C. Barns — Use of Compensators. 299 



Art. XXIII. — The Use of Compensators, Bounded by Curved 

 Surfaces, in Displacement Interferometry ; by Carl 

 Bartjs.* 



1. Introduction. — The method of increasing the sensitive- 

 ness of the displacement interferometer by increasing the dis- 

 persion of the grating readily suggests itself. Unfortunately 

 the interference pattern loses sharpness in the same ratio and 

 ultimately becomes too diffuse for practical purposes. Similar 

 sensitiveness is secured when the glass and the air paths of the 

 component beams of light are respectively identical, with the 

 same inadequacy in the huge mobile figures, for the purpose of 

 adjustment. In fact, if for simplicity we consider the inci- 

 dence normal (7 = B, = 0, linear interferometer), the sensitive- 

 ness becomes 



dO/dn = X'/\2eD cos 0.(0* + 2b /^) — N )\ 



where 6 is the angle of diffraction for the wave length X, e the 

 thickness of the plate of the grating, fi its index of refraction, 

 D the grating space, n the order of the fringe and b, ^con- 

 stants. Hence other things being equal, dd/dn increases as D 

 and e grow smaller, where e = is obtained by a compensator 

 counteracting the thickness of the plate of the grating. 



It occurred to me that the difficulty of diffuse interference 

 patterns might be overcome, in part, by the use of compensators 

 with curved faces, when the case would become similar to the 

 conversion of the usual interference colors of thin plates into 

 Newton's rings. Naturally a cylindric lens with its elements 

 normal to the slit is chiefly in question, though an ordinary 

 lens also presents cases of interest because of the easy conver- 

 sion of elliptic into hyperbolic patterns and the lens is more 

 easily obtained. 



Other methods were tried. For instance in using a Fresnel 

 biprism with its blunt edge normal to the slit, two sets of inter- 

 ference patterns, one above the other in the spectrum, are 

 obtained. When the blunt edge is parallel to the slit, either 

 side of the prism gives its own interferences, but they cannot 

 be made clearly visible at the same time. A doubly reflecting 

 plate or a thin sheet of mica covering one half of the beam 

 will produce two intersecting patterns, but these also are of 

 little use for measurement. A very promising method, how- 

 ever, consists in the use of compensators of equivalent thick- 

 ness, but of different dispersive powers, crown and flint glass, 

 for instance. These experiments are in progress. 



* Abridged from a forthcoming Eeport to the Carnegie Institution, of 

 Washington, D. C. 



