372 M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 
There is another means of calculating the values of ra between 
extended limits of the temperature in an approximative manner; for 
this it is necessary to admit, that the quantity of caloric contained in a 
given weight of the vapour of water is the same whatever be the tem- 
perature and the corresponding pressure; and still further, that the 
laws relative to the compression and the dilatation of the permanent 
gases are equally applicable to vapours: adopting these laws, towards 
which we have only approximated, the formula 
dp 
1 _4dt 
1¢ Tek 
will express K in function of ¢; 2 may be deduced from 0 to 100° 
from experiments long since made by several philosophers, and from 
100° to 224° from recent experiments of MM. Arago and Dulong. 
Thus we find for Values of a 
¢= 0O = 1°586 1 1°410 
er ore We have already found for es 
ing to the same values of ¢. 
= 100° = 1102 1°106 
1 
o'. 
1] 
L 
1 1 
t= 78:8 ¢= 1142 the values of re correspond- 4 1:208 
1 
ic 
1 
t= 156°8 ¢€ 
= 1-072 } | 1-078 
These last, deduced from experiments upon sound, the vapours of 
sulphuric ether, alcohol, water, and essence of turpentine, accord with 
the first ina satisfactory manner. 
These remarkable coincidences, obtained by numerical operations 
performed upon a great variety of data, furnished by phenomena of 
many different kinds, appear to us to add greatly to the evidence of our 
theory. 
§ VII. 
The function C is, as we have seen, of great importance: it is the 
connecting link of all the phenomena produced by heat upon solid, 
liquid, or gaseous bodies. It is greatly to be desired that experiments 
of the most precise exactitude, such as the researches upon the propa- 
gation of sound in gases taken at different temperatures, were instituted, 
in order to establish this function with all the requisite certainty. It 
