799; Delambre -working between Dunkirk and Paris, and Mechin between -Paris and Barcelona.</p> - -<p>The distance measured from Dunkirk to Barcelona was -9° 40´ 24·24´´ of arc, or 1,075,059 mètres, as reduced to the -new standard.</p> - -<p>The “toise de Peru” was the standard used in the work -at a temperature of 13° R.</p> - -<p>Two base-lines were measured with Borda’s compensating -bars of brass and platinum; one at Melun, near Paris, -6076 toises long, and the second at Perpignan, 6028 toises -long, and though over 900,000 mètres apart, the calculated -length differed by only 10 pouces.</p> - -<p>This meridian was afterward, in 1806, extended by -Gen. Roy to Greenwich, on the north, and by Biot and -Arago to Formentera, on the south. The results, as given -by Laplace in centesimal degrees and mètres, are as -follows:</p> - -<table summary="Measurements of the meridian"> - <tr> - <td>Greenwich</td> - <td class="right">57·19753°</td> - <td class="right">·0</td> - <td>mètres.</td> - </tr> - <tr> - <td>Pantheon, Paris</td> - <td class="right">54·27431°</td> - <td class="right">292,719·3</td> - <td class="center">“</td> - </tr> - <tr> - <td>Formentera</td> - <td class="right">42·96178°</td> - <td class="right">1,423,636·1</td> - <td class="center">“</td> - </tr> -</table> - -<p>The middle of the arc being 50·079655° Cent., or 45° 4´ -18·0822´´ Sexa., and the middle degree centesimal being -very nearly 100,000 mètres.</p> - -<p><span class="pagenum"><a name="Page_11" id="Page_11">[11]</a></span></p> - -<p>The determination of the final result of these geodetic -measurements was referred to a committee of 20 members; -9 named by the French Government, and the others by the -governments of Holland, Savoy, Denmark, Spain, Tuscany, -and of the Cisalpine, Ligurian, and Swiss republics, on the -invitation of France.</p> - -<p>This committee established the meridian quadrant at -5,130,740 toises; making the mètre 0·513074 of the toise, -or 36·9413 pouces, or 443·296 lignes, and the toise -1·94903659 mètres.</p> - -<p>Iron standard mètre bars, 12 in number were made by -Borda, also 2 of platinum and 4 standard toise bars.</p> - -<p>The 12 standard iron mètre bars were sent to different -countries, after being verified by the French Government, -and on the 2d of November, 1801, the mètrical système -was legalized by France, and the standard unit of length -declared to be the ten millionth part of a meridian quadrant -of the earth, as defined by the distance at a temperature -of 0° Centigrade (32° F.) between two points on a -platinum bar in the keeping of the Academy of Science -at Paris. This standard bar is used only once every ten -years for exact comparisons, as stated by Dr. F. A. P. -Barnard.</p> - -<p>About 1837 Bessel, by a combination of 11 measured -arcs of meridian, deduced the quadrant of meridian as -5,131,179·81 toises instead of 5,130,740 toises, as fixed by -law. This would make to quadrant 10,000,565·278 legal -mètres, or would increase the mètre length from 443·296 -lignes to 443·334 lignes, agreeing very nearly with -result obtained by Airy in 1830, from a combination of -13 measured arcs.</p> - -<p>The following are the measured arcs used by Bessel and -Airy; the combinations being indicated by initial letters, -A and B.</p> - -<p><span class="pagenum"><a name="Page_12" id="Page_12">[12]</a></span></p> - -<table summary="Measurements of the arcs of the meridian"> - <tr> - <th></th> - <th>Measurer.</th> - <th colspan="4">Mid. Lat.</th> - <th colspan="3">Arc.</th> - <th colspan="2">Length.</th> - </tr> - <tr> - <td class="right">B.—</td> - <td>Svanberg, Sweden</td> - <td class="center">+</td> - <td class="right">66°</td> - <td class="right">20´</td> - <td class="right">10·0´´</td> - <td class="right">1°</td> - <td class="right">37´</td> - <td class="right">19·6´´</td> - <td class="right">593,277</td> - <td>feet</td> - </tr> - <tr> - <td class="right">A.—</td> - <td>Maupertuis, Sweden</td> - <td class="center">+</td> - <td class="right">66°</td> - <td class="right">19´</td> - <td class="right">37·0´´</td> - <td class="right">0°</td> - <td class="right">57´</td> - <td class="right">30·4´´</td> - <td class="right">351,832</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">A.—</td> - <td>Struve, Russia</td> - <td class="center">+</td> - <td class="right">58°</td> - <td class="right">17´</td> - <td class="right">37·0´´</td> - <td class="right">3°</td> - <td class="right">35´</td> - <td class="right">5·2´´</td> - <td class="right">1,309,742</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">B.—</td> - <td>Struve and Tenner, Russia</td> - <td class="center">+</td> - <td class="right">56°</td> - <td class="right">3´</td> - <td class="right">55·5´´</td> - <td class="right">8°</td> - <td class="right">2´</td> - <td class="right">28·9´´</td> - <td class="right">2,937,439</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">B.—</td> - <td>Bessel and Bayer, Prussia</td> - <td class="center">+</td> - <td class="right">54°</td> - <td class="right">58´</td> - <td class="right">26·0´´</td> - <td class="right">1°</td> - <td class="right">30´</td> - <td class="right">29·0´´</td> - <td class="right">551,073</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">B.