126 Prof. Kelland's Reply to some Objections against the 



the production of sound ; we are certain that the particles of 

 air act repulsively on each other : our analysis shows, that if 

 repulsive forces produce normal vibrations, attractive forces 

 must act to produce the transverse ones which constitute light. 

 There are, however, two things connected with the mutual 

 action of the particles of air, which are here left out of the 

 account ; the one arises from the repulsion of their sur- 

 rounding aether, the other from its pressure against them. 

 I do not think, therefore, that anything has been offered in 

 favour of the hypothesis of attractive forces, so strong as to 

 induce us to reject the contrary. I would be understood 

 rather as waiting for more evidence previous to pledging my- 

 self to the adoption of either. The arguments, then, to which 

 I am about to reply are arguments against the law of force. 

 Those which I have met with are the following : — 



1. That a particle placed in a medium constituted of dis- 

 crete molecules which exert actions varying according to the 

 law of the inverse square of the distance will not vibrate. 



2. That the equilibrium of such a medium will not be stable. 



3. That the principal action on a vibrating particle will be 

 due to the remoter parts of the system ; and, 



4. That the velocity of transmission will not depend on the 

 length of the wave. 



1. The first argument is brought forward by Mr. Earn- 

 shaw in a memoir "On the Nature of Molecular Forces," 

 printed in the Transactions of the Cambridge Philosophical 

 Society, vol. vii. p. 97. The memoir is one of great interest, 

 and the analytical equations are very valuable, but I cannot ad- 

 mit the correctness of the interpretation which the author has 

 assigned to them, in deducing " that the molecular forces 

 which regulate the vibrations of the aether do not vary ac- 

 cording to Newton's law of universal gravitation." 



The following is an outline of the argument. V is taken for 

 the sum of each particle divided by its distance from the one 

 which is under discussion. The coordinates of any particle 

 m are x, y, z, whilst those of the particle attracted are^ g, h: 

 then, as Laplace and others have shown, the forces are 



dV . , , . . . . d 2 V d*V cPV 



—T-jTi &c., and the relation existing is -jjv + \j * + ~jT<f 



- 0. 



Now if V = C, V = C be two values of V for different 

 positions of the same particle, it is shown that 2 (C — O) 



= -j-73 S / 2 -l p-s- 8 £ 2 + ? ... 8 h- is the equation to a sur- 



rf/ 2 J dg* b dk* ^ 



face, in any point of which, if the particle be placed, it will 



