of a Mass of Matter. 203 



a consequence of (17), 



dE M N Y 



we obtain, for the differential coefficients which here occur, the 

 equation of condition 



^VT7 = f 7TVT)' • ' ■• ' ' (20) 



which exactly corresponds to equation (18). 



By carrying out the differentiations, this equation becomes 



1«_1<ZN_N , 2n 



TdX~TdT T 2; \ ' 



and, by applying equation (18) to this, we get 



N=0 (22) 



According to (17), N is the differential coefficient of H accord- 

 ing to X ; and if this differential coefficient is to be generally 

 equal to nothing, H itself must be independent of X ; and since 

 we may understand by X any magnitude whatever which is inde- 

 pendent of T, and together with T determines the condition of 

 the body, it follows that H can only be a function of T. 



§ 8. This last conclusion appears, according to commonly 

 received opinions, to be opposed to well-known facts. 



I will choose as an illustrative example, in the first place, a 

 case which is very familiar, and in which the discrepancy is par- 

 ticularly great, namely, water in its various states. We may 

 have water in the liquid state, and in the solid state in the form 

 of ice, at the same temperature ; and the above theorem asserts 

 that the quantity of heat contained in it is in both cases the same. 

 This appears to be contradicted by experience. The specific heat 

 of ice is only about half as great as that of liquid water, and this 

 appears to furnish grounds for the following conclusion. If at 

 any given temperature a unit of weight of ice and a unit of 

 weight of water in reality contained the same quantity of heat, 

 we must, in order to heat or cool them both, impart to or with- 

 draw from the water more heat than we impart to or withdraw 

 from the ice, so that the equality in the quantity of heat could 

 not be maintained at any other temperatures. A similar differ- 

 ence to that existing between water and ice also exists between 

 water and steam, inasmuch as the specific heat of steam is much 

 smaller than that of water. 



To explain this difference, I must recall the fact that only 

 part of the heat which a body takes up when heated goes to 

 increase the quantity of heat actually present in it, the remainder 

 being consumed as work. I believe now that the differences in 



P2 



