380 EEV. J. T. GULICK OK INTENSITE SEGREGATION. 



lacking in instincts or qualities that secure the pairing together 

 of those of one kind. 



Tor example, let A, B, C represent three females of three 

 varieties of pigeons, and a, b, c three males of the same varieties, 

 all occupying one aviary. Now supposing they are devoid of 

 Seo-regating instincts, and that they all pair, what are the pro- 

 babilities concerning the pairing of the males with their own 

 kind? These will be clearly shown by arranging the letters 

 representing one of the sexes in one fixed order, placing the letters 

 representing the other sex underneath in every possible permuta- 

 tion of order. If we make six experiments the ABC 

 probability is that in 2 cases none, in 3 cases a h c 



one, and in one case 3, will pair with their own « c b 

 kind. These numbers constitute the four terms cab 

 of the third line. The first, second, .and fourth b a c 

 lines were constructed in the same way, but for b c a 

 the construction of the tenth line in this way I c & a 

 estimated that several years of constant writing would be required. 

 The remaining lines here given were therefore constructed ac- 

 cording to the following rules, which were discovered by studying 

 the first four lines. The discussion of different methods of con- 

 structing the Permutational Triangle, and the interesting pro- 

 perties of the same when constructed, must be deferred ; but I 

 may say here that I believe it will be found an important instru- 

 ment for estimating a large class of probabilities. 



One method of constructing any line of the Permutational 

 Triangle from the ^preceding line. 

 (1) Of any given line, any desired number, except the first, 

 may be obtained by multiplying the preceding number of the 

 preceding line by the factor of the given line and dividing the 

 result by the figure marking the degree of correspondence of the 

 column of the desired number. (2) The first number of any line 

 is one less or one more than the second number of the same line, 

 according as the factor of the line is an odd or an even number. 



