Effect of the Badiatiohof Heat on the Pi'dpat/dtion of Sound. 305 



moudian notation from simple to compound determinants is 

 grounded, would be better apprehended if the biliteral symbols of 

 simple quantities were written with the umb^'al elements disposed 



veitically, as , , instead of horizontally/ as arft j which latter is the 



method for the purpqs^? of, t;ypograpliicaI uniformity adopted in 

 the text above. The other mode is, however, much to be pre- 

 ferred, and is what I propose hereafter to adhere to. For my 

 two general umbra? a, b, Vaudermonde uses two numbers, one set 

 a-cock upon the other, as 5''. The objection to the use of num- 

 bers is apparent as soon as it becomes necessary to treat of the 

 mutual relations of diverse systems of determinants, and his 

 mode of writing the vmbrfe militates against the perception of 

 the most A'aluable algebraical analogies. The one important 

 point in which Vandermonde has anticipated me, consists in ex- 

 pressing a simple determinant by two horizontal rows of umbrae 

 one over the other. But the idea vipon which this depends is so 

 simple and natural, that it was sure to reappear in any well-con- 

 stinicted system of notation. 



lu'Ci 



1>J) tiiirfO(fr(((i'i 



XXXVIII, An Examination of the possible effect oftlie Radiation 

 of Heat on the Propar/ation of Sound. By Professor Stokes*. 



THE appearance of an article by Professor Potter in a former 

 Number of this Magazine, in which he attacks the received 

 explanation of the excess of, the observed velocity of sound over 

 that calculated from Newton's theory, indices me to offer a few 



'I 1 



remarks on the subject. 



In the first place, I would observe that Professor Potter seems 

 to have supposed that Laplace's explanation was equivalent to 

 this — that the condensation produced in the course of the motion 

 causes an elevation of temperature, and that therefore the velocity 

 of propagation is increased, inasmuch as the velocity increases 

 with the temperature; Such a view 6f the subject would be 

 altogether erroneous. The actual explanation is simply as fol- 

 lows. In consequence of the heat and cold produced by sudden 

 condensation and rarefaction respectively, the pressure changes 

 more rupidhj with a change of density than it would do if it varied 

 as the density; The mathematical calculation of the velocity of* . ' 

 sound, when account is taken of the change of teniperatiu'e prq^', 

 duced by sudden condensation and rarefaction, is very simple. .. 

 and is too well kn(jwn to make it necessary for me here to enter , 

 into it. The slightest examination of the process is sufficient ^0 

 show, that the development of cold bij sudden rarefaction is as ' 

 m uch an essential part of Laplace's explanation of the increase in 

 -r.i.iK;/ '.(ii \* Comihtiriidated by the Author. '.-V " '" " 



