405 



when ill approximation m :^ T : Tk='^/^ is put. When 7R7\, is 

 written for ^Vi-," '^^^^ 1 RTjc for 7^., and farther 



in which bk^:b]c^ can be calculated from {7\ : pk^) : {7\.^ : pkX we 

 get finally : 



:= 7 n,n, -R7";i„ — 



(1-r)' + 



IT" 1 1 • 



.(10) 



When equimolecular quantities of the components are used, 

 n^ = 1 — X =: '/, and also n^=: x =z Vj, and we get: 



^"H — jR'l^. 7 



+ 



4 ^V.K'' + ^/)L 



1 V,(^A,+7X) 



(1-^)' + 



(l_r) U\-]/<f) 



1 



-(l-r)(l4-9n) 



as I'o = n^v° -\- n^v,\ and approximately 7\. = Vz (^'iti + ^y- The 

 latter is strictly accurate only when the critical pressures of the 

 two components are equal (see § 5 under b). When by way of 

 abbreviation 





V,(7X4-:ro 



rnA, 



is put, then finally with R = 2, so that iv is expressed in gr. kal. : 



roy,=- ;^7'^^[(l_r)= + 7^;.,(l_r)j(l-l/r^)-V,;.,(l-T)(l+r/)|]. (10-) 



This formula is, of course, asymmetrical on account of J^, only 

 in appearance, in as much as we have placed v^'y'a, in y/i/'^rt, — 

 — r," I ^a, outside the parentheses. If we had done this with v," \/a, 

 1\ would have appeared as fore-factor, but then l^ipki'Pk,) — i 

 would also have been substituted for 1 — V'^ipht-Pki)- We now hence- 

 forth take T always <^ 1, so that that component is chosen as the 

 first, of which the critical pressure is lowest. 



In consequence of the fore-factor Rl\ = 7? "^/r^y ^^ is duly of 

 the dimensions of an energy. Further only ratios of quantities occur 

 in (10'). If, therefore, the components belong to the same family 

 of substances, e.g. to the extensive family of "ordinary" substances 

 (critical temp, between 400° and 600° abs., y = 0,9, /= 7, 

 r = fjt : 6jt = 2,1, etc.), the error committed by putting v,* -. v^" = 

 = bk, : bjc^ and a, . ai = ay^ ■ cik^ i» ^ and <f, is certainly negligible. 



