118 Prof. W. E. Story on Partial 



putting 



««>-««= e «<?>-«r=c, (08) 



o 14 



+ uVl4 + 



}*="(£> 



(59-) 



*? + %-i + 2c 02'2 + ^2i4+ ¥n+ ?>4+^i+ 3*22^2 



+ ^^+^ 04 4=ln(j-g); (61'>) 



C = ln (lT I - „7 c n- g(^o+Cu)-54(^i+Ci8), 



Ws/ * [. . . (60") 



v 3 / J 



c = , 2 In (B l P ll )+ i (^ -.« I1 +fl bt )+ T8 (^o-% + ^2- c i3+^ i ( H3 ") 



Equations (59) and (61) are here combined into one set 

 with the double number (59") (61''). Each observation 

 furnishes a pair of such equations. Together they involve 

 14 constants to be determined, namely, 



^0 > C 20' C 30> C 40> ^0 » C 02> C 03' C 04> C 1V C 2V C 12' C 3V C 22) C 13> 



and seven observations will, therefore, suffice to determine 

 these constants. But it is better to use a much larger 

 number of observations and to solve these equations by 

 the method of least squares, This solution is effected as 

 follows. 



For any given values of g 1 and g 2 P u ^ 



: 4 ~? = [ft*], ^ *f :?ln (fj) = [g^ v 2 4-^ln (&fj = [^J f . 



obs. \P3' l l/ obs. \pz&2' 



where 2 denotes the sum of the expression that follows 



obe. 



