\jL V (L V tJL V * * 



established that -j-^p t ■ , 2 and ^ 7a are zero, in the case 



Theory of Molecular Action according to Newton's Law. 129 



We have taken it for granted that by " a position of equili- 

 brium" is meant the place originally occupied by a particle 

 in its state of rest. The arguments adduced by Mr. T irn- 

 shaw evidently require that this should be the case. 



d?V d?Y d 2 V '■ 



Having shown that ■ . no , . „ , and T 7C) - are all zero, it 

 ° dj z dg* dk? 



follows that any argument based on the express assumption 



of the contrary is invalid. 



But now it may be urged that we have only removed the 



objection from one point to another. For, admitting it to be 



d 2 V d 2 V d 2 V 



■^ri -jjf an(l ~IW 



in question, the argument against the possibility of vibration 

 remains in full force. For " the displacements of particles 

 placed in such positions as those here considered would not 

 bring into action any forces of restitution, on which account 

 the particles would not vibrate." (Earnshaw, art. 8.) This is 

 the argument. I fear I do not rightly see the connexion 

 between it, and the inference which follows : " it is evident 

 therefore that the phaenomena of light and sound are not due 

 to the motions of particles placed in such positions." If I am 

 wrong in conjecturing the inference, I hope to be set right ; 

 but so far as I am able to make out, it is as follows : a particle 

 is moved, its motion calls no force into play to draw it back, 

 therefore it will remain in its new position, and will not vi- 

 brate. Now we reply, that before it can be inferred that the 

 particle will not vibrate, it is necessary to show, not only that 

 it receives no instantaneous action owing to its change of po- 

 sition, but that it likewise exerts none on the surrounding 

 particles. But the latter requirement is assuredly not fulfilled. 

 The particles in advance of that which has been moved are 

 more acted on than they were before. Motion will therefore 

 inevitably ensue. This argument then falls to the ground. 

 We have thus shown that the objections are based on a state 

 of things different from that which the hypothesis requires ; 

 and that nothing which has been said on the contrary sup- 

 position is available against the theory. 



b. But were it otherwise, were we to admit the correctness of 

 all the reasonings referred to — should we thereby be subject to 

 the inference which has been drawn, "that a force, whether 

 attractive or repulsive, varying , according to Newton's law, 

 cannot possibly actuate the particles of a vibrating medium ?" 

 (Earnshaw, Int.) By no means. The inference rests on the 

 assumption that a particle of the aether, when disturbed, must 

 be acted upon by forces in the line of displacement. Now 



Phil. Mag. S. 3. Vol. 21. No. 136. Aug. 1842. K 



