Page:Scientific Memoirs, Vol. 1 (1837).djvu/384

There is another means of calculating the values of ${\frac {1}{C}}$, 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 temperature 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

${\frac {1}{C}}={\frac {\frac {d\,p}{d\,t}}{K}}$

will express $K$ in function of $t$; ${\frac {d\,p}{d\,t}}$ 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 ${\frac {1}{C}}.$
$t=0\centerdot$	${\frac {1}{C}}=1\centerdot 586$		$1\centerdot 410$
$t=35\centerdot 5$	${\frac {1}{C}}=1\centerdot 292$	We have already found for the values of ${\frac {1}{C}}$ corresponding to the same values of $t$.	$1\centerdot 365$
$t=78\centerdot 8$	${\frac {1}{C}}=1\centerdot 142$		$1\centerdot 208$
$t=100\centerdot$	${\frac {1}{C}}=1\centerdot 102$		$1\centerdot 106$
$t=156\centerdot 8$	${\frac {1}{C}}=1\centerdot 072$		$1\centerdot 078$

These last, deduced from experiments upon sound, the vapours of sulphuric ether, alcohol, water, and essence of turpentine, accord with the first in a satisfactory manner.

These remarkable coincidences, obtained by numerical operations performed upon a great variety of data, furnished by phænomena 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 phænomena 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 propagation of sound in gases taken at different temperatures, were instituted, in order to establish this function with all the requisite certainty. It