This is the complete solution from four ordinates y being 



In selecting the four abscissae to obtain a solution of the 

 constant, it is often necessary to locate two of them and 

 determine the positions of the others therefrom. To do 

 this q must be found from one of the following expressions 



q = !K«v/«k) = «*JxJ- ,>(x :i lx l ) = x 4 /x :i = x 3 /x 2 = x i /x 1 (33) 



Although for any four points, conditioned as indicated, the 

 solution is unique, in general it is not sufficient to depend 

 upon a single solution, however well the set of coordinates 

 is selected. We may therefore take two or more sets (con- 

 forming to the condition of a constant ratio between the 

 abscissae) and proceed as follows : — 

 For brevity writing equation (29a) in the form 



q v =Q (29b) 



we shall have 



p = logQ/logq (34) 



It may be noted that the quantity Q is unaffected by chang- 

 ing the values of y in any constant ratio, for if y become ky 

 the value of both numerator and denominator in (29a) 

 remains unaltered. Calling the successive sets, each of 

 which furnishes a complete solution, a, b, c, d, etc., the 

 number of equations will be equal to the number of sets 

 taken. These however will not in general be of equal 

 weight. 



The algorithm of computations with more than four 

 ordinates will be referred to later, § 9. 



8. Weight of results.-The complete solution of the 

 weight of any result is as follows:— 



We have from the theory of probability the weight, u\ 

 of any quantity is proportional to the reciprocal of the 



