404 



wliicli For smaller vahies of x (f/) passes into 



p?,=: ;?/(! + 7,(1 -/?/')^/'), 



SO that we get: 



li, -^,' = V, 3^0 (1-/?/^) rp = V, ^/ (1_/?/*)^ i±??. 



Now for small values of i' we may put /?, = 1 and /:?,=/?/, so 

 tliat finally becomes in approximation: 



(.r small) |i,-^/ = -^i?/ (1 -/?/), (9) 



1 — .r 



and ^/?/(l— lij") may be written for ^ZiOij — /i/) = (1 — .f) f^,— ^Z). 



8. Reduction of the formula for in in normal components. 



When we want to test the formulae derived above by some expe- 

 rimental data, we can only dó so with mixtures of normal compo- 

 nents. With regard to anomalous components (water, alcohol, acids, 

 etc.) we lack the knowledge of the quantities q and A. On the 

 contrary we calculated them approximately at the time (loc. cit.) 

 from the experimental results, e.g. froni the volume-contraction of 

 water-alcohol mixtures. We must, therefore, confine ourselves, to 

 formulae (1) and (3), and when we apply these also to abnormal 

 components, we shall be able to find something regarding the probable 

 values of q and A from the deviations between the calculated values 

 and those found experimentally. 



For Lv we found (cf. besides (3), also (3") and (3&)): 



V,m u/^/a,(l-TU 1 ï^iVa, ) 



1— VyW a^a^ { 2 v^ ) 



when 



v/ i/«i ^/fc, ycik^ 



I/- 



1/ PJc 



is written. Therefore, according to (1), with omission of ^;, w becomes: 



a Vj m u/ l/a, (1— t) 





fn V. V. 



(1-r)^ + 



vv^\ — ^l^m a^o^ 



or also 



a, u, 



1 a Ü,' 



(l-T)' + -(l-r)-^ 



a, V 



i~y 



1/ 



-(^-r) 



)} 



