75 



November 27, 1848. 



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 be the tempera- 

 ture where the pressure is p and density p, and 0[ the temperature in 

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



p=a*p(l + x.Q — 9,). 

 Hence 



d*2 dp a"dp „ , fl a N dp . dQ ,, , 



dt* pdz pdz pdz 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 9 — Sj." 



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 



Q-^=k(l-p), 



where k 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. 



Observations of the Aurora Borealis of Nov. 17, 1848, made at 

 the Cambridge Observatory. By Professor Challis. 



These observations relate principally to the corona, or point of 

 apparent convergence of the streamers, the remarkable display of 

 Nov. 1 7 being peculiarly favourable for noting the position of this 

 critical point. They were taken partly by estimation of distances 

 from stars, and partly by a small altitude and azimuth instrument 

 (called by the author a meteor o scope) , which is furnished with a bar, 

 eighteen inches long, carrying at one end a rectangular piece whose 

 edges are horizontal and vertical, by looking at which through an 

 eyelet-hole, about the size of the pupil of the eye, at the other end, 

 the collimation is performed. Each observed position is compared 



