456 
PEOFESSOE STOKES ON THE COMMUNICATION OF VIBEATION 
gas, the second the pressure p, in atmospheres, the third the density D under the pres- 
sure p, referred to the density of air at the atmospheric 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 l) 4 . Then follow the values of q, I 2 , and Q, the last 
being the actual intensity referring to air as before. 
Gas. 
P- 
D. 
Qr. 
c-98. 
£=•49. 
2- 
I 2 . 
Q. 
2- 
I 2 . 
Q. 
Air 
1 
1 
1 
•2427 
1136 
1 
•06067 
20890 
l 
Hydrogen 
1 
•0690 
•2627 
•01674 
284700 
•001048 
•004186 
4604000 
•001191 
Air, rarefied 
•01 
•01 
•01 
•2427 
1136 
•01 
•06067 
20890 
•01 
The same filled with H 
1 
•0783 
•2798 
•01900 
220600 
•001440 
•004751 
3572000 
•001637 
Air of same density ... 
■0783 
•0783 
•0783 
•2427 
1136 
•0783 
•06067 
20890 
•0783 
Air rarefied £ 
•5 
•5 
•5 
•2427 
1136 
•5 
•06067 
20890 
•5 
The same filled with H 
1 
•5345 
•7311 
•1297 
4322 
•1921 
•0324 
74890 
•2039 
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 smaller, and I 2 is 16 or 18 times larger, for 
c— -49 than 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 and namely, 
1 and 81 ^~ 2 , the most important, so that I„ does does not greatly differ from 81^ -2 . If 
this result had been exact instead of approximate, the intensity in different gases, sup- 
posed for simplicity to be at a common pressure, would have varied as D® ; and it will be 
found that for the cases in which p—\ the values of Q in the above Table, especially 
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 respecting which we cannot infer what would 
be true of a bell of the ordinary shape from what we have proved for a sphere. 
Secondly, the radius must be sufficiently small, or the pitch sufficiently low, to make q 
small ; at the other extremity of the scale, in which c is supposed to be very large, or A 
very small, Q varies nearly as instead of D^, whatever be the order of the Laplace’s 
function. Hence no simple relation can be expected between the numbers furnished 
by experiment and the numerical constants of the gas in such experiments as those of 
M. Perolle *, in which the same bell was rung in succession in different gases. 
B. Solution of the Problem in the case of a Vibrating Cylinder. 
I will here suppose the motion to be in two dimensions only. In the case of a 
vibrating string, which I have mainly in view, it is true that the amplitude of excursion 
* Memoires de l’Academie des Sciences de Turin, t. iii. (1786-7) ; Mem. des Correspondans, p. 1. 
