114 



5. Généralisation. In the meanwhile it must be évident, 

 how utterly improbable the supposée! efFect of the various 

 causes is. Not only will the several causes certainly not 

 ail hâve the same eflFect, but the influence of any one cause 

 on différent individuals will in gênerai certainly not be to 

 make half of them deviate a determined amount in one 

 sensé and the other half the same amount in the other 

 sensé. On the contrary, what we will look for is to find 

 that the several individuals will dérive the most various 

 advantages of one and the same occasion, so that between 

 the individual who makes the very best use of it and the 

 individual who dérives from it the smallest advantage, we 

 will hâve individuals for whom the avantage has any of 

 the infinité number of intermediate values. 



Bessel has shown (Astr. Nachr. vol. 15, pp. 369 — 405) 

 that, whatever be the efFect of the various causes of 

 déviation, as long as they are: 



a. very numerous; 



b. independent of each other; 



c. such that the eff^ect of any one cause is small as 

 compared to the efFect of ail the causes together, 



we will still obtain a curve which approximates the nearer 

 to the normal curve the greater n is. 



6. Dissymmetrical Point-Binomials. Bessel considers 

 only causes, the efFect of which is to give equal frequency 

 to déviations of equal amount in the positive and négative 

 direction (l.c. p. 378). 



If now, with Quételet and Pearson we take into 

 considération causes which give a "tendency to déviation 

 on one side of the mean unequal to the tendency to 

 déviation on the other side" and if, as in the preceding 

 case, we admit in the first place only causes, which, taken 

 singly, produce no other déviations than those of i" A or 

 — A; if further we assume that the frequency of the 

 déviation + A stands to the frequency of the déviation 