—</td> - <td>Schumacher, Denmark</td> - <td class="center">+</td> - <td class="right">54°</td> - <td class="right">8´</td> - <td class="right">13·7´´</td> - <td class="right">1°</td> - <td class="right">31´</td> - <td class="right">53·3´´</td> - <td class="right">559,121</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">A, B.—</td> - <td>Ganss, Hanover</td> - <td class="center">+</td> - <td class="right">52°</td> - <td class="right">32´</td> - <td class="right">16·6´´</td> - <td class="right">2°</td> - <td class="right">0´</td> - <td class="right">57·4´´</td> - <td class="right">736,425</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">A.—</td> - <td>Roy and Kater, England</td> - <td class="center">+</td> - <td class="right">52°</td> - <td class="right">35´</td> - <td class="right">45·0´´</td> - <td class="right">3°</td> - <td class="right">57´</td> - <td class="right">13·1´´</td> - <td class="right">1,442,953</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">B.—</td> - <td><span class="ditto1">“</span> <span class="ditto1">“</span> <span class="ditto1">“</span></td> - <td class="center">+</td> - <td class="right">52°</td> - <td class="right">2´</td> - <td class="right">19·0´´</td> - <td class="right">2°</td> - <td class="right">50´</td> - <td class="right">23·5´´</td> - <td class="right">1,036,409</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">A.—</td> - <td>Lacaille and Cassini, France</td> - <td class="center">+</td> - <td class="right">46°</td> - <td class="right">52´</td> - <td class="right">2·0´´</td> - <td class="right">8°</td> - <td class="right">20´</td> - <td class="right">0·3´´</td> - <td class="right">3,040,605</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">A, B.—</td> - <td>Delambre and Mechin, France</td> - <td class="center">+</td> - <td class="right">44°</td> - <td class="right">51´</td> - <td class="right">2·5´´</td> - <td class="right">12°</td> - <td class="right">22´</td> - <td class="right">12·7´´</td> - <td class="right">4,509,832</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">A.—</td> - <td>Boscovich, Rome</td> - <td class="center">+</td> - <td class="right">42°</td> - <td class="right">59´</td> - <td class="right">·0´´</td> - <td class="right">2°</td> - <td class="right">9´</td> - <td class="right">47·0´´</td> - <td class="right">787,919</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">A.—</td> - <td>Mason and Dixon, America</td> - <td class="center">+</td> - <td class="right">39°</td> - <td class="right">12´</td> - <td class="right">·0´´</td> - <td class="right">1°</td> - <td class="right">28´</td> - <td class="right">45·0´´</td> - <td class="right">538,100</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">A, B.—</td> - <td>Lambton, India</td> - <td class="center">+</td> - <td class="right">16°</td> - <td class="right">8´</td> - <td class="right">21·5´´</td> - <td class="right">15°</td> - <td class="right">57´</td> - <td class="right">40·7´´</td> - <td class="right">5,794,598</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">A, B.—</td> - <td>Lambton and Everest, India</td> - <td class="center">+</td> - <td class="right">12°</td> - <td class="right">32´</td> - <td class="right">20·8´´</td> - <td class="right">1°</td> - <td class="right">34´</td> - <td class="right">56·4´´</td> - <td class="right">574,318</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">A, B.—</td> - <td>Lacondamine, Peru</td> - <td class="center">-</td> - <td class="right">1°</td> - <td class="right">31´</td> - <td class="right">0·4´´</td> - <td class="right">3°</td> - <td class="right">7´</td> - <td class="right">3·5´´</td> - <td class="right">1,131,050</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">A.—</td> - <td>Lacaille, Cape Good Hope</td> - <td class="center">-</td> - <td class="right">33°</td> - <td class="right">18´</td> - <td class="right">30·0´´</td> - <td class="right">1°</td> - <td class="right">13´</td> - <td class="right">17·5´´</td> - <td class="right">445,506</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">B.—</td> - <td>Maclear, <span class="ditto1">“</span> <span class="ditto1">“</span></td> - <td class="center">-</td> - <td class="right">35°</td> - <td class="right">43´</td> - <td class="right">20·0´´</td> - <td class="right">3°</td> - <td class="right">34´</td> - <td class="right">34·7´´</td> - <td class="right">1,301,993</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right">A.—</td> - <td>Plana and Cartessi, Piedmont</td> - <td></td> - <td colspan="3">———————</td> - <td class="right">1°</td> - <td class="right">7´</td> - <td class="right">31·1´´</td> - <td colspan="2">——————</td> - </tr> -</table> - -<p><span class="pagenum"><a name="Page_13" id="Page_13">[13]</a></span></p> - -<p>The following different lengths of the mètre have been -obtained:</p> - -<table summary="Lengths of the mètre by different standards"> - <tr> - <td>As adopted by France, 1801</td> - <td class="right">443·296</td> - <td>lignes.