198 HOLTZMANN ON THE HEAT AND ELASTICITY 
when p is the original and p! is the subsequent pressure. Since 
! 
in this case Mariotte’s law obtains, we can also write for - the 
U 
relation of the densities ©. 
With the introduction of Briggs’s logarithms the amount of 
heat given off for atmospheric air is 5; 
! 
0°180 (273 + 2) . log oe 
At the temperature 0° the quantities of heat given off are, 
14°78, 23°42, 29°56, 34:32, 49:1, 
for equal 2, 3, 4, 5, 10. 
With an equally great rarefaction the same quantities of heat 
are absorbed. Moreover, as will be seen from the formula, the 
quantity of heat given off with the same compression increases 
with the temperature at which the gas expands. 
11. The above expression (4.) refers to the unit of weight; if 
it be desired to calculate the quantity of heat which is given off 
by the unit of volume at the pressure p, it is requisite to multiply 
by the density of the gas at this pressure, 7. e. by °F pal) 
In this manner the quantity of heat given off in the compression 
of one volume is found to be equal to 
a Pp 
Consequently for equal primitive pressure, equal volumes of all 
gases, the condensation being the same, give off egual quantities 
of heat. 
Already Dulong advanced the same proposition, founded on 
his experiments and those of De la Roche and Bérard on the 
specific heats of gases; it likewise occurs in Clapeyron. 
12. From the formule III. in No. 5, it is evident that the dif- 
ference of the two specific heats referred to the unit of volume 
equals pe 
a(l1+at) 
For different gases, taken at the same pressure and the same 
temperature, this difference varies only with the coefficient of 
expansion a@, and, since this is almost equal for the various gases, 
is itself nearly equal for all gases. Dulong has assumed this 
equality, and has calculated with it and the observed values of 
