Theory of Molecular Action according to Newton's Law. 341 



was with great pleasure that I read in Professor Kelland's 

 letter that the attention of the greatest mathematicians in Eu- 

 rope is now alive to the necessity and importance of having 

 " the difficulties which attend the theory" removed: and I 

 rejoice that Professor Kelland has undertaken the task of 

 thoroughly reviewing the grounds of my opinion. In my 

 memoir on the subject printed in the Cambridge Philosophical 

 Transactions, I have shown, apparently to Professor Kelland's 



^«V d 2 V dV 

 satisfaction, that when - , f2 > , ■ 2 - , — , r t are not zero, the 



medium is incapable of transmitting light, and have dismissed 

 at once as foreign to the subject the case where these quan- 

 tities are zero, which case the Professor argues " embodies 

 the real state of things." The grounds on which I dismissed 

 this case in so summary a manner were these : — 



1st. The acknowledged experimental fact of the superpo- 

 sition of waves of light requires that the forces called into 

 play by a displacement should depend only (or at any rate 

 chiefly) on the^r^ power of the displacement. 



2ndly. The received explanations of refraction through cry- 

 stals and of other pheenomena, assume that the force of restitu- 

 tion depends only on the^r^ power of the displacement ; and, 



3rdly. If -tj^ > , 2 ? ~JW zero > tne nrst powers ol the 



displacement disappear ; and therefore this case is inconsist- 

 ent with the known results of experiment and the require- 

 ments of received and established theory. Yet Professor 

 Kelland thinks that the real state of things is embodied in the 

 excepted case, and founds his belief on arguments drawn from 

 analytical expressions in his memoir. It appears to me, then, 

 that the shortest way of bringing the controversy to an end, 

 will be to show that the Professor's own investigations, under 

 proper mangement, lead us to the same results as were given 

 in my memoir. At pages 162, 163 of the Professor's paper 

 on Dispersion, we are told that on the hypothesis which he 

 has adopted each of the quantities 



2X {^ + ^8^}sin 2/ 4i 

 2s|*r+^83/ 2 ^sin 2 ~ 



Q 



1 <p r ^ \-L h 2 ^ si" 2 



is equal to n\ It follows therefore that » 2 is equal to one 

 third of their sum, i. e. 



