Velocity of Sound. 131 



Take the fluxions, making dx and F constant, which gives 



ff£ = - 1 f ^^ ^T V ^ = - ± (l-Y X — 

 P' 3 Vdr+rfz J dx 3 \p' J dx' 



Multiply by F and divide by § (c^x+cZa:) = q'dxy as before, and 

 we have 



Hence the velocity of sound should be 



t- (jrY X v/(f ) 



which, though a very different expression from the former, is 



uniform or independent of the degree of condensation, because 



dx and dr are constant ; and yet it is affected by the intensity 



or degree of condensation, because g is so affected. 



We have thus, even when working more correctly, obtained 



a result which is evidently contradictory or absurd. Nor can 



it be admitted as an excuse, to say, that § and §' are nearly 



equal ; for we have already seen that the principles acted on in 



this investigation imply that p may exceed p' in any proportion, 



dx 



By using unit for the index of , we do not, when 



•' ^ dx+dz 



nothing is omitted, obtain Newton's result, as Mr. Ivory alleges, 

 but the very different expression 



which is just as absurd as the other. Indeed, when in this mode 

 of investigation, none of the powers of dz have been rejected, 

 the velocity can never come out uniform or independent of the 

 degree of condensation, and be at the same time real or possi- 

 ble. For, taking the only two supposable cases, — were the 

 index = 0, neither the elasticity of air, nor sound, which de- 

 pends on it, could exist; and were the index = — 1, the 

 elasticity would vary inversely as the density, which is a perfect 

 contradiction, not to mention that the velocity of sound would 

 come out an impossible quantity. 



Any further evidence would be superfluous to show that this 

 sort of investigation is not only inefficient, but full of error 

 and incongruity, view it which way we will ; and that it will be 



K2 



