The Project Gutenberg eBook of Standard Measures of United States, Great Britain and France 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 will 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 Author: Arthur S. C. Wurtele Release date: February 19, 2017 [eBook #54208] Language: English Credits: 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) *** START OF THE PROJECT GUTENBERG EBOOK STANDARD MEASURES OF UNITED STATES, GREAT BRITAIN AND 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 STANDARD MEASURES OF UNITED STATES, GREAT BRITAIN AND FRANCE *** Updated editions will replace the previous one—the old editions will be renamed. Creating the works from print editions not protected by U.S. copyright law means that no one owns a United States copyright in these works, so the Foundation (and you!) can copy and distribute it in the United States without permission and without paying copyright royalties. Special rules, set forth in the General Terms of Use part of this license, apply to copying and distributing Project Gutenberg™ electronic works to protect the PROJECT GUTENBERG™ concept and trademark. Project Gutenberg is a registered trademark, and may not be used if you charge for an eBook, except by following the terms of the trademark license, including paying royalties for use of the Project Gutenberg trademark. If you do not charge anything for copies of this eBook, complying with the trademark license is very easy. You may use this eBook for nearly any purpose such as creation of derivative works, reports, performances and research. Project Gutenberg eBooks may be modified and printed and given away—you may do practically ANYTHING in the United States with eBooks not protected by U.S. copyright law. Redistribution is subject to the trademark license, especially commercial redistribution. START: FULL LICENSE THE FULL PROJECT GUTENBERG LICENSE PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK To protect the Project Gutenberg™ mission of promoting the free distribution of electronic works, by using or distributing this work (or any other work associated in any way with the phrase “Project Gutenberg”), you agree to comply with all the terms of the Full Project Gutenberg™ License available with this file or online at www.gutenberg.org/license. Section 1. General Terms of Use and Redistributing Project Gutenberg™ electronic works 1.A. By reading or using any part of this Project Gutenberg™ electronic work, you indicate that you have read, understand, agree to and accept all the terms of this license and intellectual property (trademark/copyright) agreement. If you do not agree to abide by all the terms of this agreement, you must cease using and return or destroy all copies of Project Gutenberg™ electronic works in your possession. If you paid a fee for obtaining a copy of or access to a Project Gutenberg™ electronic work and you do not agree to be bound by the terms of this agreement, you may obtain a refund from the person or entity to whom you paid the fee as set forth in paragraph 1.E.8. 1.B. “Project Gutenberg” is a registered trademark. It may only be used on or associated in any way with an electronic work by people who agree to be bound by the terms of this agreement. There are a few things that you can do with most Project Gutenberg™ electronic works even without complying with the full terms of this agreement. See paragraph 1.C below. There are a lot of things you can do with Project Gutenberg™ electronic works if you follow the terms of this agreement and help preserve free future access to Project Gutenberg™ electronic works. See paragraph 1.E below. 1.C. The Project Gutenberg Literary Archive Foundation (“the Foundation” or PGLAF), owns a compilation copyright in the collection of Project Gutenberg™ electronic works. Nearly all the individual works in the collection are in the public domain in the United States. If an individual work is unprotected by copyright law in the United States and you are located in the United States, we do not claim a right to prevent you from copying, distributing, performing, displaying or creating derivative works based on the work as long as all references to Project Gutenberg are removed. Of course, we hope that you will support the Project Gutenberg™ mission of promoting free access to electronic works by freely sharing Project Gutenberg™ works in compliance with the terms of this agreement for keeping the Project Gutenberg™ name associated with the work. You can easily comply with the terms of this agreement by keeping this work in the same format with its attached full Project Gutenberg™ License when you share it without charge with others. 1.D. The copyright laws of the place where you are located also govern what you can do with this work. Copyright laws in most countries are in a constant state of change. If you are outside the United States, check the laws of your country in addition to the terms of this agreement before downloading, copying, displaying, performing, distributing or creating derivative works based on this work or any other Project Gutenberg™ work. The Foundation makes no representations concerning the copyright status of any work in any country other than the United States. 1.E. Unless you have removed all references to Project Gutenberg: 1.E.1. The following sentence, with active links to, or other immediate access to, the full Project Gutenberg™ License must appear prominently whenever any copy of a Project Gutenberg™ work (any work on which the phrase “Project Gutenberg” appears, or with which the phrase “Project Gutenberg” is associated) is accessed, displayed, performed, viewed, copied or distributed: 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 will have to check the laws of the country where you are located before using this eBook. 