Pressures in Liquid Mixtures. 113 



coefficient c the sum of whose suffixes exceeds a certain 



number. What the limit of the degree of terms considered 

 shall be will depend on the accuracy and number of the 

 observations. The number of observations must be at least 

 sufficient to furnish as many equations (59) (« — 1 for each 

 observation) as there are coefficients of w to be determined 

 plus k— 1 (for the k— 1 constants a^ — a^ } ). It is preferable, 

 however, to use a much larger number of observations and to 

 solve the equations (59) by the method of least squares. 

 The larger the number of observations the more accurate the 

 values of the coefficients calculated from them may be 

 expected to be. In fact, by increasing the number of obser- 

 vations, formulae can be obtained from which the partial 

 pressures for given molar proportions of the components can 

 be calculated much more accurately than they can be observed. 

 But, to effect this increase of accuracy, it will be necessary 

 to carry out the numerical computations to several places 

 more than are given by the observations. 



When the es for 2< G have been determined from (59), 

 the a's for 1^ G can be calculated from (52) and (53), 

 with due regard to (50), and then, by (28) and (41), 

 a o } ( r =l>2, 3, ... , k) can be found from any one observation 

 as 



% = ln \xr)~ 2 « V S 2 V---~K-l( r==1 ' 2 > 3 > "•>*)■ O 2 ) 



Finally, P r (r = l, 2, 3, ... , tc — 1) and P K are found from 



(57) and (58). 



After the values of the as have been calculated, the 

 partial pressures for any composition of the mixture can be 

 easily found from (62) without going back to (28). 



The constant term of co plays no part in the determination, 

 but, if wanted, its value, by (46) and (57), is 



«b=j^ I Jn(PiP,P....P.-0 



k=K.-l q a 



, y "••-■ r v (-1) Hk-1) *. (63) 



Special Method for Binary Mixtures. 



6. For a binary mixture, the alternative method given in 

 the footnote to (35) is preferable to the general method 

 developed above, but we give still another method for this 



Phil Mag. S. 6. Vol. 20. No. 115. July 1910. I 



