INTENSIVE SBGEEGATION. 313 



succeed in propagating in eaeli district, the probability of com- 

 plete correspondence in integration will be as 1 to the factorial 



ot 2, or as ^^^ = 2 ' 



if the same 3 varieties, the probability = j^ .^ » = ^ ; 



4, the probability = ,^2x3x4 = k 5 



5 - 1 - 1 ■ 



" 1x2x3x4x5 ~ 120' 



1_ 



" ~720' 



^ 1 

 " 5,040' 



_ 1 

 " ~ 40,320 ' 



1 



362,880 ■ 

 1 



" 3,628,800' 



These fractious represent the probability of complete corre- 

 spondence as to the varieties that intercross and those that remain 

 segregated in the different districts when the same varieties occur 

 in each district ; and the squares of these fractious represent the 

 probability that any special combination that may be indicated 

 will occur in both districts at the same time. If there are, for 

 example, the same ten varieties in each district, the probability 



that they will combine in the same way is o 628 800 ' ^^^ ^^® pro- 

 bability that this way will be the breeding of each variety with 

 its own kind, without any intercrossing, will be (ykossoo) " ^^^ 

 there may be degrees of correspondence in the combinations of 

 different districts. As we have just seen, the probability that 



there will be correspondence in ten points is ., „^ „^ . , that there 



45 ' . ' . 



will be in eight points is o (-90 qqa i that there will be in but one 



point is o'c 28800 ' '^^^^^^ ^^^^ probability that there will be no cor- 



, . 1,334,961 ^ 



respondenceis-3-g^g-^*. 



We have thus far considered only the divergences that come 



* The denominator of these fractions is the factorial of ten, that is 1x2x3 

 X4x5x6x7x8x9x 10, and the numerators are found in the tenth Hue of 

 the Permutational Triangle. See Appendix. 



LINN. JOTJEN. — ZOOLOGY, TOL. XXIII. 23 



