August 15, 1889] 



NATURE 



379 



evidence indicate that it shpuld be accepted to the exclusion of 

 the other. 



In 1668 the italoit of the new loise, since known as the toise- 

 Union (hi Ciiatelet, was fixed against the wall at the foot of the 

 staircase of the grand Chdtelet dc Paris — by whom or at what 

 season of the year is not known Strange as it now seems, this 

 standard — very roughly made, exposed in a public place for use 

 or abuse by everybody, liable to rust, and certain to be falsified 

 by constant wear — was actually used for adjusting the toise of 

 Picard, thnt of Cassini, the toise of Peru and of the North, that 

 of La Caille, that of Mairan ; in short, all the toises employed 

 by the French in their geodetic operations during the seventeenth 

 and eighteenth centuries. The lack of any other recognized 

 standard made the use of this one imperative, but the P'rench 

 Academicians were well aware of its defects, and took precau- 

 tions to guard against them. 



The first toise copied from the etalon of the Chatelet for 

 scientific purposes was that used by Picard in his measurement 

 of a degree of the meridian between Paris and Amiens. It was 

 made about the year 1668, and would doubtless have become the 

 scientific standard of Prance had it not unfortunately disappeared 

 before the degree measurements of the eighteenth century were 

 begun. The second toise copied from the etalon of the Chatelet 

 for scientific purposes was that used by Messrs. Godin, Bou_2;uer, 

 and La Condamine for measuring the base of their arc of the 

 meridian in Peru. This toise, since known as the toise dn Peroii, 

 was made by the artist Langlois under the immediate direction 

 of Godin in 1735, and is still preserved at the Paris Observatory. 

 It is a rectangular bar of polished wrought iron, having a breadth 

 of I '58 English inches and a thickness of 0"30 of an mch. All 

 the other toises used by the Academy in the eighteenth century 

 were compared with it, and, ultimately, it was made the legal 

 standard of France by an order of Louis XV., dated May 16, 

 1766. As the toise of Peru is the oldest authentic copy of the 

 toise of the Chatelet, the effect of this order was simply to 

 perpetuate the earliest known state of that ancient standard. 



The metric system originated from a motion made by Talley- 

 rand in the National Assembly of France, in 1790, referring tlie 

 question of the formation of an improved system of weights and 

 measures, based upon a natural constant, to the French 

 Academy of Sciences ; and the preliminary work was intrusted 

 to five of the most eminent members of that Academy — namely, 

 Lagrange, Laplace, Borda, Monge, and Condorcet. On March 

 19, 1791, these gentlemen, together with Lalande, presented to 

 the Academy a Report containing the c -mplete scheme of the 

 metric system. In pursuance of the recommendations in that 

 Report, the law of March 26, 1791, was enacted for the con- 

 struction of the new system, and the Academy of Sciences was 

 charged with the direction of the necessary operations. Those 

 requisite for the construction of a standard of length were : — 



(i) The determination of the difference of latitude between 

 Dunkirk and Barcelona. 



(2) The remeasurement of the ancient bases which had served 

 for the measurement of a degree at the latitude of Paris, and for 

 making the map of France. 



(3) The verification by new observations of the series of 

 triangles employed for measuring the meridian, and the pro- 

 longation of them as far as Barcelona. 



This work was intrusted to Mechain and Delambre, who 

 carried it on during the seven years from 1791 to 179S, notwith- 

 standing many great difficulties and dangers. The unit of length 

 adopted in their operations was ihe toise of Peru, and from the 

 arc of 9' 40' 45" actually measured, they inferred the length of 

 an arc of the meridian extending from the equator to the Pole 

 to be 5, 130, 740 toises. As the metre was to be 1/10,000,000 

 of that distance, its length was made 0"5I30740 of a toise, or, 

 in the language of the Committee, 443*296 lines of the toise of 

 Peru at a temperature of 13° Reaumur (r6|° C. or (i\\° F. ). 



Before attempting to estimate how accurately the standards 

 we have been considering were intercom pared, it will be well 

 to describe briefly the methods by which the comparisons were 

 effected. In 1742, Graham used the only instruments then 

 known for the purpose — namely, very exact beam compasses of 

 various kinds, one having parallel jaws for taking the lengths of 

 the standard rods, another with rounded ends for taking the 

 lengths of the hollow beds, and still another having fine points 

 in the usual manner. The jaws, or points, of all these instru- 

 ments were movable by micrometer screws having heads divided 

 to ^how the eight-hundredth part of an inch directly, and the 

 tenth of that quantity by estimation ; but Mr. Graham did not 



consider that the measurements could be depended upon to a 

 greater accuracy than 1/1600 of an inch. 



