and the Velocity of Sound. 215 
force of Newton; and yet it appears to be the only correct mea- 
sure of the elastic force of bodies. 
Let F be the force producing a compression E in a body 
whose magnitude in its natural state is expressed by unity; then 
Bist inoks ne = the weight of the modulus of elasticity. 
Boyle, Marriotte, and some other experimentalists infer, from 
‘their experiments, that air is compressed into half its natural 
space by the addition of a pressure equal to the weight of the 
‘atmosphere. Let the weight of the atmosphere be equal to thirty 
inches of mercury, of the specific gravity 13-500; then iit = 
ae = 29-3lbs. the weight of the modulus of elasticity for a 
‘base of an inch square. And the weight of 100 cubic inches of 
air being 30°5 grains, the height of the modulus of elasticity of 
air will be 56,038 feet. It is shown by writers on dynamics, that 
the velocity of sound is equal to that acquired by a heavy body 
in falling through half the height of the modulus of elasticity of 
the medium ; consequently it will be nearly equal to the square 
‘root of half the height of the modulus of elasticity multiplied by 
8; and taking the value of the modulus stated above, it gives 
1339 feet per second as the velocity of sound. Otherwise the 
height of an uniform etmosphere, according to Professor Leslie*, 
is 27,800 feet; and = anne = 55,600 feet, the height of the 
modulus of elasticity of air; and, accordingly, the velocity of 
sound would be 1333 feet per second. 
In these calculations the elasticity of the air is supposed to be 
perfect, and that the compression is as the force producing it; 
-neither of which are true of atmospheric air: besides, it always. 
_contains a considerable quantity of vapour, sometimes, according 
to Dr. Thomson, as much as a sixtieth part of its bulk, and it is 
well known that the elasticity of damp air is much inferior to 
that of dry. 
But the chief cause of error appears to arise from considering 
atmospheric air a perfectly elastic fluid, and the elastic force to be 
as the compression. The rude experiments of Boyle and Marriotte 
were insufficient to establish the law of compression, More accu- 
rate experiments have, I believe, been made; but I have not an 
opportunity of referring to them at present. 
The imperfect elasticity of air appears to be owing to the heat 
extricated during compression. The temperature being the same, 
-every change in the density of the air must be accompanied bya 
“corresponding change in the quantity of heat it contains, When 
* Supp. Ency. Brit. ae Acoustics, p, 44. ¥ 
air 