</td> - </tr> - <tr> - <td>According to Delambre</td> - <td class="right">443·264</td> - <td class="center">“</td> - </tr> - <tr> - <td><span class="ditto3">“</span> Bessel</td> - <td class="right">443·33394</td> - <td class="center">“</td> - </tr> - <tr> - <td><span class="ditto3">“</span> Airy</td> - <td class="right">443·32387</td> - <td class="center">“</td> - </tr> - <tr> - <td><span class="ditto3">“</span> Clarke</td> - <td class="right">443·36146</td> - <td class="center">“</td> - </tr> - <tr> - <td>From Peru Meridian</td> - <td class="right">443·440</td> - <td class="center">“</td> - </tr> -</table> - -<p>The length of a pendulum vibrating 100,000 times in a -mean solar day was determined in numerous careful experiments -by Biot, Arago, and Mathieu, in mètres of -443·296 lignes, as follows:</p> - -<table summary="Measurements taken using pendulum"> - <tr> - <td>Dunkirk</td> - <td class="right">56·67</td> - <td>lat. Cent.</td> - <td class="right">0</td> - <td>above sea</td> - <td class="right">0·7419076</td> - <td>mètres.</td> - </tr> - <tr> - <td>Paris</td> - <td class="right">54·26</td> - <td class="center">“</td> - <td class="right">65</td> - <td class="center">“</td> - <td class="right">0·7418870</td> - <td class="center">“</td> - </tr> - <tr> - <td><span class="ditto1">“</span> by Borda</td> - <td class="right">54·26</td> - <td class="center">“</td> - <td class="right">0</td> - <td class="center">“</td> - <td class="right">0·7416274</td> - <td class="center">“</td> - </tr> - <tr> - <td>Bordeau</td> - <td class="right">49·82</td> - <td class="center">“</td> - <td class="right">0</td> - <td class="center">“</td> - <td class="right">0·7412615</td> - <td class="center">“</td> - </tr> - <tr> - <td>Formentera</td> - <td class="right">42·96</td> - <td class="center">“</td> - <td class="right">196</td> - <td class="center">“</td> - <td class="right">0·7412061</td> - <td class="center">“</td> - </tr> -</table> - -<p>Borda also determined the length of the seconds -pendulum at Paris, in vacuo:</p> - -<table summary="Length of the seconds pendulum at Paris, in vacuo"> - <tr> - <td>First result</td> - <td class="right">440·5595</td> - <td>lignes</td> - <td>= 0·9938267</td> - <td>mètre.</td> - </tr> - <tr> - <td>Second result</td> - <td class="center">“</td> - <td class="center">“</td> - <td>= 0·9938460</td> - <td class="center">“</td> - </tr> - <tr> - <td>As given by Ganot</td> - <td class="center">“</td> - <td class="center">“</td> - <td>= 0·9935</td> - <td class="center">“</td> - </tr> -</table> - -<p>In 1812 the système usuelle was established, of which -the unit was one third of the mètre, with the old name of -pied, and duodecimally divided into pouces and lignes.</p> - -<p>This system continued in use till 1840, when it was -abolished by law, and the names of pied, pouce, and ligne -forbidden under penalties. So the mètre, decimally divided, -remains the only legal measure of length in France.</p> - -<h3>COMPARISONS OF UNITED STATES AND -ENGLISH STANDARDS.</h3> - -<p>In 1832, under resolution of Congress, Mr. Hassler -compared the different standard yards in America, with<span class="pagenum"><a name="Page_14" id="Page_14">[14]</a></span> -the following results, using the yard between the twenty-seventh -and sixty-third inches on the scale made of bronze -by Troughton, of London, for the United States Coast -Survey, as the reference, that being identical with Sir -George Schuckburg’s standard:</p> - -<table summary="Comparative lengths of the “standard” yard measures in America"> - <tr> - <td>Troughton Scale, mid. yard</td> - <td class="right">36·0000000</td> - <td>inches.</td> - </tr> - <tr> - <td><span class="ditto2">“</span> <span class="ditto2">“</span> between platinum points</td> - <td class="right">35·9989758</td> - <td class="center">“</td> - </tr> - <tr> - <td>Jones yard in State Department</td> - <td class="right">35·9990285</td> - <td class="center">“</td> - </tr> - <tr> - <td>Iron yard in Engineer Department</td> - <td class="right">35·9987760</td> - <td class="center">“</td> - </tr> - <tr> - <td>Brass yard, Albany, Sec. of State</td> - <td class="right">36·0002465</td> - <td class="center">“</td> - </tr> - <tr> - <td>Gilbert yard, University of Virginia</td> - <td class="right">35·9952318</td> - <td class="center">“</td> - </tr> -</table> - -<p>In 1856 the Troughton standard bronze scale was -compared with the bronze standard yard No. 11, which -was sent over by Airy as a copy of the English imperial -standard, as restored after destruction of the original -standard by fire in 1834, and the United States -standard was found to be longer by 0·00085 inch.</p> - -<p>Later comparisons by J. E. Hilgard, of the Coast Survey, -of the bronze standard No. 11 with the imperial -standard yard, at the British Standards Office, gave No. -11 as 0·000088 shorter than the imperial standard.</p> - -<p>Hassler’s reduction of the mètre, as deduced by Beach -at 62° F., 39·36850154, compared with the English reduction -of the mètre, 39·37079 inches, gives an excess to the -United States Standard of 0·002029 inch.