308 
Velocity of Sound. 
[Oct. 
tion of airs very different from that generally embraced. This theory, after un- 
folding to me the laws of an immense variety of phenomena, I was anxious to apply 
to solving the celebrated problems of sound and atmospheric temperature and pres- 
sure. No difficulty whatever occurred in developing the general laws ; but this was 
not enough ; if the theory to which 1 had arrived was right, 1 felt assured there must 
be some method of getting at the exact quantities of the phenomena, without draw- 
ing on experiments for more than indispensable elements. For instance, in esti- 
mating the velocity of sound, I conceived no just theory ought to require morg from 
experiment than the elastic force and specific gravity of the air. The same elements 
only, I apprehended, ought to be sufficient for determining the exact rate of dimi- 
nution in temperature and pressure at any elevation. For a long time iny efforts 
were unsuccessful ; at last, however, a very simple idea, which I am surprised 
should have so long eluded my attempts to reduce the equations of comparison I had 
previouslv used to equations of equality, enabled me to solve the hitherto refractory 
problem of sound, and with it several of much more importance and utility. 
What, probably, will appear not the least remarkable is, that this problem, which 
has obstinately resisted the abilities of Newton, Euler, Lagrange, Laplace, and 
other eminent mathematicians for 150 years, and the highest powers of analysis, 
should at last yield to a process scarcely requiring simple equations of Algebra ; 
and at the same time open solutions to other phenomena, with which 1 think, I may 
venture to say, no analyst ever expected it had the remotest connection. But the 
theorems will speak best for themselves.* 
Let, as usual, S ED g denote the velocity of sound, elasticity of the air, its 
density, and the velocity acquired by a falling body at the end of the first second. 
Then by the theory alluded to, 
and if S be the velocity of sound at any elevation x , and P p, the barometric pres- 
sures at the lower and higher stations ; 
V / S x 6 
P v 1 3y^ 2 ) (2) 
and 
3^2 (S 2 — s*)z=gx (3) 
For, comparing these formula: with observation, we have 
E 488 
D — 
rh (F-f-448) 
in which h is the altitude of the barometer at the temperature of water freezing ; 
r — 10463 by Biot, the ratio of the specific gravity of mercury to that of dry air, at 
32° Fahr., and barometric pressure metres, the metre being 3,28085 Eng- 
lish feet, and F the Fahr. temperature. Therefore, since feet. 
S= 1089,41 Eng. feet. (4) 
Now, from a mean of Captain Parry’s experiments in the north, at — 17°> 72 Fahr. 
it appears the velocity was 1035,2 feet per second, or, allowing for the difference 
in the value of g in that high latitude, probably about 1034 feet reduced to our 
latitude; our theory gives 1031,5. The French academicians, in 1738, at about 42 ,8 
Fahr. found it 1103,5 feet ; our theory makes it 1101,6. Dr. Gregory, by the mean 
of his observations, determined the velocity to be 1107 feet at 48°, 62 temp. ; by our 
theory it should be 1 108,1. In 1821 Arago and his colleagues made the mean at 
60°, 62 to he 1118,43 ; our theory gives 1121,5, and from an article on sound, no 
yet published, with which the author has kindly favoured me, it appears Molls 
late experiments, reduced to dry air at 32°, give 1089,4 feet, the same as our theo- 
ry. In the same article, some of Goldingham’s experiments at Madras, when in- 
duced to 32°, it seems make 1089,9 ; the mean of his other experiments ditten»a 
as much as 10 feet. 
Collecting these observations together, we have, 
