﻿Molecular Thermodynamics . 625 



Comparing this with (57) and the remarks which immediately 

 follow (57), we see that we can easily translate " experi- 

 mental " into " estimated " concentrations and express our 

 experimental data in terms of the latter, so that it is now 

 only necessary to express (56) in terms of these " estimated }> 

 concentrations. 



Now a being really expressible as some series 



« = a + £C + 7 C 2 + SC 3 , .... (6G) 



of which we do not know the coefficients accurately, let this 

 be equivalent to some series 



Z = a + 8C"+y"C" 2 +~S' / C"\ . . . (67) 

 Then 



M =M '-N(« + /3C'' + y'C'' 2 + S''C'' 3 ). • (68) 



But from (65) 



M "=M '-X(« '+'p'C' / + v f C'' 2 + 8V' / *), . (69) 

 so that 



M =M "-N[(Aa) + (A/3)C /, 4-(A 7 ')C" 2 +(A8 / )0" 3 ], (70) 



where 



(A«) = ("o-aoO, (A 7 = ft"-?), etc. . (71) 



And then we have 



C J^ = ^ = ^=1-[(A*)C'> + (A/3)C" 2 



+ (A 7 / )C" 3 +(AS')C //4 ], . (72) 

 which can readily be shown to be equivalent to 



c s "~C"~ M 



Cs 77 = £=^ = l + (A a )C + (A/5)C 2 +(A 7 )C 3 + (ASjC 4 , 



. . . (73) 

 where 



(A 7 ') = [(A 7 ) + (A«)(A/3)] ; 



(AS') = [(Ao)+2(A«)(A 7 ) + (A/3) 2 +(A«) 2 (A^)]. (74) 



On comparing this with (57), it is at once obvious that 

 the result of introducing (c g ", C") the "estimated" concen- 

 trations into (56) can be written down at once from 

 equations (58) to (64) by simply writing c s " , C" in place 

 of c/ and C respectively, and (A«), (A£), (Ay), (AS) in 

 place of Sq, /3, y, and 8 respectively. 



(A/3) being small, and (Aa) very small, it is clear that the 

 new t and t' series will converge with the necessary rapidity. 



Phil. Mag. S. 6. Vol, 44. No. 261. Sept. 1922. 2 S 