</p> - -<p>The following reductions have been given for the -United States yard in English inches:</p> - -<table summary="Conversions of the U.S. yard to inches"> - <tr> - <td>Report of Sec. of Treas., 1857</td> - <td>36·00087</td> - <td>= 1·00002416</td> - </tr> - <tr> - <td>Chambers’ Encyclopædia, 1872</td> - <td>36·00087</td> - <td></td> - </tr> - <tr> - <td><span class="ditto3">“</span> <span class="ditto3">“</span> <span class="ditto1">“</span></td> - <td>36·0020892</td> - <td>= 1·0000580334</td> - </tr> - <tr> - <td>Trautwine</td> - <td>36·0020894</td> - <td>= 1·000058038</td> - </tr> - <tr> - <td>Mathewson, U. S. surveyor</td> - <td>36·00208944</td> - <td>= 1·00005804</td> - </tr> - <tr> - <td>Hassler and Beach</td> - <td>36·002092</td> - <td>= 1·00005811</td> - </tr> - <tr> - <td>J. E. Hilgard, Coast Survey</td> - <td>36·00076</td> - <td>= 1·000021</td> - </tr> -</table> - -<p><span class="pagenum"><a name="Page_15" id="Page_15">[15]</a></span></p> - -<p>To Mr. Hassler’s reduction the name of United States -inch has been applied; but his reduction is not correct, as -he used a rate of expansion for brass deduced by himself -of 0·0003783 inch in one yard for 1° F., and later experiments -show that the smaller rate of 0·000342, deduced by -Airy, is more correct.</p> - -<p>By correcting Hassler’s reduction with the later rate of -expansion, J. E. Hilgard shows that the difference would -be very small, or only 36·0002286 = 1·00000635, or about -⅖ of an inch in a mile.</p> - -<p>In Coast Survey report for 1876, J. E. Hilgard calls attention -to another difficulty in the matter of extreme -accuracy, in the uncertainty with regard to the -permanence in the length of a bar, and states that -the bronze standard bar No. 11 and the Low Moor iron -standard bar No. 57, presented to the United States by -Great Britain, are found to have changed their relative -length by 0·00025 inch in 25 years; the bronze bar being -now relatively shorter by that amount. This subject, he -states, is undergoing further investigation.</p> - -<h3>COMPARISON OF UNITED STATES AND -FRENCH STANDARDS.</h3> - -<p>In 1817 Mr. Hassler examined the French standards in -America, for the Coast Survey, using the Troughton bronze -standard scale, which is identical with Sir George Schuckburg’s -standard, as the reference, with the following results, -all being reduced to temperature of 32° F.</p> - -<table summary="The French standard mètres in inches, measured at 32° F."> - <tr> - <td>Original Iron Mètre,</td> - <td>1799</td> - <td class="right">39·381022708</td> - <td>inches.</td> - </tr> - <tr> - <td>Lenoir Iron Mètre,</td> - <td>Coast Survey</td> - <td class="right">39·37972015</td> - <td class="center">“</td> - </tr> - <tr> - <td><span class="ditto1">“</span> Brass <span class="ditto1">“</span></td> - <td class="center">“</td> - <td class="right">39·380247972</td> - <td class="center">“</td> - </tr> - <tr> - <td><span class="ditto1">“</span> <span class="ditto1">“</span> <span class="ditto">“</span></td> - <td>Eng. Dept.</td> - <td class="right">39·38052739</td> - <td class="center">“</td> - </tr> - <tr> - <td>Canivet Iron Toise,</td> - <td>1768</td> - <td class="right">76·74334472</td> - <td class="center">“</td> - </tr> - <tr> - <td>Lenoir <span class="ditto">“</span> <span class="ditto1">“</span></td> - <td></td> - <td class="right">76·74192710</td> - <td class="center">“</td> - </tr> -</table> - -<p><span class="pagenum"><a name="Page_16" id="Page_16">[16]</a></span></p> - -<p>In 1814 Troughton had compared with his own scale in -London two of the above.</p> - -<table summary="Troughton’s measurements"> - <tr> - <td>Lenoir Iron Mètre,</td> - <td>C. S.</td> - <td class="right">39·3802506</td> - <td>inches.</td> - </tr> - <tr> - <td><span class="ditto1">“</span> Brass <span class="ditto">“</span></td> - <td class="center">“</td> - <td class="right">39·3803333</td> - <td class="center">“</td> - </tr> -</table> - -<p>In 1832, under resolution of Congress, Hassler again -compared the French standards in the United States, using -as before the Troughton scale, and reducing all to temperature -of 32° F. as follows:</p> - -<table summary="Hassler’s measurements"> - <tr> - <td>Original</td> - <td>Iron Mètre,</td> - <td>1799</td> - <td class="right">39·3808643</td> - <td>inches.</td> - </tr> - <tr> - <td>Lenoir</td> - <td class="center">“</td> - <td><span class="ditto">“</span> C. S.</td> - <td class="right">39·3799120</td> - <td class="center">“</td> - </tr> - <tr> - <td class="center">“</td> - <td>Brass Mètre</td> - <td>C. S.</td> - <td class="right">39·380447</td> - <td class="center">“</td> - </tr> - <tr> - <td class="center">“</td> - <td class="center">“</td> - <td>Eng. Dept.</td> - <td class="right">39·3801714</td> - <td class="center">“</td> - </tr> - <tr> - <td class="center">“</td> - <td class="center">“</td> - <td><span class="ditto2">“</span> in 1829</td> - <td class="right">39·3807095</td> - <td class="center">“</td> - </tr> - <tr> - <td>Fortin</td> - <td class="center">“</td> - <td>State Dept.