OF ARTS AND 8CIBNCE8. 297 



of the bars to be compared, the error due to curvature will be eliminated 

 in proportion to the ratio between the length of the chords described 

 by t lie microscope for the two positions of the bars. 



The necessity for taking into account the error due to curvature in 

 any given case will clearly appear from the following provisional in- 

 vestigation of its magnitude in my own comparator: — 



A a 



o 



B b 



C c 



D d 



E e 



A steel meter by Froment was placed in the constant position O o. 

 A copper meter of the new form by Tresca was placed successively in 

 the positions A a, B b, C c, D d, and E e. The microscopes were 

 attached firmly to the plate, moving freely upon the ways of the bed- 

 plate, each having its own adjustment for focus. Microscope B was 

 adjusted for coincidence with the end line of the bar o at O, and 

 microscope A was at the same time adjusted for coincidence with the 

 end line of bar A a at A. The plate was then moved along the ways 

 until microscope B was adjusted on the terminal line at o, and for this 

 position the micrometer of microscope A was read. Since the two 

 microscopes remain in the same position with respect to each other, the 

 difference between the two readings of A will indicate the difference 

 between the length of the bars. By reading B for the positions O o, 

 — A being a constant, — the relation between the two bars will be 

 expressed in terms of the micrometer of B also. 



Differences in the Apparent Length of the Bars compared, varying with the Position of 

 Bar A with respect to Bar B. 



For the radius of curvature, we have approximately, 



.00658 : 34.4 = 100 : x. 

 .: x + = 5228 meters. 



