Abstract
1. The Problem .—When we have a set of quantities u 1 , u 2 , ... u m , which may be regarded as the observed values of certain unknown quantities U 1 , U 2 , ... U m , and we form the hypothesis that these U’s can be represented by a formula which either is completely determined by a priori considerations or involves constants which have to be determined from the data, how are we to decide whether the hypothesis is justified ? The classic method of testing a hypothesis of this kind is Prof. Karl Pearson’s "χ 2 " method, published in 1900 (ref. 6). But in one important class of cases the accuracy of his formula is open to doubt. The problem has not yet been finally solved: the object of the present paper is to take a step towards its solution.