730 PROCEEDINGS OF THE SOCIETY. 



is always in phase with the direct light. 1 ' The argument is indeed 

 somewhat loose, for Mr. Conrady does not go on to show that this 

 equality of phase affects the formation of the image in the image plane. 

 On the contrary, when he comes to deal with that point, at the bottom of 

 page 621, he gives the go-by to the spectra altogether, and argues from 

 the principle of equal optical paths that since the diffracted beams leave 

 the grating in equal phase with the direct light, they will arrive in equal 

 phase at the conjugate image. This is a perfectly valid argument, but 

 it is simply the old-fashioned " dioptric " theory, and has nothing what- 

 ever to do with the Abbe theory, or with the phase relations of the 

 spectra inter se. The argument, therefore, has not even the merit of 

 being coherent, but for some reason Mr. Conrady thinks it necessary to 

 insist upon the equality of phase of the direct light and the spectra of 

 the first order. The matter, therefore, must be examined again, although 

 probably other Members of the Society as well as myself will think it 

 strange that this question should now be brought up, and brought up in 

 the form which it assumes in Mr. Conrady's paper. Only in June last 

 Prof. Everett contributed a paper to our Proceedings in which he showed 

 that the phase relation between the direct light and the two spectra of 

 the first order is quite indeterminate, and goes through a complete cycle 

 of change as the grating is made to move across the stage in a direction 

 perpendicular to the bars through a distance equal to the distance from 

 centre to centre of two contiguous bars. It is sufficiently surprising to 

 find this result called in question, and still more surprising that Mr. 

 Conrady, while denying Prof. Everett's conclusion, should not think it 

 necessary even to allude to the argument by which that conclusion was 

 reached. 



By the Society's leave I propose, therefore, to examine Mr. Conrady's 

 argument ; and since Prof. Everett is no longer among us to defend nis 

 own position, I will venture to offer some observations in its defence. 



First of all, to deal with Mr. Conrady's argument. This appears on 

 page 617, and it is there shown, with the aid of a diagram, that the 

 resultant phase in the diffracted beam of the first order is equal at any 

 given time to the contemporary phase in the beam of direct light. With 

 that conclusion nobody will quarrel. It might be extended to the beams 

 of the second, third, and other orders. Mr. Conrady, indeed, thinks not. 

 He says on page 620 : " This is my great point, in this second cycle the 

 sign of the resulting amplitude is reversed, i.e. the combined phase is in 

 this case the opposite one to or is £ wave-length different from that given 

 by indefinitely narrow slits." On looking for the proof of this pro- 

 position, one finds that it is due to a mere error in calculation. Mr. 

 Conrady deduces quite correctly for the resultant disturbance due to the 

 impulses from a pair of points, E and F, situated symmetrically on either 

 side of the middle point of a slit, the following expression — 



x z -f x v = 2 c . cos /? . sin a. 



He then proceeds to obtain the whole result of the radiation from the 

 slit by integrating this expression, and everything proceeds (so far as it 

 goes) quite correctly except that he omits to observe the proper limits of 



