124 PROCEEDINGS OF THE SOCIETY. 



foremost for the proofs offered in support of the innovation, and one 

 expects these proofs to be the more ample and convincing the better 

 established the views happen to be which are to be swept aside. 



Now Sir George Airy's paper on the diffraction of object-glasses* 

 which helped to win for him the Copley Medal of the Royal Society in 

 1831, takes high rank among the classical papers on optical subjects, and 

 has been universally accepted as an exhaustive and final treatise on the 

 spurious disc. Yet it is chiefly by trying to prove that Sir George Airy 

 had failed to fully grasp the problem he attacked, that Mr. Gordon seeks 

 to establish his own ideas about the spurious disc. 



Mr. Gordon finds fault with the principal result of Airy's paper, 

 namely, the interesting phase relation between the central disc and the 

 rings, which is brought to light in Airy's table of simultaneous ampli- 

 tudes, and which, owing to the method by which the table was computed, 

 cannot be wrong unless the numerical values of the amplitudes themselves 

 were utterly wrong. Now it so happens that this remarkable fact, viz. 

 that the whole of the central disc and the even-numbered rings are at. 

 any instant in a uniform phase exactly opposed to that of the odd- 

 numbered rings, is the one easily demonstrated peculiarity of the spurious 

 disc, for it is the necessary consequence of the symmetry of a circular 

 aperture with regard to a diameter, and comes about in much the same 

 manner as the exactly similar phase relation which I proved to exist in 

 the case of diffraction spectra, in a paper which I contributed last month. 



The only argument in support of Mr. Gordon's objection to Airy's 

 result consists in a wholly inadmissible suggestion that amplitudes had no. 

 positive or negative signs. For those who have not sufficient faith in the 

 great Astronomer-Royal to accept his conclusions, it may be pointed out 

 that the painstaking pioneer in the study of diffraction phenomena, 

 Schwerd, arrived at precisely the same results quite independently of 

 Airy. Mr. Gordon tries to put his contention into mathematical form 

 by two equations purporting to yield the result of the combination of two 

 amplitudes. Both these formulas are irreconciliable with the undulatory 

 theory, and can easily be shown to be erroneous. Taking the first — 



A(x + 2) = Aj 4- cos ^ 2 7T . A 2 . 



*9 

 A. 



This is impossible, for purely mathematical reasons, because it is not 

 symmetrical with regard to Aj and A 2 . For it is purely arbitrary which 

 amplitude we are to designate as A t and which as A 2 ; the exchange of 

 Aj and A 2 should, therefore, yield the same result. But Mr. Gordon's 

 formula yields two different results by this perfectly legitimate exchange ; 

 for instance, if the phase difference should happen to be 00°, the second 

 term of the formula becomes zero, and we obtain the surprising result 

 that one of the amplitudes vanishes, leaving the other in sole and un- 

 disturbed existence ; and the absurdity becomes more manifest when we 

 exchange A T and A 2 , as we then find that the combined effect must be 

 equal to either amplitude, although they are assumed to be different. 



The second formula may be proved to be wrong by similar reasoning j 

 for instance, if the two phase angles are both equal to ± !)0°, the result- 



