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VI. On some Points in the received Theory of Sound. By G. 

 G. Stokes, M.A., Fellow of Pembroke College, Cambridge*. 



BEFORE entering on the main subject of this communi- 

 cation, I will make a few remarks with reference to Pro- 

 fessor Chaliis's last paper in this Magazine. (Vol.xxxiii,p.4)G2.) 



I have no intention of rendering my reasoning liable to the 

 epithet " illogical," by attempting to explain away admitted 

 contradictions. It was my endeavour in a former communi- 

 cation, and will be my endeavour in this, to show that the 

 contradictions in question have no real existence. Since it 

 would seem from Professor Chaliis's words, near the bottom 

 of page 4:63, that he does not perceive that any step of the 

 mathematical reasoning by which the contradiction in the 

 case of plane waves was arrived at has been called in question, 

 I beg to state that I do not admit the validity of any mathe- 

 matical results obtained by a process which is equivalent to 

 integrating over an infinite ordinate, without inquiring whether 

 the passage be legitimate or not. Such a proceeding would 

 lead to contradictions in other subjects as well as in hydrody- 

 namics; for example, in central forces. It was not until after 

 I had pointed out, at page 352, what I conceived to be the 

 flaw in Professor Chaliis's reasoning, that I entered on the 

 physical considerations alluded to by Professor Challis at 

 page 462 : and when I did so, it was not in the slightest de- 

 gree with any intention of explaining away an admitted con- 

 tradiction (for I have already stated that I do not admit the 

 validity of the contradiction), but simply because those con- 

 siderations seemed to be of some interest on their own account. 

 I was particularly careful (see page 353) to keep the purely 

 mathematical question quite distinct from the physical consi- 

 derations which followed. 



It will be necessary, in order to prevent confusion, that I 

 should say a few words with reference to the admission that 

 " plane waves are wholly incompatible with the transmission 

 of articulate and musical sounds." What signifies it if the 

 ideal elastic fluid which forms the basis of our mathematical 

 reasoning be wholly incompetent to transmit such sounds un- 

 changed ? The purely mathematical question of contradiction 

 or no contradiction is not in the slightest degree affected, al- 

 though it forms an interesting subject of physical inquiry how 

 far air, as agreeing approximately with our elastic fluid, may be 

 incapable of transmitting musical sounds without modification. 



To turn now for a moment to the physical question, I would 

 observe that a fluid in which pap would be capable of trans- 

 * Communicated by the Author. 



