MECHANICAL ACTION OF HEAT. 167 
Ratio of those two specific heats :— 
ei 
Ka1tN |. . Ql) 
This ratio is the quantity called by Porsson +, in his researches on the pro- 
pagation of sound. 
(11.) It is unnecessary to do more than to refer to the researches of Poisson, 
and to those of Lapiacer, for the proof that the effect of the production of heat by 
the compression of air is the same as if the elasticity varied in proportion to that 
power of the density whose index is the ratio of the two specific heats; so that 
the actual velocity of sound is greater than that which it would have if there were 
no such development of heat, in the proportion of the square root of that ratio. 
The following is the value of the velocity of sound in a gas, as given by 
Poisson, in the second volume of his 7raité de Mécanique :— 
a=Jg .y. (1+ ET)™ phen ogee 
where a denotes the velocity of sound, g the velocity generated by gravity in 
unity of time, E the coefficient of increase of elasticity with temperature, at the 
freezing point of water, T the temperature measured from that point, m the spe- 
cific gravity of mercury, 4 that of the gas at the temperature of melting ice, and 
pressure corresponding to a column of mercury of the height . It follows that 
the ratio y is given by the formula 
awa 
gmhG+hT) °°): (23.) 
Calculations have been made to determine the ratio y from the velocity of 
sound; but as many of them involve erroneous values of the coefficient of elasti- 
city E, the experiments have to be reduced anew. 
The following calculation is founded on an experiment quoted by Poisson 
on the velocity of sound in atmospheric air, the values of E, m, and a being taken 
from the experiments of M. Reenavtr. 
a = 340-89 métres per second. 
= 9™-80896. = 0™-76. T = 15°9 Centigrade. 
E = 0:003665 ; = = 10513. 
y=1+N nearly = 
Consequently, for atmospheric air, 
ry = 1-401. 
The results of a reduction, according to correct data, of the experiments of 
DuLone upon the velocity of sound in atmospheric air, oxygen, and hydrogen, 
are as follows :— 
Atmospheric air, : F : Sui nie (as 023 
Oxygen, : : £ Z : ‘ c 1-426 
Hydrogen, . : : c : : 2 1-426 
VOL. XX. PART I. 2Y 

