Theory of Chance to Racial Differentiation. Ill 



(Jj) The assumption is made that the frequency type is 

 normal. 



My friend Prof. Ed geworth has kindly described the method 

 as a beautiful " conception " *, but 1 fear he has done so solely 

 because on this occasion I dealt with that u normal''' atmosphere 

 in which he lives and moves and has his being. 1 can only 

 recognize the occurrence of the normal curve — the Laplacian 

 ■curve of errors — as a very abnormal phenomenon. It is 

 roughly approximated to in certain distributions ; for this 

 reason, and on account of its beautiful simplicity, we may, 

 perhaps, use it as a first approximation, particularly in theo- 

 retical investigations. That is the only justification for my 

 method, for I cannot recognize any special claim in expe- 

 rience, as apart from the weight of authority, for the use of 

 this normal curve |- 



(c) The process is said to be laborious. 



Prof. Edgeworth writes (R. Stat. Soc. Journ. he. cit.) : — 

 " The method is attended with one disadvantage : it is very 

 laborious." The method certainly involves the solution of a 

 nonic, but when once that equation has been determined its 

 numerical solution is not difficult, especially as in most cases 



* R. Stat. Soc. Journ. vol. Ixii. part i., December 1898. 



t It is through no want of courtesy that I have not replied to the very 

 numerous criticisms of my methods which Prof. Edgeworth has pub- 

 lished during the last six years in the R. Stat. Soc. Journ. and elsewhere. 

 Partly I have been overwhelmed with more urgent work; partly T 

 believe that if one's position is strong — and the solid ground of nature is 

 stronger than any mathematical reasoning — it is as well to let your 

 opponent exhaust his ammunition before replying. In a paper published 

 in the Phil. Mag. for July last, I have to some extent criticised the usual 

 text-book treatment of the curve of errors. Prof. Edgeworth in a 

 humorous letter tells me that while I have been getting my Long Tom 

 into position, he has retreated under a bomb-proof casement. By this I 

 understand him to refer to his "method of translation" (R. Stat. Soc. 

 Journ. vol. lxi. Dec. 1898). In this every member of a group is supposed 

 •to be some function of a member of a hypothetical group which obeys 

 the normal law. In other words, the generalized type of frequency is 

 given by 



z=z e-fftf. 



Since / is perfectly arbitrary, it is clear that Prof. Edgeworth's method 

 covers every type of frequency-curve that can be suggested. My own 

 skew-curves can be looked upon as giving values of / which correspond 

 to close fits. The generality of Prof. Edgeworth's method cannot be 

 denied. We might even venture to put s=F(x), F being unknown ! 

 But I am inclined to look upon this method rather as a complete dis- 

 persal of Prof. Edgeworth's forces, than the erection of a bomb-proof 

 casement. For, after all, is not the problem before us the discovery of a 

 suitable value for F, or, if Prof. Edgeworth likes, for f? Some day I 

 hope to show him that the logical and philosophical arguments in 

 favour of my form of/ are even greater than he supposes. 



