294 PROCEEDINGS OF THE AMERICAN ACADEMY 



themselves ; and if the bar be laid symmetrically upon them, all the 

 individual pressures will be equal." * 



Mr. Baily decided upon the adoption of eight rollers for the support 

 of the National Standards, requiring for the distance between each 



roller and the one next adjacent -r— - inches = 4.54 inches. As a 

 further precaution, the defining lines were traced upon gold plugs in- 

 serted in wells sunk to the plane of the neutral axis. This form of 

 support is the one now employed in the Standards Office. The reader 

 who desires to pursue this subject will find elaborate discussions by 

 Bessel and by Clarke. 



At the International Bureau only two supports are used, the dis- 

 tance between them being determined bj r Bessel's formula. At the 

 Conservatory, the bars are placed directly upon a plane surface, 

 which is nearly in the neutral axis of the support itself. 



In 1870 Professor Wild proposed a form of support which seems to 

 leave very little to be desired. The bars are placed one above the other 

 with the graduations in the same vertical plane. Here we have con- 

 ditions quite unlike those which occur with bars supported in the way 

 already described, and under which it would seem that no flexure can 

 occur which will affect the distance between the defining lines. This 

 method, therefore, affords a rigorous test of the flexure formula? of 

 Bessel and Airy. It appears from the discussion of Professor Wild, 

 that, while the mean effect of observed flexure upon the relative 

 lengths of the separate decimeters of the same bar agrees nearly with 

 the mean computed value, the numerical mean of the differences be- 

 tween the observed and the computed effects is no less than 0.0004 nun., 

 or nearly one half of the whole mean effect. On the other hand, a 

 rigorous comparison instituted by Clarke showed a substantial agree- 

 ment between the computed and the observed effects of flexure. It is 

 evident, therefore, that this subject requires further investigation. In 

 the case where eight, or even four rollers are employed, it is mechani- 

 cally impossible to make them so that planes tangent to each roller 

 shall fall in a common plane, which shall be parallel with the plane of 

 the defining lines. Unless this takes place, the upward pressures will 

 not be equally distributed, and the formula? will not hold. In the case 

 of bars of the Tresca form, I am compelled to admit that, at least with 

 a bar of copper, attention must be paid to the form of the support. 



In the comparator which has been constructed from designs fur- 

 nished by myself, I have dealt with the question of supports in the 



* Astron. Trans., xv. 157, &c. 



