On the Be-heating of Jets of Air, §fc. 129 



that the velocity of sound in air is \/^times greater than it would 

 be, if the pressure during the passage of the wave of sound varied 

 simply as the density. It is an approximate result of Carnot's 

 theory of heat, and also of the dynamical theory of heat as de- 

 veloped by myself in a paper read to the Royal Society of Edin- 

 burgh, and by Clausius, in Poggendorff^ 8 Annalen for 1850. 



The peculiar feature in Mr Petrie's paper is his assigning a par- 

 ticular value to the index of y, viz., IJ, as a consequence of certain 

 hypothetical views of molecular action. He supposes that the elasti- 

 city of a gas arises from the mutual repulsions between the centres of 

 atoms — the repulsion of each pair of centres varying, for any instari' 

 taneous change of position, inversely as the square of this distance. 

 This law of repulsion Mr Petrie characterises as " self-evident.'* 

 It gives rise to an elasticity varying as the 1 J power of the density : 

 and this is a particular case of a proposition demonstrated by New- 

 ton in the Principia, viz., that if the mutual repulsion of each pair of 

 a system of atoms varies inversely as the nth power of their distance 



ft -4- 2 

 apart, the elasticity will vary as the — k — power of the density. 



Newton, however, did not assign any preference, a priori, to one 

 law of repulsion above another. 



It follows from Mr Petrie's supposition that y— 1 = |, so the 

 temperature of a gas, as measured from the absolute zero, when its 

 volume is suddenly changed, varies as the cube root of the density ; 

 and upon this basis he has founded a table, shewing the rise and 

 fall of temperature produced by various compressions and dilata- 

 tions of a gas at 60° Fahr., which would be very useful if the value 

 of the index y — 1 were correct. 



The hypothetical views of Mr Petrie, though ingenious, are open 

 (as it appears to me) to the following objections : — 



First. The a priori necessity of the law of the inverse squares 

 in molecular actions is a doubtful assumption, whigh, as I have 

 stated, Newton himself never proposed to make. 



Secondly/, A system of mere atomic centres of force would con- 

 stitute, not a gas, but a solid. On this objection, however, I do not 

 insist, as it results from theoretical views of my own, which hare 

 not yet been generally received. 



Thirdly. The value of the index y for air, as determined by most 

 careful and precise experiments on the velocity of sound, is not 1^, 

 but 1-4, the limits of probable error being about 0-01. The tem- 

 perature, therefore, measured from the absolute zero, varies for a 

 sudden change of volume, not as the cube root of the density, but 

 as the 1^ power of the density, or the f power of the pressure ; 

 and this index I have used in calculations which, as you are aware, 

 agree with your experiments to about a degree of Fahr. 



Fourthly. The index y is not the same for all gases. It is 1»426 



VOL. LI. NO. CI, — JULY 1851. I 



