288 PROCEEDINGS OF THE AMERICAN ACADEMY 



Tresca, at two o'clock on the morning of February 6, transferred to it 

 the Conservatory line meter No. 19, whose relation to the Metre des 

 Archives had been previously determined with great exactness by 

 Professor Tresca. There are three defining lines at each end, with an 

 interval of 17.4 /a. The width of each line is about 5 /a. It appears 

 from a large number of subsequent comparisons of the three meters 

 defined by these lines, that they do not differ inter se by a measurable 

 quantity. 



Immediately after the transfer was completed, a direct comparison 

 with meter No. 19 was made. Comparisons were continued during 

 the next day and the next night. 



The certificate which accompanied this meter states that it is 1.00 ix 

 longer than the corrected value of meter No. 19 at 13°.70 C. 



Employing in the reduction the coefficient of expansion for No. 19, 

 .000008G0860, we find, therefore, that 



Tis 118.94 /A <oo long at 13°.70 C. 



II. The Froment Meter, designated F. 



This meter was originally an end measure only. The metal is steel, 

 but the end surfaces were not hardened. This meter has been com- 

 pared indirectly with the Metre des Archives through a comparison 

 with a meter belonging to the Observatory of Kazan, which, by a com- 

 parison with the meter of the Conservatory, had been found to be 

 2.431 yu, too long. During a visit to the establishment of Messrs. 

 Demoulins-Froment, I ascertained that M. Froment had a line meter 

 upon steel, which was supposed to be the equivalent of the end meter. 

 Having purchased the latter, I asked M.- Diner, who has this class of 

 work in charge, to transfer to its upper surface this line meter, with 

 subdivisions into decimeters. Inasmuch as the upper part of the bar 

 extends beyond the defining surfaces of the meter at each end, this 

 transfer was fortunately feasible. The transfer by M. Diner was made 

 with great care, and from a comparison which I was permitted to make 

 with the comparator of M. Froment, I became convinced that the claim 

 of M. Diner, that the limit of error did not exceed 2 fi, was clearly 

 substantiated. 



The defining surfaces of the end meter are parallel only in the ver- 

 tical plane, which is perpendicular to the axis of the bar. It will 

 appear from the discussion which will follow, that, if the measurements 

 are made from contacts on either side of the vertical line passing 

 through the centre of the bar, an error will be introduced which is 



