110 Prof. K. Pearson on some Applications of the 



whereas in the paper referred to the corresponding equation is 



where ft is the amplitude of the wave, and /3' a parameter. 



The similarity is seen on writing /3 = XkVl- — ^— , and 

 therefore 



/ \{£- 9 K) _ / c 2 /3 / 3/3 



which will become 



V" 5^ ~ • ~/3 + /3 7 * 



This would require /3 2 + /3/3' + /3 /2 = /^^W to make 

 the results identical. . \ c / 



VIII. On some Applications of the Theory of Chance to 

 Racial Differentiation. From the Work ofW. R. Macdonell, 

 M.A., LL.D., and Cicely D. Fawcett, B.Sc. By Karl 

 Pearson, F.R.S., University College, London f. 



(1) TN a memoir published in 1894 % I have dealt with 

 JL the problem of resolving the frequency of hetero- 

 geneous material into two normal components. The object 

 that I had then in view was that of differentiating races 

 which could not be definitely separated by any special 

 outward characteristics. But the method of course applies 

 to all statistical investigations wherein there is any suspicion 

 that the material has been drawn from two heterogeneous 

 sources. The objections to the process of resolution suggested 

 in my memoir are threefold : — 



(a) The heterogeneous material may consist not of two 

 diverse types, but of three or more §. A development of 

 theory is required here, which shall act for statistics like 

 harmonic analysis in physics ; in particular a mechanical 

 analyser would be a great boon, resolving any given curve 

 into a series of normal curves. My method gives only an 

 approximation to the two chief types, supposing the first 

 two terms of the series to be largely preponderant. 



* Zoc. cit. p. 430, eqn. (20). 

 t Communicated by the Author. 

 % Phil. Trans, vol. 185. pp. 71-110. 

 § Ibid. p. 72. 



