598 RICE ART. L 



Also Sj'Des consists of as many terms as there are surfaces, and 

 similar remarks apply to Sj'gzDm^. It will be quite sufficient 

 to limit the system to one with two homogeneous masses and one 

 surface of discontinuity. 



The transformation from the equation [599] to [600] is one 

 which calls for careful scrutiny on the part of the reader. The 

 difficulties are hinted at in the beginning of the paragraph 

 succeeding equation [600], but perhaps the fact that they are 

 fully met in the transformation may not be so "evident" to 

 every reader as it was to Gibbs. Take for instance one inclu- 

 sive term such as Sj'De^ in [599]. (We omit accents and 

 consider it as referring for the moment to either homogeneous 

 mass.) We know that 



De^ = tDr]^ - pDv + fiiDmi^ + mDmz^ 



and so Sj'Di^ should apparently be equal to 



SftDriy - 8fpDv + SfniDmiy + 8fnJ)miy. 



But if we carry the sign of variation, 5, within the sign of 

 integration, we ought in strict mathematical procedure to write 

 Sj^tDrjy as J'ditD'qy), bfpDv as J'8(pDv) and so on. Instead 

 they are written J'tdDn], J'pSDv, etc. Later, near the top of 

 page 280, XpbDv is transformed back into J'dipDv) —J'SpDv, 

 and to the unwary this might seem to a veritable "trick" 

 in order to get the first two terms of equation [611] and 

 thereafter the equation [612]. The matter seems still more 

 mystifying when we consider an inclusive term in [599] such as 

 Sj^gzDmy] for it is written J'SigzDmy) and expanded to 

 J'gzSDmy + SgSzDmy, and not merely left as equivalent to 

 the first integral of that sum. However, the solution is not 

 obscure when pointed out. Looking back to [15] and [497] we 

 recall that the conditions of equilibrium without gravity are not 



8{t7]) - 8{pv) + Simmi) + Sifjuiui) = 

 but 



t8r} — p8v + fii8mi + iJizSnii = 0. 



