Oil the Va)'iation>< of Potential Enenjy of Lvjuld Surfacei^. 41 



We thus see how the ideas first expressed by M. Weber*, and 

 quite recently by M. Walthere Spring f, according to which 

 '' the variations of specific heat follow the variations of volume 

 of bodies by heat," would be justified. Moreover the value of 

 K would be composed of two parts : — one, k, depending at 

 once on the temperature, the volume, and the pressure ; the 

 other a function of t, S, and T. Now it is conceived that a 

 body may have very different surfaces for one and the same 

 initial volume ; hence it follows that, for large values of S, the 

 variations of k will be very slight in comparison with those of 

 the second term, which depends on S and T. We shall by- 

 and-by see a very curious consequence of this deduction. 



I will now apply equation (3) to the examination of various 

 questions of general physics, upon which my theory appears 

 to throw a bright light. 



I. Let us suppose, in the first place, that the variations of 

 S are very inconsiderable and can be neglected pending the 

 variations of the temperature t ; then formula (3) becomes 



K = i-A<sg^ (4) 



In truth we do not at present know the exact form of the 

 function which expresses T by means of t for any liquid what- 

 ever : but we can at least, for a given liquid, seek the values 

 of the coefficients of an equation such as 



^=u+pt+r^e+ 



Now it follows from the researches of M. Wolf that, for 

 water, the coefficients ^ and 7 are very small and permit us 

 to neglect the powers of t higher than the second. Besides, 



for the same liquid, -p- is negative ; from this it follows that 



the quantity of heat to be supplied to or taken away from the 

 unit weight of water, to raise or lower the temperature 1°, in 

 general increases not only wdth t, but also with S. Conse- 

 quently, if we imagine a sphere of water weighing 1 kilo- 

 gram, and a series of n spheres of water of which the total 

 weight is also equivalent to 1 kilogr., it will be necessary to 

 supply or withdraw much more heat to raise or lower the 

 temperature 1° in the series of n spheres than in the single 

 sphere ; and the difference will be by so much the greater as 

 the globules shall be more numerous and consequently more 



* " Ueber die specifische Warme fester Korper, insbesondere der Me- 

 talle," Pog-g. Anti. vol. xx. p. 177. 



t '' Siir la dilatation, la cbaleur specifique des alliages fiisibles," &c., 

 Bull, de VAcad, Roy. de Belgiqiie, t. xxxix. p. 548. 



