412 Prof. Stokes on the Communication of Vibration 



of propagation, and therefore as the pressure into the square 

 root of the density under a standard pressure, if we take the 

 factor depending on the development of heat as sensibly the 

 same for the gases and gaseous mixtures with which we have to 

 deal. In the following Table the first column gives the gas, the 

 second the pressure p, in atmospheres, the third the density D 

 under the pressure p, referred to the density of air at the atmo- 

 spheric pressure as unity, the fourth, Q r , what would have been 

 the intensity had the motion been wholly radial, referred to the 

 intensity in air at atmospheric pressure as unity, or, in other 

 words, a quantity varying as p x (the density at pressure 1)*. 

 Then follow the values of q, I 2 , and Q, the last being the actual 

 intensity referred to air as before. 



Gas. 



P- 



D. 



Q'-. 



c = -98. 



e = -49. 



?• 



I 2 . 



Q. 



1- 



h- 



Q. 



Air 



01 

 1 



•0/83 



•5 

 1 



•0690 



•01 



•0783 



•0/83 



•5 



•5345 



1 



•2627 

 •01 

 •2798 

 •0783 

 •5 

 •7311 



•2427 

 •01674 



2427 

 •0190 

 •2427 

 •2427 



1297 



1136 

 284700 

 1136 

 220600 

 1136 

 1136 

 4322 



•001048 



•01 



•001440 



•0783 



•5 



•1921 



•06067 



•004186 



•06067 



004751 



•06067 



06067 



•0324 



20890 

 4604000 

 20890 

 3572000 

 20890 

 20890 

 74890 



•001191 

 •01 



•001637 

 0783 

 •5 

 •2039 





Air, rarefied 



Air filled with H.. . 

 Airof same density. 



Air rarefied ^ 



Air filled with H... 



An inspection of the numbers contained in the columns headed 

 Q will show that the cause here investigated is amply sufficient 

 to account for the facts mentioned by Leslie. 



It may be noticed that while q is 4 times as small, and I 2 is 

 16 or 18 times as large, for c = '49 as for c=*98, there is no 

 great difference in the values of Q in the two cases for hydrogen 

 and mixtures of hydrogen and air in given proportions. This 

 arises from the circumstance that q is sufficiently small to make 

 the last terms in /lcJ and \j\, namely, 1 and 81 q~ 2 , the most im- 

 portant, so that I n does not greatly differ from 81q~ 2 . If this 

 result had been exact instead of approximate, the intensity in 

 different gases, supposed for simplicity to be at a common pres- 

 sure, would have varied as D^ ; and it will be found that for the 

 cases in which p = l the values of Q in the above Table, especi- 

 ally those in the last column, do not greatly deviate from this 

 proportion. But the simplicity of this result depends on two 

 things. First, the vibration must be expressed by a Laplace's 

 Function of the order 2; for a different order the power of D 

 would have been different; and this is just one of the points re- 

 specting which we cannot infer what would be true of a bell of 

 the ordinary shape from what we have proved for a sphere. 



