732 PROCEEDINGS OF THE SOCIETY. 



it follows that the path from 



M, to A x = i + 04 + X. 



Now Mr. Conrad j wants the spectrum of the first order to be in 

 phase with the image formed by the direct light, and as this is a per- 

 fectly possible condition of things, we will assume it for a starting point, 

 and in order to express this clearly we will write for the optical paths 



M t to A x = | + nX (1) 



M 2 to A x = i + (n + 1) X . . . . (2) 



n being some positive integer. 



Next, suppose the grating to be moved across the stage in the direc- 

 tion from C to Aj through a distance = s. It is clear that in the new 

 position it will give rise to the same phenomena in the focal plane a& 

 when it occupied the original position. The optical paths from Mj and 

 M 2 to A x will have been shortened by one whole wave-length, and the 

 optical paths to C will be unchanged. Therefore the principal image 

 and the first spectrum will still be in phase. 



But the grating might have been moved through a less distance 

 than s. Suppose it moved through x. Then the optical path from M 

 will become t / *\ * 



M 1 toA 1 = ^ + U-?U .... (3) 



and similarly 



M 2 toA 1 = ^+U+ 1 - ; |) A . . . (4) 



But the optical paths to C remain unchanged, and therefore in this new 

 position of the grating there is a phase difference corresponding to 



- X between the direct light and the spectrum of the first order. 



It is now evident that as x increases from x = to x = s the phase 

 difference between the direct image and the first spectrum must run 

 through a complete cycle of change, and that this relation, far from 

 being determinate, in a general sense, is determined only by the acci- 

 dental position of the grating on the stage of the instrument. This is 

 the conclusion at which Prof. Everett arrived, and it appears to be 

 irresistible. 



Towards the end of Mr. Gordon's remarks the Chairman interposed, 

 and suggested that as it was nearly half -past ten o'clock, Mr. Gordon 

 might close the subject by simply stating that on other points he did 

 not accept Mr. Conrady's conclusions. Mr. Gordon at once acquiesced, 

 and concluded his remarks in that way.* 



The Chairman said that the subject referred to in the paper read was 

 no doubt of much interest to some of their number, but at that late hour 

 he thought that the discussion could not be prolonged. He felt sure, 

 however, that they would return their thanks to all who had addressed 

 them, for the light they had thrown on the matter. 



* For Mr. Conrady's'rejoinder, see next page. 



