116 

 so that 



Prof. W. E. Story on Partial 



•y'^KD^MSM-iFi 4 '' ] 



j 



from which follows, by (33') and (34 ; ), 



V • (65) 



(fiC) 

 (67) 



Then ai 1} and a^' are determined from a single observation by 

 (65), or by (C)^) and (67). Finally, P x and P are deter- 

 mined by (57') and (58'). 



Ternary Mixtures. 



7. For the sake of showing how the general method 

 works out in practice, we give the formula? and equations 

 for the case of a ternary mixture (/c = 3), neglecting terms 

 of o> that are of higher than the fourth degree in the z 9 s. 

 This implies, by (52) and (53), that terms of u u u 2n u z that 

 are of higher degree than the fourth in the z's are also to be 

 neglected. The formula? shall be numbered as in the general 

 method, with two accents attached to each number to distin- 

 guish this particular case. 



ft =«/\ i> 2 =*2«" 2 , a=V; ( 28 ") 



u^lnPj for *,=1, u 2 =lnP 2 for x 2 -\, « 3 -1nP 3 for a>,=l; (23") 



(33") 



h=\~ z v - r 2=|- z 2 ' "V^i+V- • 



(34") 



_( Ml +u 2 )=«»; 



„ : -af + <, 1 + ^ 2 + a^ + <V 2 + *I+ a 3 3 o^ + <^ 



.(3U ~3_L„(*)~4 . 

 04 2 s 