1.E.2. If an individual Project Gutenberg™ electronic work is derived from texts not protected by U.S. copyright law (does not contain a notice indicating that it is posted with permission of the copyright holder), the work can be copied and distributed to anyone in the United States without paying any fees or charges. If you are redistributing or providing access to a work with the phrase “Project Gutenberg” associated with or appearing on the work, you must comply either with the requirements of paragraphs 1.E.1 through 1.E.7 or obtain permission for the use of the work and the Project Gutenberg™ trademark as set forth in paragraphs 1.E.8 or 1.E.9. 1.E.3. If an individual Project Gutenberg™ electronic work is posted with the permission of the copyright holder, your use and distribution must comply with both paragraphs 1.E.1 through 1.E.7 and any additional terms imposed by the copyright holder. Additional terms will be linked to the Project Gutenberg™ License for all works posted with the permission of the copyright holder found at the beginning of this work. 1.E.4. Do not unlink or detach or remove the full Project Gutenberg™ License terms from this work, or any files containing a part of this work or any other work associated with Project Gutenberg™. 1.E.5. Do not copy, display, perform, distribute or redistribute this electronic work, or any part of this electronic work, without prominently displaying the sentence set forth in paragraph 1.E.1 with active links or immediate access to the full terms of the Project Gutenberg™ License. 1.E.6. You may convert to and distribute this work in any binary, compressed, marked up, nonproprietary or proprietary form, including any word processing or hypertext form. However, if you provide access to or distribute copies of a Project Gutenberg™ work in a format other than “Plain Vanilla ASCII” or other format used in the official version posted on the official Project Gutenberg™ website (www.gutenberg.org), you must, at no additional cost, fee or expense to the user, provide a copy, a means of exporting a copy, or a means of obtaining a copy upon request, of the work in its original “Plain Vanilla ASCII” or other form. Any alternate format must include the full Project Gutenberg™ License as specified in paragraph 1.E.1. 1.E.7. Do not charge a fee for access to, viewing, displaying, performing, copying or distributing any Project Gutenberg™ works unless you comply with paragraph 1.E.8 or 1.E.9. 1.E.8. You may charge a reasonable fee for copies of or providing access to or distributing Project Gutenberg™ electronic works provided that: • You pay a royalty fee of 20% of the gross profits you derive from the use of Project Gutenberg™ works calculated using the method you already use to calculate your applicable taxes. The fee is owed to the owner of the Project Gutenberg™ trademark, but he has agreed to donate royalties under this paragraph to the Project Gutenberg Literary Archive Foundation. Royalty payments must be paid within 60 days following each date on which you prepare (or are legally required to prepare) your periodic tax returns. Royalty payments should be clearly marked as such and sent to the Project Gutenberg Literary Archive Foundation at the address specified in Section 4, “Information about donations to the Project Gutenberg Literary Archive Foundation.” • You provide a full refund of any money paid by a user who notifies you in writing (or by e-mail) within 30 days of receipt that s/he does not agree to the terms of the full Project Gutenberg™ License. You must require such a user to return or destroy all copies of the works possessed in a physical medium and discontinue all use of and all access to other copies of Project Gutenberg™ works. • You provide, in accordance with paragraph 1.F.3, a full refund of any money paid for a work or a replacement copy, if a defect in the electronic work is discovered and reported to you within 90 days of receipt of the work. • You comply with all other terms of this agreement for free distribution of Project Gutenberg™ works. 1.E.9. If you wish to charge a fee or distribute a Project Gutenberg™ electronic work or group of works on different terms than are set forth in this agreement, you must obtain permission in writing from the Project Gutenberg Literary Archive Foundation, the manager of the Project Gutenberg™ trademark. Contact the Foundation as set forth in Section 3 below. 1.F. 1.F.1. Project Gutenberg volunteers and employees expend considerable effort to identify, do copyright research on, transcribe and proofread works not protected by U.S. copyright law in creating the Project Gutenberg™ collection. Despite these efforts, Project Gutenberg™ electronic works, and the medium on which they may be stored, may contain “Defects,” such as, but not limited to, incomplete, inaccurate or corrupt data, transcription errors, a copyright or other intellectual property infringement, a defective or damaged disk or other medium, a computer virus, or computer codes that damage or cannot be read by your equipment. 1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the “Right of Replacement or Refund” described in paragraph 1.F.3, the Project Gutenberg Literary Archive Foundation, the owner of the Project Gutenberg™ trademark, and any other party distributing a Project Gutenberg™ electronic work under this agreement, disclaim all liability to you for damages, costs and expenses, including legal fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH DAMAGE. 1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a defect in this electronic work within 90 days of receiving it, you can receive a refund of the money (if any) you paid for it by sending a written explanation to the person you received the work from. If you received the work on a physical medium, you must return the medium with your written explanation. The person or entity that provided you with the defective work may elect to provide a replacement copy in lieu of a refund. If you received the work electronically, the person or entity providing it to you may choose to give you a second opportunity to receive the work electronically in lieu of a refund. If the second copy is also defective, you may demand a refund in writing without further opportunities to fix the problem. 