94 



BUTLER 



ART. D 



for all possible variations which do not conflict with the condi- 

 tions imposed or necessitated by the nature of the case. These 

 conditions may be expressed in the following equations, which 

 are termed the equatio7is of co7idition. 



(1) The entropy of the whole system is constant; or 



bri' + h-n" + hri'" + etc. = 0, (65) [16] 



(2) The volume of the whole system is constant; or 



bv' + bv" + bv'" + etc. = 0, (66) [17] 



(3) The total mass of each component is constant; or 



bmi' + bnii" + 5mi'" + etc. = 0, ^ 

 bm2' + bnii" + 5m2'" + etc. = 0, 



bnin' + bnin" + bnin'" + etc. = 0. ^ 



(67) [18] 



Now since all the quantities like brj', bv', bmi, . . . brtin may be 

 either positive or negative, the left-hand side of (64) is only incap- 

 able of having negative values when (65), (66) and (67) are sat- 

 isfied, if 



t' = t" = t'" = etc. 



p' = p" = p'" = etc. 



Ml = Ml = Ml — etc. 



M2' = M2" = M2'" = etc. 



Hn = fin — IJ'Ti — etc. 



(68) [19] 



(69) [20] 



(70) [21] 



For example, consider the terms ixi'bmi + ixi'bmi" + iix"bmi" 

 -f etc. Since 



6mi' + bmi" + bmi'" + etc. = 0, 

 it follows that 



Mi'6wi' + ii,"bnh" + ixx"'bmi"' + etc. = 



(71) 



