﻿344 Mr. F. L. 0. Wadsworth on 



It will readily be seen that if we do not impose the con- 

 dition that the reflected ray shall be parallel to the line of 

 collimation, we may place the mirror so that the displacement 

 will be almost nil for even very considerable values of r. This 

 general case may be readily worked out by introducing into 

 the above another angle, /?, which is the angle between the 

 axis of collimation and the ray reflected from the mirror, 

 connected with the angles 6 and a by the relation 



<9 + &> = 180-(2* + /3). 



In this case it will be found, as might have been expected, 

 that the displacement is a minimum when the angle a is as 

 nearly as possible equal to 0, viz., when the angle of incidence 

 on the mirror is as nearly as possible 90°. In the most 

 unfavourable case, however, the correction, although con- 

 siderable, is not of sufficient magnitude to become objection- 

 able in spectroscopic work. In such work it is not even 

 necessary to apply the correction, as the effect is the same as 

 would be produced by a slight change in the optical pro- 

 perties of the prism. The displacement might in this, as in 

 the former case, have been eliminated by making R=oo , viz., 

 by substituting for the concave mirror at a a plane reflector 

 and placing the image-forming objective beyond the reflecting 

 surface m ; but the additional reflecting surface was ob- 

 jectionable as diminishing the brightness of the spectrum. 



Case III. — The arrangement last described was used with 

 a considerable degree of success for some time, but when 

 some very accurate angular measurements were attempted 

 with it a difficulty of a mechanical character presented itself. 

 It will be noted that the correct working of this — as of all 

 systems so far described — depends on the maintenance of an 

 exact ratio of 2 to 1 between the angular motions of the 

 spectroscope-arm and of the reflecting mirror. It is necessary 

 to maintain the prism at minimum deviation in all spectro- 

 metric measurements ; but not with any great degree of 

 exactness, as an error of 2' or 3' in the angular position of 

 the prism will not affect the deviation by more than ^- of 

 this amount. But with the mirror any error in angular 

 position with respect to the arm will change the angular 

 direction of the refracted and reflected ray by double that 

 amount; and hence if we wish to determine any angle of 

 deviation to within 10", we must be sure of the position of 

 the mirror to within less than 5'' '. To secure this degree 

 of accuracy mechanically and automatically with any ordi- 

 nary minimum deviation attachment is out of the question, 

 for an error of h" in angular position means in linear measure- 

 ment an error of only y^oo millim. at the end of an arm 



