Pressures in Liquid Mixtures* 110 



it for all the observations. In particular, if n is the number 

 of observations. 



[00] =», foOJ-S**, [0^]=2^, 



obs. obs. 



COOL-Slnraj), [^-S^nP-f), [<VJ,-2*?In(^) f 



obs. V'3<<V obs. \P3^1/ obs. KpaXi/ 



[00] 2 =2l„(^Y [^01 2 =2^1n(^ 3 \ [0y 2 ].= 2^1n(^n 



obs. \/^V obs. \P3X2/ obs. - V^3^/ 



In addition to [00] =w there are 47 of these sums to be 

 calculated from the observations, namely, 27 sums [^1 <? 2 J f° r 

 all values of g y and <7 2 whose sum does not exceed 6, 10 sums 

 \jj\9%\i ana " 10 sums [^1^2] 2 f° r a ^ values of </, and </ 2 whose 

 sum does exceed 3, — as is indicated in the adjoined table of 

 normal equations. 



Each line of this table corresponds to one of the 14 normal 

 equations ; each of the first 14 columns contains the multipliers 

 of the constant that stands at the top of that column in the 

 14 equations, and the last column (after the sign of equality) 

 contains the right members of the several equations. The 

 first 27 sums mentioned above occur only in the left members, 

 and the 20 other sums only in the right members. The 

 multiplier of any one of the last 6 constants in any one of 

 the last 6 equations is the sum of two terms, as is also the 

 right member of each of the last 6 equations. It will be 

 noticed that the first four constants do not occur in the second 

 four equations, nor the second four constants in the first four 

 equations. The simplest mode of solving these equations is, 

 therefore, to eliminate the first four constants successively 

 from the first four and the last six equations, and then the 

 second four constants successively from the second four 

 equations and the six equations resulting from the previous 

 elimination. When the last six constants have been found 

 from the six resulting equations, their substitution in the 

 equations previously obtained by elimination from the first 

 four and the second four equations will give the first four 

 and the second four constants. The advantage of this order 

 of elimination is that we never have to deal with more than 

 ten equations at once, and that we do not have to introduce 

 any constant into an equation in which it did not previously 

 occur in order to eliminate another constant. 



When the c's have been thus found, the a's are easily cal- 

 culated by (53") and (52"), excepting a$\ a%\ and af, which 

 are found from (41") and (21") by means of the other a'n 