</td> - <td class="right">39·3796084</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td class="center">“</td> - <td>Treas. <span class="ditto">“</span></td> - <td class="right">39·3795983</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Iron Mètre</td> - <td><span class="ditto1">“</span> <span class="ditto">“</span></td> - <td class="right">39·3807827</td> - <td class="center">“</td> - </tr> - <tr> - <td>Gilbert</td> - <td class="center">“</td> - <td>Univ. of Virg.</td> - <td class="right">39·365408</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Platinum Mètre</td> - <td></td> - <td class="right">39·3803278</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td class="center">“</td> - <td>(Nicollet)</td> - <td class="right">39·380511</td> - <td class="center">“</td> - </tr> - <tr> - <td>Canivet</td> - <td>Iron Toise,</td> - <td>1768</td> - <td class="right">76·74290511</td> - <td class="center">“</td> - </tr> - <tr> - <td>Lenoir</td> - <td class="center">“</td> - <td>1799</td> - <td class="right">76·74047599</td> - <td class="center">“</td> - </tr> -</table> - -<p>From the mean of his comparisons between the United -States brass Troughton standard yard and the authentic -French standard mètres used by the Coast Survey, Hassler, -in 1832, deduced the value of the mètre at 39·3809172 -inches, at 32° F., and by correction for expansion to -United States standard temperature of 62° F., he made -the mètre at 32° equal to 39·36850154 inches at 62° F.</p> - -<p>The British imperial standard and the United States -Troughton standard differ by only 0·000762 inch, which -applied to the English reduction of 39·37079, would give -39·36996 as the relative value according to Troughton -standard.</p> - -<p><span class="pagenum"><a name="Page_17" id="Page_17">[17]</a></span></p> - -<p>The difference between these reductions is probably to -be attributed to the use of different rates of expansion, -in correcting for standard temperatures, which vary considerably, -according to high authority as follows for brass -at 1° F.</p> - -<table summary="Measurements of the rate of expansion for brass"> - <tr> - <td>Whitworth, 1876</td> - <td>0·00000956</td> - <td>= 0·00034416</td> - <td>in. per yard.</td> - </tr> - <tr> - <td>Borda, 1799</td> - <td>0·000009913</td> - <td>= 0·00035687</td> - <td class="center">“</td> - </tr> - <tr> - <td>Smeaton, 1750</td> - <td>0·000010417</td> - <td>= 0·00037501</td> - <td class="center">“</td> - </tr> - <tr> - <td>Hassler</td> - <td>0·000010508</td> - <td>= 0·0003783</td> - <td class="center">“</td> - </tr> - <tr> - <td>Ramsden, 1760</td> - <td>0·000010516</td> - <td>= 0·0003786</td> - <td class="center">“</td> - </tr> - <tr> - <td>Faraday, 1830</td> - <td>0·00001059</td> - <td>= 0·00038124</td> - <td class="center">“</td> - </tr> -</table> - -<p>And for the bronze of which the British imperial standards -are made:</p> - -<table summary="Measurements of the rate of expansion for bronze"> - <tr> - <td>Airy and Sheepshanks</td> - <td>0·0000095</td> - <td>= 0·000342</td> - <td>in. per yard.</td> - </tr> - <tr> - <td>Fizeau</td> - <td>0·00000975</td> - <td>= 0·000351</td> - <td class="center">“</td> - </tr> -</table> - -<p>The correction at Ramsden’s rate is nearly identical with -Hassler’s, and gives 39·3684933; at Whitworth’s rate it -would give 39·36962, very nearly the same as deduced -from the difference between the British Imperial standard -and the United States Troughton standard. The results of -Sir Joseph Whitworth were obtained by use of all late -improvements for scientific precision, and they must be -accepted as most reliable.</p> - -<p>It would appear preferable to give comparisons at the -same temperature in connection with the corrected result, -so that international comparisons of scientific measurements -may not be vitiated by accidental variations.</p> - -<h3>COMPARISON OF ENGLISH AND FRENCH -STANDARDS.</h3> - -<p>When the mètre standard was established in France, -1799, it was compared with Sir George Schuckburg’s<span class="pagenum"><a name="Page_18" id="Page_18">[18]</a></span> -standard yard by Captain Kater. The quadrant of -10,000,000 mètres, or 5,130,740 toises, was determined to be -32,808,992 English feet, giving the mètre equal to -3·2808992 English feet, or 39·37079 inches, and the toise -equal to 6·3945925921 English feet.</p> - -<p>In 1814 Wollaston and Playfair, by comparison with the -platinum mètre standard at 55° F., deduced the mètre as -equal to 39·3828 English inches.</p> - -<p>During the geodetic operations of General Roy in 1802, -who used 60° F. as standard temperature, Pictet’s comparisons, -using means capable of measuring the 10,000th part -of an inch, gave the mètre standard, which is used at 32° F. -as standard temperature, at 39·3828 English inches; this -corrected for temperature by Dr. Young, gave 39·371 English -inches at 62° F.; which result was confirmed by Bird, Maskelyne -and Laudale.</p> - -<p>In 1823, by Act of Parliament on report of committee, -the mètre is fixed as 39·37079 English inches.</p> - -<p>In 1800 the Royal Society, by comparison with two toise -standards sent by Lalande to Maskelyne, deduced the -mètre as 39·3702 English inches.