102 MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. 



than a millionth part. The value of R 1876 in terms of Clarke yard A was very carefully deter- 

 mined. But the comparison of aline meter with an end measure yard is one involving many oper- 

 ations, and of great delicacy. While the computed probable error in the value of R 1876 in terms 

 of Clarke yanl A at 57° 93 F. was less than s-o-o^oTo pai't, the real error may be considerably greater. 



Considering these sources of error or uncertainty, it would not be safe to assign a probable 

 error to the vahie of R 1876, given above, less than from joifoiro to sWooo P'^i't of its length. 



The value of R 1876 in terms of the English yard having now been given, its value in terms of 

 the meter, will next be considered. 



The Buieau International des Poids et Mesures in their comparisons of R 1876 have designated 

 it as U. S. (Repsold,) and give for its length at 0° C. 



U. 8.0=1000097^.81. 



and for its coeflflcieut of dilatation between about 0° and 36° C. a, =0.000010563 ±0.000000011. 

 The details of the work may be found in Tome III, Travaux et Meinoires Bureau International des 

 Poids et Mesures. 



This value of U. S. (Rei)sold) results from its comparisons with a meter of the International 

 Bureau known as type II. The value of type II has been determined by the International Bureau 

 in terms of another platinumiridium meter designated as I,, with the highest accuracy. 



L, has been directly compared with the metre des archives and the committee in adopting 

 provisorily as a unit of length Ij— 6"=l meter at 0° C. state that this value can only be changed 

 by some tenths of a micron when the prototype meter is finally adopted. 



As the probable error in tlie difference of U. S. (Repsold,) and type II is but a few tenths 

 of a micron, that of type II and I2 less than one-tenth, and that of I2, with reference to the proto- 

 type yet to be adopted, oidy some tenths of a micron, it will l)e seen that the value of U. S. (Rep- 

 sold) = R 187G, given above, is i)robably not in error by one micron. 



From the value of U. S. (Repsold) at 0° C. and from its mean coefficient of dilatation given by 

 the International Bureau, its length at 57° 92 F. is U. S. (Rei)sold) = l ■".0002499. Comparing 

 this with its value at the same temperature in terms of the English yard previously given, there 

 results : 



?^L^^= 1.093607, or ineter=39'°.3699 

 yard 



In the Primary Triangulation of the Lake Survey a value for U. S. (Repsold) is given, 

 furnished me by Professor Foerster of the Standards Bureau at Berlin. Tlie value is R 1876 

 = 1'". 00008618 at 0" C. a value ll.'*6 less than the one now given by the International Bureau. 

 The value given by Professor Foerster depended on the value of the meter type I of the Interna- 

 tional Bureau, for which he used the value at 0° C, type I = l™.0000676. This was doubtless the 

 best value then known to the International Bureau, and was derived from indirect com|)arisous 

 with the mfetrii des archives. Tome III, Travaux et Memoires, now gives — 



Tyi)e I„=l"'.00007604 at 0° C 



a value Si'A greater than the preceding one, and accounting for the larger part of the change in 

 the value of U. S. (Repsold). 



Nothing could show more clearly the importance of the work the International Bureau is now 

 doin^; than the fact that the value of one of their princii)al meters, supposed known in 1880 

 within l** or 2** hns since had its value increased by the t2o"ooo part. 



This increase in the value of type I, resulting from recent direct comparisons of L with the 

 meter of the archives corres])on(Is to a similar diminution in the length of the ideal meter. But 

 the change from Colonel Clarke's value of the meter in terms of the yard, to the value found above, 

 corres[)onds to a reduction in the length of the meter of about 70^50^ part, and the recent change of 

 12^00 '" tlie value of type I accounts for but little over one-half of this 70000- 



It .seems probable that a considerable part of the discrepancy must be due to errors in the 

 values heretofore used of the ratio at diifereut temperatures of the meter of the archives to the 

 toise of Peru and its derivatives. 



