296 PROCEEDINGS OF THE AMERICAN ACADEMY 



are determined by a sufficient number of observations, at a wide range 

 of temperature. This operation generally requires two or three 

 weeks. With the corrections thus determined, a second series of 

 graduations are laid ofF, the lines beiug in the same field of the 

 microscope as the first ones. One can now proceed nearly indepen- 

 dently of temperature, by comparison with the first set of graduations. 



Even when the correct length is obtained, it is often found necessary 

 to make a third, and even a fourth set, in order to reduce the errors of 

 the subdivisions to sufficiently narrow limits. According to my pres- 

 ent arrangement, after a transfer has been made, all the subdivisions, 

 both of the meter and the yard, can be made without disturbing the 

 position of the two bars. But with the utmost care I have not found 

 it possible to make the subdivisions exactly equal. In fact, one must 

 be content to admit errors of small magnitude as long as the conditions 

 of transfer vary in the slightest degree from the conditions under 

 which the required corrections were obtained. The corrections due to 

 curvature give great trouble, and require the most careful determina- 

 tion. With the universal comparator, this difficulty is obviated ; but 

 on account of the better illumination obtained in the comparing-room 

 at the Observatory, all transfers have thus far been made upon the 

 comparator first constructed. 



The provisional set of graduations upon G^ and G., were laid off" from 

 i?i"=, on January 7, 1883. They consist of bands of three lines, 

 separated by an interval of 50 /x. They are designated G^"""' and 



The relations between E^, G^, and G^ were then determined from 

 observations extending from January 8 to January 17. 



In July of the present year, (?, and G.^ were placed upon the com- 

 parator for the transfer of the graduations G^g"' ^^ ^v gi^'ing » set of 

 graduations designated (?j^'=^«. After the comparison of the latter 

 with G"-, and with the series of corrections thus obtained, the bars 

 were placed in reversed positions, and lines G^ ' were made the basis 

 of a new transfer to G,^, giving G^ '". 



Graduations GJ'' having been compared with each other and with 

 G^^, the following sets were laid off, viz. : — 



C/"^ with lines one half the width of G^/'". 

 G^'^ with lines having about the same width as G^ '". 

 Gf^ with exceedingly fine lines. 

 The distance between the lines in the final sets both of G^j and G^ 

 is 50 [I. 