</p> - -<p>Later comparisons by Clarke in the Ordnance Survey -Office at Southampton, in 1866, give the mètre as 39·37043 -inches.</p> - -<p>The French Academy of Sciences by comparison with -Sir George Schuckburg’s standard at temperature of 32° F., -deduced the mètre as 39·3824 English inches, which reduced -to standard temperature of 62° F., would be 39·3711, or -slightly in excess of the value deduced by Dr. Young from -Pictet’s comparisons.</p> - -<p>The legal value in England is one mètre equal to -39·37079, and the latest reduction is 39·37043 inches by -Clarke in 1866, which is probably the most exact reduction.</p> - -<p><span class="pagenum"><a name="Page_19" id="Page_19">[19]</a></span></p> - -<h4>DIFFERENT REDUCTIONS OF THE FRENCH TOISE INTO -ENGLISH FEET.</h4> - -<table summary="Different reductions of the French toise into English feet"> - <tr> - <td>Captain Kater, 1799</td> - <td>6·3945925921</td> - <td>feet.</td> - </tr> - <tr> - <td>Hassler, 1832</td> - <td>6·3951409</td> - <td class="center">“</td> - </tr> - <tr> - <td>Chambers’ Encyclopædia</td> - <td>6·39456</td> - <td class="center">“</td> - </tr> - <tr> - <td><span class="ditto3">“</span> Mathematics</td> - <td>6·394662</td> - <td class="center">“</td> - </tr> - <tr> - <td>Wallace</td> - <td>6·39462</td> - <td class="center">“</td> - </tr> - <tr> - <td>Nystrom</td> - <td>6·39625</td> - <td class="center">“</td> - </tr> - <tr> - <td>Alexander</td> - <td>6·39435</td> - <td class="center">“</td> - </tr> - <tr> - <td>Dana</td> - <td>6·3946</td> - <td class="center">“</td> - </tr> -</table> - -<p>The following table of reductions as used shows clearly -how great a confusion exists in the matter of comparisons:</p> - -<h4>MÈTRE IN INCHES.</h4> - -<table summary="Different reductions of the mètre in inches"> - <tr> - <td>Phœnixville Hand-book</td> - <td>39·368</td> - <td>inches.</td> - </tr> - <tr> - <td>Hassler</td> - <td>39·36850154</td> - <td class="center">“</td> - </tr> - <tr> - <td><span class="ditto2">“</span></td> - <td>39·370788</td> - <td class="center">“</td> - </tr> - <tr> - <td><span class="ditto2">“</span></td> - <td>39·3809172</td> - <td class="center">“</td> - </tr> - <tr> - <td>Trautwine</td> - <td>39·368505</td> - <td class="center">“</td> - </tr> - <tr> - <td><span class="ditto2">“</span></td> - <td>39·37079</td> - <td class="center">“</td> - </tr> - <tr> - <td>Silliman</td> - <td>39·368505</td> - <td class="center">“</td> - </tr> - <tr> - <td><span class="ditto2">“</span></td> - <td>39·37079</td> - <td class="center">“</td> - </tr> - <tr> - <td>Chambers’ Encyclopædia</td> - <td>39·36850535</td> - <td class="center">“</td> - </tr> - <tr> - <td><span class="ditto3">“</span> <span class="ditto3">“</span></td> - <td>39·3707904</td> - <td class="center">“</td> - </tr> - <tr> - <td>Act of United States Congress, 1866</td> - <td>39·37</td> - <td class="center">“</td> - </tr> - <tr> - <td>Smithsonian Report</td> - <td>39·37</td> - <td class="center">“</td> - </tr> - <tr> - <td>Youmans</td> - <td>39·37</td> - <td class="center">“</td> - </tr> - <tr> - <td>Davies</td> - <td>39·37</td> - <td class="center">“</td> - </tr> - <tr> - <td>Homan’s Encyclopædia</td> - <td>39·37008</td> - <td class="center">“</td> - </tr> - <tr> - <td>Weale</td> - <td>39·3702</td> - <td class="center">“</td> - </tr> - <tr> - <td>Ordnance Survey (England, 1866)</td> - <td>39·37043</td> - <td class="center">“</td> - </tr> - <tr> - <td>Clerk Maxwell</td> - <td>39·37043</td> - <td class="center">“</td> - </tr> - <tr> - <td>Capt. Clarke</td> - <td>39·3704316</td> - <td class="center">“</td> - </tr> - <tr> - <td>J. M. Rankine (1870)</td> - <td>39·3704316</td> - <td class="center">“</td> - </tr> - <tr> - <td><span class="ditto3">“</span> (1866)</td> - <td>39·3707904</td> - <td class="center">“</td> - </tr> - <tr> - <td>Alexander (weights and measures)</td> - <td>39·37068</td> - <td class="center">“</td> - </tr> - <tr> - <td>Ganot</td> - <td>39·370788</td> - <td class="center">“</td> - </tr> - <tr> - <td><span class="pagenum"><a name="Page_20" id="Page_20">[20]</a></span>Vose</td> - <td>39·370788</td> - <td class="center">“</td> - </tr> - <tr> - <td>Act of British Parliament, 1823</td> - <td>39·37079</td> - <td class="center">“</td> - </tr> - <tr> - <td>Encyclopædia Britannica</td> - <td>39·37079</td> - <td class="center">“</td> - </tr> - <tr> - <td>Hymer</td> - <td>39·37079</td> - <td class="center">“</td> - </tr> - <tr> - <td>Davies and Peck</td> - <td>39·37079</td> - <td class="center">“</td> - </tr> - <tr> - <td>J. W. Clarke</td> - <td>39·37079</td> - <td class="center">“</td> - </tr> - <tr> - <td>Dana</td> - <td>39·37079</td> - <td class="center">“</td> - </tr> - <tr> - <td>Whittaker</td> - <td>39·37079</td> - <td class="center">“</td> - </tr> - <tr> - <td>Sommerville</td> - <td>39·3707904</td> - <td class="center">“</td> - </tr> - <tr> - <td>Chambers’ Mathematics</td> - <td>39·3707904</td> - <td class="center">“</td> - </tr> - <tr> - <td>Gwilt’s Encyclopædia</td> - <td>39·3707904</td> - <td