(31), and finally that for A from (32), and combinations 

 could be made having regard to the weights. 



Assuming that the sets of ordinates have been appro- 

 priately chosen so as to give each determination of p 

 approximately equal weight, we may however, iu practical 

 computations proceed as follows : — 



From (28) and (28a) we obtain 



u = log JjiSj |/{*P(Q*-l)(qP-l)} (54) 



in which the values taken for q v and p are those given by 

 equation (51) furnishing a geometric mean value. But if 

 there were r sets of values for the ordinates, we shall have 

 r sets of equations like this last (54). Hence we have 



n r m n; (log ;/i + iog //, - log //, - log //,) ( 55 ^ 



H[ {&(tf» -1)(QP -1)} 

 IIJ denoting as before the product of the r different values. 

 In this equation, if ?/, be the same for each set, q alone 

 being varied, we shall have .« r "H[f(q) as the value for the 

 denominator in this last expression ; or if as, be varied, and 

 Q be kept constant, we shall have for the value of this 

 denominator f(q)IIJ(as) p . 



When n has been found, there are three equations to 

 determine m— see (26a) and (26b)— the third being for Y«. 

 They are not however independent. If we give double 

 weight to the results dependent on »/. and ij, equation (26b) 

 —the validity of assigning a higher weight is in most cases 

 self evident— then we obtain 



Log 9 •''• = I m log q r Mn& ^ - 1) (Q p + l) a ...(56) 

 which gives 



m= log !(,,,,,.) ( !h{h ): - M,i.V(qr - 1) *q> +IT ...(57) 



