128 PROCEEDINGS OF THE SOCIETY. 



showing us, say, a normal specimen of Pleurosigma angulatum plainly 

 resolved with an object-glass of N.A. less than •;'), or a normal specimen 

 of Amphipletira peUucida similarly resolved with a dry objective under 

 • !) N.A., or indeed any test object resolved under conditions under which 

 it could not be resolved according to the accepted theories ? 



Mr. Gordon having been invited to reply, said : Mr. Conrady has 

 been good enough to furnish me with a copy of his criticism of my paper. 

 To a considerable extent these remarks, like those read by Mr. Rheinberg, 

 consist of oracular utterances on the subject of my incompetence, and 

 with these I do not propose to occupy your time. They express, no 

 doubt correctly, the opinions of these gentlemen, and, as they do not 

 purport to express more, they do not properly admit of an answer. 



Mr. Conrady, however, does not confine himself to inarticulate 

 •criticism. He puts forward specific objections to certain of my points, 

 and, with a singular lack of caution, selects for the object of his prin- 

 cipal attack equation No. 2, which appears on page 7 of my paper, and 

 ■expresses a resultant amplitude as follows — 



A(i + 2) = (a x cos ^ 2 7T + A 2 cos ^- 2 2 7T J 



Mr. Conrady thinks that I ought to have compounded these two 

 amplitudes according to a different rule, and one which, oddly enough, 

 does not yield a true resultant amplitude at all. When undulation trains 

 combine which have originated in independent sources of light and have 

 no fixed phase relation inter se, it is impossible to calculate their actual 

 resultant, for the simple reason that the actual components are in such a 

 case unknown. The best we can do is to calculate an average resultant, 

 and for this purpose the equation has been devised which Mr. Conrady 

 has selected and recommended as an alternative to that which I have 

 above set out. The case, however, with which I was dealing is a case of 

 undulations which have a fixed and permanent phase relation between 

 themselves, and what I wanted to get at is, not an average, but an actual 

 resultant. In the case contemplated the actual resultant can be computed, 

 and by the ordinary equations applicable to the composition of co-planar 

 forces. 



Now Mr. Conrady, in fact, does himself less than justice by this 

 erratic criticism. The formula which he speaks of as having been in- 

 vented by me, is very far indeed from having been newly devised, and 

 on the contrary has been employed before, and invariably, by other 

 writers attacking the same problem. If we assume, instead of two im- 

 pulses, an indefinite 'number, say n, the above equation is written in the 

 following form : 



A(i + 2 + . . + n) = 2( A x cos - 1 2 7T + A 2 cos ^ 2 2 tt + . . . + A n cos-— 2 - ) 



\ A A A ' 



If now we assume that all the several impulses A 15 A 2 , etc., are equal 

 to one another, then we may for these individual symbols substitute a 

 common factor which may be written c. 



Again, if we find it convenient to take our impulses in pairs and for 



