1 36 Cambridge Philosophical Socictjj, 



eophy. The present memoir is employed in illustrating the proposi- 

 tion that the progress of science consists in the transfer of some truth 

 from the factorial to the ideal side of the antithesis, or as it may be 

 termed, in the idealization of facts. This is exemplified in mecha- 

 nics, astronomy, botany and chemistry. 



In a note, the author remarks on certain German systems of phi- 

 losophy with reference to this antithesis. The Sensatorial school 

 having reduced all knowledge to facts, Kant re-established the neces- 

 sity of Ideas, which Fichte made almost the exclusive element. Schel- 

 ling founded his philosophy upon the absolute, from which he derives 

 both facts and ideas, but which a wiser philosophy shows us that we 

 can never reach ; and Hegel took the same foundation, but in a cer- 

 tain degree rightly pointed out that the progress towards the identity 

 of fact and idea is to be traced in the history of science ; which view, 

 however, he has carried into detail by rash and blind conjecture. 



Nov. 27. — On a Difficulty suggested by Professor Challis in the 

 Theory of Sound. By Robert Moon. 



In a paper by Professor Challis contained in the Supplementary 

 Number of the 32nd Volume of the Philosophical Magazine, I find 

 the following : — 



" The difficulty respecting the augmentation of the velocity of 

 sound by the development of heat, cannot be so summarily disposed 

 of as Mr. Airy appears to imagine. I shall perhaps succeed better 

 in conveying my meaning by using symbols. If S be the tempera- 

 ture where the pressure is p and density p, and fli the temperature in 

 the quiescent state of the fluid, we have, by a known equation, 



;j=a2^(H-a.9-9i). 



Hence 



d'^z dp a-dp c ft t\^P d& ., v 



— = — _£- = J:_a2a(9— 9j— L — a^a—-. . (1.) 



dt"^ pdz pdz paz dz 



" The usual theory explains how the third term of the right-hand 

 side of this equation may be in a given ratio to the first ; but my 

 difficulty is to conceive how the same can be the case also with the 

 second term, since it changes sign with the change of sign of — fl,." 



I conceive that the explanation, according to the usual theory to 

 which Professor Challis here alludes, depends upon the principle, 

 " that for very small condensations of air, the rise of temperature will 

 be proportional to the increase of density." (Vide Herschel On 

 Sound, Encyc. Met., art. 72.) Thus we may put 



where A is a constant, and 1 is put for the density of equilibrium : 

 on which hypothesis it is obvious that the third term of equation (1.) 

 will be a multiple of the first, as described by Prof. Challis. It also 

 follows that the second term vanishes, since it has (1 — p) for a fac- 

 tor, and in reducing (1.) to the ordinary form of the differential 

 equation of sound the difference between p and 1 is neglected. It 

 thus, I think, appears that the difficulty suggested by Prof. Challis 

 has no real existence. 



