Theory of Molecular Action according to Newton's Law. 269 



rection of transmission." This is assumed by Mr. Earnshaw 

 when he omits D, E, and F, and hence all his objections. 



2. " There can be no connexion between the directions of 

 the vibrations and the law of molecular force." It has been 

 proved by me in the Transactions of the Cambridge Philoso- 

 phical Society, vol. vi. p. 180, and Philosophical Magazine, 

 May, 1837, p. 841, that if the law of force in a medium of 

 symmetry be that of the inverse square of the distance, the 

 vibrations must be altogether transversal or altogether normal. 

 I call on Mr. Earnshaw to point out an error in my reasoning. 



3. But Mr. Earnshaw has attempted to impugn, not in- 

 deed my reasoning, but my inference. He says (p. 49, last 

 line), " since v v' v" are the velocities of the wave, and not of 

 the particles, the inference should have been, that there is one 

 direction in which waves cannot be transmitted', or, in other 

 words, that the cether is opa/ce in one direction." Mr. Earn- 

 shaw ought, I repeat, to have attempted to show that there is 

 some error in the argument, for he must know that such an 

 inference as he draws tends to throw discredit (if legitimate) 

 upon any reasoning from which it is made to follow. The 

 hypothesis is that the aether is equally affected in all directions, 

 the conclusion, that it is opake in one. 



The inference, however, cannot follow from my equations, 

 for Mr. Earnshaw will see, if he turns to my Memoir, that o' 

 is the velocity of a normal vibration which is assumed to exist. 

 Since then (I argue) the normal vibration has not a possible 

 velocity of transmission, it does not exist. In fact, if there be 

 a normal motion at all it must be a transmissory one, due 

 to exponential in place of circular functions. On this last fact 

 I have based my Theory of Heat (Preface, p. 8, and Me- 

 moirs, Sec, passim). Since Mr. Earnshaw quotes Mr. O'Brien, 

 I will refer him to the same quarter to be set right, for his 

 conclusions are equally controverted by Mr. Earnshaw's ob- 

 jections. 



4. " But I am unable to discover on what ground it is stated 

 that y' is impossible," &c. Had Mr. Earnshaw read through 

 the page he refers to he would have found the reason : all that 

 he suggests is there plainly discussed, the inference that the 

 cether is opa/ce in one direction only excepted. 



5. Mr. Earnshaw concludes with a suggestion that the in- 

 ference ought rather to have reference to the instability of the 

 medium according to the Newtonian law. How he connects 

 the impossibility of transmission of an assumed vibration with 

 instability it is easy to see, and that it arises from the assump- 

 tion of the want of dependence of the equations of motion on 

 the direction of transmission. But I shall not dwell on this 