Troughton is generally regarded as the author of the applica- 

 tion of micrometer microscopes to the comparison of standards 

 of length, but the earliest record of their use for that purpose is 

 by Sir George Shuckburgh in his work for the improvement of 

 the standards of weight and measure in 1796-98. Since then 

 their use has been general ; first, because they are more 

 accurate than beam compasses, and, second, because they avoid 

 the injury to standard scales which necessarily results from 

 placing the points of beam compasses upon their graduations. 

 As the objective of ihe microscope forms a magnified image of 

 the standard, upon which the micrometer wires are set by the 

 aid of the eye-piece, it is evident that in order to reduce the 

 effect of imperfections in the micrometer, the objective should 

 have the largest practicable magnifying power. To show the 

 progress in that direction, the optical constants of the micro- 

 scopes, by means of which some of the most important 

 standards have been compared, are given in the accompanying 

 table. 



Date. 



1797 

 1817 



1834 

 1834 

 1850 

 1804 



Observer. 



Sir Geo. Shuckburgh 



Capt. Henrj' Kater 



Francis Baily 



l.ieut. Murphy, R.E 



R. Sheepshanks 



Gen. A R. Clarke, R.E. ... 

 Prof. W. A. Rogers, lin. obj. 



» I, J-in. obj. 



,, ,, 4-in.obj. 

 International Bureau 



°° a 



o c »- 



c «J 



— 3 S 



Inches. 



o'oioco 

 'C0428 

 "00500 

 "oosco 

 ■003 s8 

 "00287 

 ■0C079 

 "00035 

 ■00019 



000394 



NdiE.— The magnifying power of Sir Geo. Shuckburgh's microscope 

 seems to be referred to a distance of 12 inches for distinct vision. 'Ihe powers 

 inclosed in parentheses are estimated upon the assumption that the respective 

 micrometer screws had 100 threads per inch. 



In the Memoirs of the French Academy nothing is said 

 respecting the method adopted by the Academicians for com- 

 paring their various toises ; but in his " Astronomy," Lalande 

 states that the comparisons were effected partly by beam com- 

 passes ^nd partly by superposing the toises upon each other 

 and examining their ends, both by touch and with magnifying 

 glasses, they being all end standards. For the definitive adjust- 

 ment of the length of their metres, which were also end 

 standards, the French Metric Commission used a lever comparator 

 by Lenoir. 



In 1742, Graham used beam compasses, which he considered 

 trustworthy to o '00062 of an inch, in comparing standards of 

 length ; but at that time the French Academicians made their 

 comparisons of toises only to one-twentieth or one-thirtieth of a 

 line, say o '00300 of an inch, and it was not until 1758 that La 

 Condamine declared they should be compared to o'oi of a line, 

 or 0*00089 of an English inch, " if our senses, aided by the most 

 perfect instruments, can attain to that." Half a century later, 

 ten times that accuracy was attained by the lever comparator of 

 Lenoir, which was regarded as trustworthy to 0'oooo77 of an 

 inch (" iiase du Systeme Metrique," t. iii. pp. 447-62). 



The heads of micrometer microscopes are usually divided into 

 100 equal parts, and if we regard one of these parts as the least 

 reading of a microscope, then in 1797 Sir George Shuckburgh's 

 microscopes read to 1/10,000 of an inch ; and the least reading 

 of microscopes made since that date has varied from 1/20,000- 

 to 1/35,000 of an inch. A few investigators, among whom may 

 be mentioned Prof W. A. Rogers, of Colby University, have 

 made the least reading of their microscopes as small as 1/90,000 

 of an inch, but it is doubtful if there is any advantage in so 

 doing. At the present day the errors committed in comparing 

 standards arise, not from lack of power in the microscopes, but 

 from the difficulty of determining suflSciently exactly the tempera- 

 ture of the standard bars, and the effect of flexure upon the 

 position of their graduations. In order to ascertain the length 

 of a 3-fool standard with an error not exceeding o "000020 of an. 



