242 APPENDIX II—INTENSIVE SEGREGATION. 
A method of constructing the permutational triangle from the arithmet- 
ical triangle.—Pascal’s arithmetical triangle, which is the same as the 
table of binomial coefficients, is a series of figures, each line of which 
may be formed by adding the previous line to itself, as shown in the 
table below. Now, if we compare this arithmetical triangle with my 
permutational triangle we find that the first and third diagonal lines 
in each table are composed of the same numbers arranged in the same 
way. The fourth diagonal line of the permutational triangle can be 
obtained by multiplying each number of the arithmetical triangle by 2- 
1 
1 
Ble Wl Nie Kj} 
QW WIM -]— 
wlo Ble 
_— 

In short, by using the numbers here indicated as multipliers, each 
line of the arithmetical triangle may be transformed into the corre- 
sponding line of the permutational triangle. It may further be noted 
that these numbers by which we multiply are the occurrents standing 
in the first column of the permutational triangle; and these are found 
to be the same as the sub-factorials described by Whitworth in 
‘‘Choice and Chance,”’ Chapter IV. 
