194 HOLTZMANN ON THE HEAT AND ELASTICITY 
5. The specific heat is the quantity of heat which must be 
added to the gas to raise the temperature 1°. If the addition 
of the quantity of heat dq increase the temperature by d¢, the 
quantity of heat = would be required to increase the temperature 
1°. Or the relation between g and ¢ gives the specific heat of 
the gas, viz. the specific heat under a constant pressure when 
is considered constant, and the specific heat under a constant 
volume when g is considered constant. 
Let c denote the specific heat with constant pressure, and 
C ty ae! cee ee volume, 
we have 
dq dad¥ ka p 
Odean Wk ai ee 
ody dq tp at ke pep 
gt dah weet gt Sige ne 
In this the unit of weight is the basis; if it be desired to refer 
the specific heats to the volume, we have to multiply by the 
specific gravities, or by g@ = Fay This affords 
d¥ a 
ee P 5 A 2 pia 
Seah ar od a a 
C= 2 a¥ Was Lode aoe N P pa 
El +int) df. off +at)° py, ot en 
6. There now remains to determine the function F,; From 
the experiments of Dulong on the value of the relation of the 
two specific heats, it follows that this relation is independent of 
the temperature. He has deduced these values, as is well known, 
from the tones which a pipe gives filled with various gases. 
He mentions an experiment in which a pipe that gave a tone 
at 22° C., which results from 500 vibrations in the second, pro- 
duced at 4° C. only 484°8 vibrations. If the relation of the spe- 
cific heats remains in this interval the same, the numbers of 
vibrations are as 
/1+0°003665 .22 : “1+0°003665 . 4, 
whence, if we start from the first tone, we obtain the number of 
vibrations 484°5 for the second. The coincidence of the calcu- 
lated and of the observed value is so great that a change in the 
relation of the two specific heats by increase of temperature 
must at least be very small. 