class="center">“</td> - </tr> - <tr> - <td>Gillespie</td> - <td>39·3707904</td> - <td class="center">“</td> - </tr> - <tr> - <td>Capt. Kater</td> - <td>39·3708</td> - <td class="center">“</td> - </tr> - <tr> - <td>Appleton’s Encyclopædia</td> - <td>39·37079</td> - <td class="center">“</td> - </tr> - <tr> - <td>Van Nostrand</td> - <td>39·3708</td> - <td class="center">“</td> - </tr> - <tr> - <td>D’Aubuisson</td> - <td>39·3708</td> - <td class="center">“</td> - </tr> - <tr> - <td>Johnson (draftsman)</td> - <td>39·3708</td> - <td class="center">“</td> - </tr> - <tr> - <td>Encyclopædia Americana</td> - <td>39·371</td> - <td class="center">“</td> - </tr> - <tr> - <td>Jameson’s Dictionary</td> - <td>39·371</td> - <td class="center">“</td> - </tr> - <tr> - <td>Herbert’s Encyclopædia</td> - <td>39·371</td> - <td class="center">“</td> - </tr> - <tr> - <td>Popular <span class="ditto3">“</span></td> - <td>39·371</td> - <td class="center">“</td> - </tr> - <tr> - <td>Molesworth</td> - <td>39·371</td> - <td class="center">“</td> - </tr> - <tr> - <td>Dr. Young (1802)</td> - <td>39·371</td> - <td class="center">“</td> - </tr> - <tr> - <td>Wallace (engineer)</td> - <td>39·371</td> - <td class="center">“</td> - </tr> - <tr> - <td>Nystrom</td> - <td>39·38091</td> - <td class="center">“</td> - </tr> - <tr> - <td>Hencke</td> - <td>39·3809172</td> - <td class="center">“</td> - </tr> - <tr> - <td>Act of Canadian Parliament, 1873</td> - <td>39·3819</td> - <td class="center">“</td> - </tr> - <tr> - <td>Paris Academy</td> - <td>39·3824</td> - <td class="center">“</td> - </tr> -</table> - -<h4>LENGTH OF THE SECONDS PENDULUM AS GIVEN BY -DIFFERENT WRITERS.</h4> - -<table summary="Different measurements of the length of the seconds pendulum"> - <tr> - <td class="right"><span class="smcap">New York.</span>—</td> - <td>Hencke</td> - <td>39·1012</td> - <td>inches.</td> - </tr> - <tr> - <td></td> - <td>Bartlet</td> - <td>39·11256</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Nystrom</td> - <td>39·1017</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Ganot</td> - <td>39·1012</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Byrne</td> - <td>39·10153</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Wallace</td> - <td>39·10153</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right"><span class="smcap">London.</span>—</td> - <td>Hencke</td> - <td>39·13908</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Gillespie</td> - <td>39·13929</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Chambers’ Encyclopædia</td> - <td>39·13929</td> - <td class="center">“</td> - </tr> - <tr> - <td><span class="pagenum"><a name="Page_21" id="Page_21">[21]</a></span></td> - <td>Williams’ Geodesy</td> - <td>39·13929</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Act of Parliament, 1823</td> - <td>39·13929</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Wallace (engineer)</td> - <td>39·1393</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Chambers’ Mathematics</td> - <td>39·1393</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Hymer Astronomy</td> - <td>39·13734</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Bartlet</td> - <td>39·13908</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Vose</td> - <td>39·1393</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Sommerville</td> - <td>39·1393</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Nystrom</td> - <td>39·1393</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Davies and Peck</td> - <td>39·13908</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Ganot</td> - <td>39·1398</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Wollaston (1814)</td> - <td>39·13047</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Galbraith</td> - <td>39·139</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Byrne</td> - <td>39·1393</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Capt. Kater</td> - <td>39·13829</td> - <td class="center">“</td> - </tr> - <tr> - <td class="right"><span class="smcap">Paris.</span>—</td> - <td>Hencke</td> - <td>39·12843</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Ganot</td> - <td>39·1285</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Galbraith</td> - <td>39·128</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Byrne</td> - <td>39·12843</td> - <td class="center">“</td> - </tr> - <tr> - <td></td> - <td>Wallace</td> - <td>39·12843</td> - <td class="center">“</td> - </tr> -</table> - -<hr /> - -<p><span class="pagenum"><a name="Page_22" id="Page_22">[22]</a></span></p> - -<h2>APPENDIX.</h2> - -<p>Having shown in the preceding pages that in the point -of view of scientific accuracy the yard, mètre, and toise -standards are on a common level, and that in the matter -of comparisons there is no extreme accuracy, I will now -refer to the proposed change of our standard from the -yard to the mètre.