292 PROCEEDINGS OF THE AMERICAN ACADEMY 



form of illumination described by Mr. Tolles in tbe Annual of Scientific 

 Discovery for 18GG-67. I found this form of illumination in use by 

 M. Tresca since 1871. It has also been since described as an original 

 invention by Professor Wild. Troughton and Simms also constructed 

 microscopes with the same method of illumination as early as 1869, at 

 the instance of Mr. Warner, a retired gentleman residing at Sussex 

 Place, Brighton. According to the present evidence, the priority of 

 publication must be assigned to Mr. Tolles. M. Tresca was without 

 doubt the first to make an actual application of the method to exact 

 measurements. The reader who is interested in pursuing this subject 

 farther will find a full description of the method in the number of the 

 Journal of the Royal Microscopical Society for August of the current 

 year. It is sufficient to say here, that, as none of the light is lost by 

 the reflection, it is easy to get all, and even more, than is needed. 

 Diffused daylight falling upon the plane face of the prism inserted be- 

 tween the two front lenses affords an abundance of light for the most 

 delicate tracings. With a one-inch objective of the form recently con- 

 structed by Mr. Tolles, lines 30,000 to the inch, ruled on a polished 

 steel surface, are resolved with the greatest ease. 



(c.) The method of support which is best adapted to neutralize the 

 effect of the flexure of the bars upon which the graduations are traced. 



In all the early measurements the standards were placed upon a 

 planed surface of wood. Troughton, in comparing Shuckburgh's scale, 

 fastened it to a bed of mahogan}^ by means of three screws. Kater was 

 the first to discover the variations due to the flexure of the bars on 

 which the graduations were traced. He was also the first to suggest 

 a neutral jflane, in which the effect of flexure upon the length would 

 be zero. At first he located this neutral plane in the middle of the 

 bar, but from subsequent investigations he concluded that it was not 

 quite one third of the thickness of the bar below the graduated surface. 

 He reached the following conclusions*: — 



(1.) "That in a standard of lineal measure, traced upon the surface 

 of a bar, an error arises from the thickness of the bar when it is placed 

 upon a table, the surface of which is not plane." 



(2.) "That this error in bars of the same material and of unequal 

 thickness is within certain limits as the thickness of the bar, and de- 

 pends upon the extension of that surface of the bar which becomes 

 convex, and the compression of the surface which is concave." 



(3.) " That the error to which the scale is liable from this cause is 



* Phil. Trans., 1830. 



