Page:Scientific Memoirs, Vol. 1 (1837).djvu/381

Rh M. Dulong has shown that the air, and all the other gases taken at the temperature of 0°, and under the pressure $$0^m\centerdot76$$ of mercury, when compressed by $$\frac$$ of their volume, disengage a quantity of heat, capable of elevating the same volume of atmospheric air by $$0.421$$.

Suppose that we operate upon a kilogramme of air occupying a volume $$v = 0.770$$ of a cubic metre, under the pressure of the atmosphere $$p$$, equivalent to $$10230$$ kilogrammes upon a square metre; we have and If a variation be suddenly effected in $$v$$ by an infinitely small quantity $$d\,v$$, without there being any variation in the absolute quantity of heat $$Q$$, we shall have and or preferably Now $$R \left( \frac - \frac \log p \right)$$ being the partial differential of $$Q$$ in respect of $$t$$, $$p$$ remaining constant, is nothing else than the specific caloric of the air at a constant pressure; it is the number of unities of heat necessary to elevate a kilogramme of air under atmospheric pressure by one degree; we have therefore  Then substituting $$-\frac$$ for $$d\,v$$, and $$0.421$$ for $$d\,t$$, we arrive lastly at This is the maximum effect producible by a quantity of heat, equal to that which would elevate by 1° a kilogramme of water taken at zero, passing from a body maintained at 1° to a body maintained at 0°. It is expressed in kilogrammes raised one metre high.

Having the value of $$C$$, which corresponds to $$t = 0$$, it is interesting to know, setting out from this point, whether $$C$$ increases or decreases, and in what proportion. An experiment of MM. De Laroche and Bérard upon the variations experienced by the specific caloric of the air,