Wadsworth — Simple and Accurate Cathetometer. 



45 



ment either by determining the distance between the image of 

 the point and the image of the nearest mm. division on the 

 scale with an ordinary form of micrometer; or better, by 

 bringing these two images into coincidence by means of a 

 Rochon double image micrometer, an opthalometer or a par- 

 allel-plate micrometer. The second method of coincidence has 

 the decided advantages both of greater rapidity, only one set- 

 ting and reading being necessary instead of two, and of greater 

 accuracy for the same reason, since any error, due to a change 

 in position of any part of the apparatus in the interval between 

 two settings, is thus avoided. This last advantage fully 

 balances the disadvantage of the greater effect of a given error 

 of leveling on account of the greater angular distance between 

 scale and object. One additional cause of error is introduced, 

 i. e., that due to a want of parallelism between the mirror A 

 and the axis of rotation C ; but since this should not exceed 

 a fraction of a second, if the first adjustment has been properly 

 made, its effect is negligible. 



Of the various instrumental means for obtaining coincidence 

 perhaps the simplest and most convenient, as well as one of the 

 most accurate, is the parallel plate micrometer first invented by 

 Clausen and quite recently reinvented and much improved by 

 Poynting,* who was the first to adopt it for cathetometric 



measurements. Figs. 3 and 4 show in plan and elevation a 

 form of this micrometer modified slightly from that described 

 by Poynting to better adapt it to this particular instrument. 

 It consists simply of a plate of plane-parallel glass, P, rotating 

 on an axis C at right angles to the axis C and carried in a 

 fork which is a prolongation of the boss D shown in the pre- 

 ceding figures. 



The rotation of the plate on its axis shifts the ray from o\ 

 which passes through it, and hence also the image of the scale, 

 by an amount A which may easily be shown to be 



*Phil. Trans., vol. clxxxii, 1891, A, p. 588. See also "On a Parallel Plate 

 Double Image Micrometer," Monthly Not. of the Royal Astron. Soc., vol. lii, No. 

 8, 1892, p. 556. 



