612 Mr. Bernard Oavanagh on 



form in " dilute solutions " enables us to learn something or. 

 the molecular condition of the solutes, the important first 

 step of all. On the other hand, we have the possibility of 

 using dynamical theory as pointed out above and exemplified 

 in section V. 



In the general case, owing to the complexity of the 

 dynamical problem, one may expect that deductions from 

 dynamical theory will be suggestive aids to empirical methods 

 rather than explicit solutions in themselves. 



III. A Useful Modification and some Examples of 

 Application. 



Though unsuitable for general treatment it is very con- 

 venient in many practical cases to use concentrations referred 

 to one molecular species called the u solvent." When such 

 a " solvent " is present in very large excess we have a 

 " dilute solution " of the kind considered by Planck. 



If n be the number of molecules of this "solvent," one 

 may express the concentrations as 



_ n Y _n s __ n _ ' 



n n n 



It is also a formal convenience to introduce the gas-constant 

 K into the " general terms," writing 



U =2,n s u s -\-Un '2 l u x ' f x (cic 2 ....). . . (22) 



" Unit quantity of the solution " containing one gram- 

 molecule of the solvent. 



6' being unity, the general terms now depend only on 

 c x c 2 ... 



Y being similarly modified it is easily seen that i/r now 

 takes the form 



f=tn e (^ s -U log |0 +JGM$,'/,(«A • • ■). 



or, since c is unity, and using suffix s for solutes, 



^ = 77. o [0 o + Rlog(l + Sc 1 )]+2n^« - R1 °g iqrg^) 



+ RnoS^x/xCciCs • • •) • ( 2 3) 

 Naturally ^- is now formally distinguishable from 



5—^ etc. The general terms in both, however, are some- 

 dni 



w 



hat shorter and more easily obtained. 

 ~dn 



=^-E[log Cs -log(l+2 Cl )-S^'|fj (24) 



