OP ARTS AND SCIENCES. 289 



proportional in magnitude to the distance from this line. Its maxi- 

 mum value is about 8 jx. 



In this discussion the end meter will be designated F^, and the line 

 meter Fi. We have, then, 



Ff — 8.43 ju, = Metre des Archives. 

 Fi — F^ nearly. 



Upon placing F^ upon my own comparator after my return to Cam- 

 bridge, I was surprised to find that, when the terminal lines were in 

 focus, the lines along the middle of the bar were barely visible under 

 the microscope. I was the more surprised, as I had examined the bar 

 with respect to this very point while at Paris. After becoming assured 

 that the ways of my own comparator had no sensible flexure, by cer- 

 tain tests which will be described later in this paper, only one conclu- 

 sion could be reached; viz. either that the microscopes employed in 

 the examination at Paris had not sufficient power to enable the observer 

 to detect the deviation of the ways of the comparator from a horizontal 

 plane, or that the curvature of the ways was the same as the curvature 

 of the bar. 



Inasmuch as it was not possible on this account to determine exactly 

 the relation of each decimeter of Fi to the entire meter, and because 

 the softness of the metal prevented the repetition of exact end contacts, 

 I decided to reconstruct this bar for my own use. Before this was done, 

 however, the following operations were performed. 



(a.) The terminal lines of Fi were transferred to T at 13°. 70 C. 

 nearly. 



Two sets of graduations werp made, one composed of five rather 

 coarse lines, and the other composed of five lines having as nearly as 

 possible the same characteristics as the Tresca defining lines. The 

 former are designated T '■■■°' and the latter T'^^"-^- Corresponding 

 lines were traced at the middle point of T upon the surface of copper. 

 At the same time, a provisional yard was laid off upon T, employing 

 one defining line of the meter as the defining line of the yard at that 

 end. 



{b.) The relations between Fi and 7""* '"^ and T ^' '^ were carefully 

 determined. 



(c.) The relation of i^^ to T"'^---^, and also to three other meters to 

 be described hereafter, was determined. 



After this work was done, hardened steel plugs were inserted at the 

 ends of F^, and the surfaces were made parallel. In order to accom- 

 plish this, it was necessary to grind off a trifle more than the 8.4 (jl, 

 VOL.. xvm. (n. s. X.) 19 



