§12 OF ARTS AND SCIENCES. ' 405 



heats are compared must be the same; and of course the 

 specific heats must be corrected for the external work 

 done in each case. For liquids this may generally be 

 disregarded ; but for vapors we must multiply the external 

 pressure in dynes by the coefficient of expansion, remem- 

 bering to divide by 42,000,000 and by the density, if the 

 result is to be expressed in heat units per unit weight. 

 Deducting this number from the ordinary specific heat, we 

 have that under constant volume. The specific heat of 

 the liquid at the same temperature necessarily exceeds 

 this by the amount of the diminution of the latent heat of 

 vaporization per unit of temperature. 



To find an expression for this difference, we have 

 merely to differentiate the equation for the latent heat 

 already found, namely, 



JLD = ^ Dvl -'' ^ ^ 



where we notice that D may be cancelled, and that K\?> 

 the principal ratio, not far from unity, which we have 

 already calculated for several liquids. 



In the liquid or solid state, it must be supposed that the 

 expansion is accompanied by a grouping of the atoms; 

 hence iTmust not be disregarded, and we have 



J dL ^ K_ v^ m, f {{l—r)—l) ^ dl . I \ 

 -^ dT z T, m\ {l—ry dT'^ i—v) 



_Kvlm, I K vlm.T V dl 



^T,,n{l—V) 3 mT, {J — IJ dT 



= J (//' — //) , where H and H' are the specific heats 

 of the liquid and of the vapor. 



Substitutincj for ——-, its value — , we have 



dr 3' 



T(TT_TT'\_ K ^. m, Te V I _ K vl m, I ^ 



