RATIO OF METER TO YARD. 



By C. B. CoMSTOCK. 



READ APRIL 21, 1885. 



Before the close of the work of the Lake Survey, a steel meter then designated R 187G, was 

 sent to the Bureau International des Poids et Mesures, at Sevres, France, for comparisons with 

 the standards of that Bureau. It has recently been returned with values for its length and for 

 its coelficient of dilatation. As it had previously been compared in the Lake Survey office with 

 the Clarke yard A, a yard which had been carefully compared by Colonel Clarke with the standard 

 yard Yjs of the Ordnance Survey, the comparisons give a value for the ratio between the yard 

 and meter. 



The value for that ratio which for some years was supposed most exact, is given by Colonel Clarke 

 in his comparisons of standards of length, and was derived from comparisons with several closely 

 agreeing toises, dependent for their length on the toise of Peru. As the meter was legally defined 

 to be 443.296 lines of the toiseof Peru, Colonel Clarke, from this definition, found the meter ecjual to 

 1.09362311 yards, or .39.370432 English inches. 



The meter of the archives was intended to satisfy this definition, but when adoi)ted as a 

 standard the ideal meter became the length at 0° V of the bar of platinum called the meter of 

 archives, and no longer depended on the toise for its length. 



In recent years it has been known that the ratio obtained by Colonel Clarke needed correc- 

 tion, and as a value for it, which cannot be lai-gely in error, can be obtained from the Lake Survey 

 comparisons already mentioned, I have thought the result might be of interest to the Academy. 

 The details have been communicated to the Chief of Engineers and will probably soon be pub 

 lished. 



The compaiisons made in the Lake Survey office of tlie Clarke yard A with the metre K 1876, 

 and by Colonel Clarke with the Ordnance Survey standard Yss, may be found in the Report on 

 the Primary Triangulation of the United States Lake Survey. From those comparisons and from 

 the value of Y55 in terms of the English prototype yard ISo. 1, there results : 



E 1876=l.y 09388063 at 57.092 F. 



The errors which enter this value are those in the value of Y55 in terms of the English i)roto- 

 type yard No. 1; those in the value of Clarke yard A in terms of Y55; and those in the value of 

 Meter R 1876 in terms of Clarke yard A. As to the probable error in the value of Y55, given by 

 Colonel Clarke as 0.y9999996 at 62° F. little is known, and Colonel Clarke's "Comparisons of Stand- 

 ards of Length" does not indicate that Yr,5 has been compared with the prototype No. 1 since 

 18.'i3. At the time of its construction the value given by Mr. Sheepshanks for Y55 at 62° P. was 

 1.^00000043, differing about one millionth of a yard from the value given above by Colonel Clarke, 

 which value results from intercomparisons by him of five standards under the assumption that 

 the mean length of these standards had, in 1864, the same relation to the yard as that found by 

 Mr. Sheepshanks in 18.53. Moreover, there is a possibility that the prototype No. 1 has changed 

 length by a small (juantity. 



The value of Clarke yard A in terms of Y55 is known with accuracy, probably to within less 



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