1.F.4. Except for the limited right of replacement or refund set forth in paragraph 1.F.3, this work is provided to you ‘AS-IS’, WITH NO OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PURPOSE. 1.F.5. Some states do not allow disclaimers of certain implied warranties or the exclusion or limitation of certain types of damages. If any disclaimer or limitation set forth in this agreement violates the law of the state applicable to this agreement, the agreement shall be interpreted to make the maximum disclaimer or limitation permitted by the applicable state law. The invalidity or unenforceability of any provision of this agreement shall not void the remaining provisions. 1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the trademark owner, any agent or employee of the Foundation, anyone providing copies of Project Gutenberg™ electronic works in accordance with this agreement, and any volunteers associated with the production, promotion and distribution of Project Gutenberg™ electronic works, harmless from all liability, costs and expenses, including legal fees, that arise directly or indirectly from any of the following which you do or cause to occur: (a) distribution of this or any Project Gutenberg™ work, (b) alteration, modification, or additions or deletions to any Project Gutenberg™ work, and (c) any Defect you cause. Section 2. Information about the Mission of Project Gutenberg™ Project Gutenberg™ is synonymous with the free distribution of electronic works in formats readable by the widest variety of computers including obsolete, old, middle-aged and new computers. It exists because of the efforts of hundreds of volunteers and donations from people in all walks of life. Volunteers and financial support to provide volunteers with the assistance they need are critical to reaching Project Gutenberg™’s goals and ensuring that the Project Gutenberg™ collection will remain freely available for generations to come. In 2001, the Project Gutenberg Literary Archive Foundation was created to provide a secure and permanent future for Project Gutenberg™ and future generations. To learn more about the Project Gutenberg Literary Archive Foundation and how your efforts and donations can help, see Sections 3 and 4 and the Foundation information page at www.gutenberg.org. Section 3. Information about the Project Gutenberg Literary Archive Foundation The Project Gutenberg Literary Archive Foundation is a non-profit 501(c)(3) educational corporation organized under the laws of the state of Mississippi and granted tax exempt status by the Internal Revenue Service. The Foundation’s EIN or federal tax identification number is 64-6221541. Contributions to the Project Gutenberg Literary Archive Foundation are tax deductible to the full extent permitted by U.S. federal laws and your state’s laws. The Foundation’s business office is located at 809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887. Email contact links and up to date contact information can be found at the Foundation’s website and official page at www.gutenberg.org/contact Section 4. Information about Donations to the Project Gutenberg Literary Archive Foundation Project Gutenberg™ depends upon and cannot survive without widespread public support and donations to carry out its mission of increasing the number of public domain and licensed works that can be freely distributed in machine-readable form accessible by the widest array of equipment including outdated equipment. Many small donations ($1 to $5,000) are particularly important to maintaining tax exempt status with the IRS. The Foundation is committed to complying with the laws regulating charities and charitable donations in all 50 states of the United States. Compliance requirements are not uniform and it takes a considerable effort, much paperwork and many fees to meet and keep up with these requirements. We do not solicit donations in locations where we have not received written confirmation of compliance. To SEND DONATIONS or determine the status of compliance for any particular state visit www.gutenberg.org/donate. While we cannot and do not solicit contributions from states where we have not met the solicitation requirements, we know of no prohibition against accepting unsolicited donations from donors in such states who approach us with offers to donate. International donations are gratefully accepted, but we cannot make any statements concerning tax treatment of donations received from outside the United States. U.S. laws alone swamp our small staff. Please check the Project Gutenberg web pages for current donation methods and addresses. Donations are accepted in a number of other ways including checks, online payments and credit card donations. To donate, please visit: www.gutenberg.org/donate. Section 5. General Information About Project Gutenberg™ electronic works Professor Michael S. Hart was the originator of the Project Gutenberg™ concept of a library of electronic works that could be freely shared with anyone. For forty years, he produced and distributed Project Gutenberg™ eBooks with only a loose network of volunteer support. Project Gutenberg™ eBooks are often created from several printed editions, all of which are confirmed as not protected by copyright in the U.S. unless a copyright notice is included. Thus, we do not necessarily keep eBooks in compliance with any particular paper edition. Most people start at our website which has the main PG search facility: www.gutenberg.org. This website includes information about Project Gutenberg™, including how to make donations to the Project Gutenberg Literary Archive Foundation, how to help produce our new eBooks, and how to subscribe to our email newsletter to hear about new eBooks.