of Potential Enciuiu of Lujuid Surfaces. 47 



closer together than on one side or the other of the nittxiniuni 



dV 

 of density ; hence it follows that -^ jj =0, and that conse- 



' / clV'\ . . 

 quently di S^^-,-77 ) is in like manner =0. It resnlts from 



this reasoning that the quantity (^ f S — j will change sign in 



passing through the maximmn, and that, if for example the 

 sign of that quantity is positive immediately before the mnxi- 

 mum of density, it will become negative after passing through 

 the latter. Therefore suppressing the terms in y and k'" as 

 too small to change the sign of the second member, and repre- 

 senting by a and /3 the absolute values of K^ and W ^ we 

 shall have: — 



-K^ dt' =Md ( S^ ^'') = -udt' ; 



-Wdt'' = 0; 



whence 



K'=a, K^^ = 0, K^^^=-/3; 



that is to say, the specific heat is positive at a temperature 

 immediately above that of the maximum densityj zero at the 

 maximum, and negative at a temperature below but very 

 near it. 



It would be very easy to show how the temperature, after 

 reascending in spite of the cooling, soon stops, and ends by 

 descending again. For this, we have only to admit that the 

 variables S and T soon satisfy the condition, 



S y- = a constant ; 



from that time the differential di S— ,— ) becomes again =0, 



and a new change of sign is effected in the value of K, 



If my demonstration were precise, one could perfectly com^ 

 prehend the anomalies just spoken of. It will be remembered 

 that in my first communication I noticed some peculiarities of 

 the same kind, observed by M. Jungk in the vicinity of the 

 maximum of density of water : in this liquid, when absorbed 

 by sand, there is a heating if the initial temperature is higher 

 than H- 4° C, while a cooling is produced if that temperatui-^ 

 is below +4° C; in like manner there is a diminution of tem^ 

 perature when water at 0° is absorbed by snoAv. These results 

 would be explained in an analogous manner to the preceding. 