</p> - -<p>Theoretically the mètre is the 10,000,000th part of the -earth’s quadrant, and the yard the 36/39·13929th part of a -seconds pendulum at London. Practically, neither the -mètre nor yard could be recovered with exactness from -their natural basis. The legal French mètre differs from -the latest reduction enough to give an excess of over three -miles to the circumference of the earth. In fact, the mètre -and yard are only the lengths of bars of metal kept in -certain offices, from which copies are made. Decimally -considered, it is as easy to divide one as the other into -tenths, hundredths, etc., and the yard standard is often so -divided.</p> - -<p>As to nomenclature, the metrical system is overloaded -with Greek and Latin prefixes, which are in no -way so easy and convenient in expression as the short, -sharp Anglo-Saxon words yard, foot, inch.</p> - -<p>In all sciences Latin and Greek names are given for -easier purposes of classification; but the different peoples -invariably keep their own household names for daily -purposes, leaving prefix and affix to specialists, probably -with advantage to both parties.</p> - -<p>The units used for different purposes are entirely distinct<span class="pagenum"><a name="Page_23" id="Page_23">[23]</a></span> -from the base of any system, and though always referable -to such base, are not practically so referred. It -therefore seems useless to burden the people with long -scientific names in the ordinary transactions of daily life.</p> - -<p>For long distances the units in the yard and metrical -systems are respectively the mile and the kilomètre.</p> - -<p>The mile has a definite meaning in our minds, being -associated, from the days of youth, with the measured distances -in race-courses, speed in walking, railway and -steamer travel, length of surveyed lots—the same being in -use among about 100,000,000 people.</p> - -<p>For mechanical structures, the units are respectively the -foot and the mètre. The foot is used instead of the yard, -as being the most convenient in practice, and is fixed in -the minds of the people by constant association with -length of foot-rules, size of buildings, doors, windows, -etc., all of which are always before us.</p> - -<p>For commercial purposes the units are respectively the -yard and the mètre. The yard is associated with length -of yard-sticks, distance between brass nails on counters, -so many finger-lengths by ladies. Probably three fourths -of the business of the world is conducted on the yard -standard.</p> - -<p>For machine and shop work the English unit is the -inch and fractions, and countries having the metrical -standard have universally adopted the millimètre.</p> - -<p>The inch is well fixed in the minds of all mechanics -by constant use, and the ease with which the fractions are -had by halving only renders the system very convenient.</p> - -<p>As more figures must be used to indicate a size by -millimètres than by inches and fractions, it appears that -the metrical system cannot shorten the work of arithmetical -computation in shop work, and is therefore of no advantage -to the mechanic or draftsman, but rather the<span class="pagenum"><a name="Page_24" id="Page_24">[24]</a></span> -reverse. This is the opinion of Coleman Sellers, the distinguished -Philadelphia engineer and manufacturer, who, -after a trial of the millimètre in his shops for some years, -returned to the use of the inch, and writes in <cite>Engineering -News</cite>: “The loss from the use of a small unit requiring -many figures to express what is needed, takes away from -the other advantages of the system when considered from -a labor-saving point of view.”</p> - -<p>In France itself the metrical system is not wholly decimal -in actual practice, as we find the following measures -in use in addition to the decimal divisions: double decamètre, -demi-decamètre, double mètre, demi-mètre, and -double decimètre.</p> - -<p>The metrical system has been adopted in the following -countries: France and colonies, Holland and colonies, -Belgium, Spain and colonies, Portugal, Italy, Germany, -Greece, Roumania, British India, Mexico, New Granada, -Ecuador, Peru, Brazil, Uruguay, Argentine Confederacy, -Chili, Venezuela; and partially in Wurtemburg, Bavaria, -Baden, Hesse, Switzerland, Denmark, Austria, and Turkey.</p> - -<p>In the past centuries all the work and records of English-speaking -peoples—now numbering about 100,000,000, -and increasing and progressing faster than all other -nationalities, as well as being closely connected by descent -and business—have been done and recorded under -the yard standard, and any change now would inevitably -render necessary continual reductions, to the great detriment -and inconvenience of the mass of our people, and -with little or no practical benefit, except perhaps to a small -class of scientific and pseudo-scientific men, who can and do -amuse themselves with the fancied uniformity of the mètre.</p> - -<p>All our numerous text-books and tables, mechanical -and scientific, would be rendered entirely useless by the -change, and this is a serious final consideration.</p> - - - - - - - - -<pre> - - - - - -End of the Project Gutenberg EBook of Standard Measures of United States, -Great Britain and France, by Arthur S. 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