134 AMPHIMIXIS OR ESSENTIAL MEANING OF [XII. 



possible combinations might repeat itself. From this point 

 of view, it might therefore be doubted whether the doubling 

 of the idants in the germ-mother-cells, together with the suc- 

 ceeding two ' reducing divisions,' are sufficient to explain the 

 fact that identical children only appear in the form of twins 

 developed from a single ovum. 



It may however be urged that the assumption of only four 

 idants may not hold for the human species, and that in such 

 animals as Ascaris megalocephala bivaleits, which undoubtedly 

 possess only four idants, we cannot appreciate the phenomena 

 of heredity when applied to the minutest individual differences, 

 as we can in the case of man. It is quite conceivable that 

 many fertiHzed ova of this species of Ascaris contain precisely 

 the same kind of germ-plasm, that is the same combination 

 of ids ; we do not however know that this is the case. 

 We are unfortunately ignorant of the number of idants which 

 is typical for man, and can only assert that it is probably 

 higher than four. But the number of possible combinations 

 increases very rapidly with an increase in the number of 

 idants. Certain Mollusca, as Carinaria and Phyllirhoe, possess 

 thirty-two idants, and in Crustacea the number is even higher. 

 Eight idants, without doubling, would render possible seventy 

 combinations, doubled, they would produce 266 : similarly, 

 without and with doubling twelve idants would yield 924 and 

 8074 combinations respectively ; sixteen would yield 12,870 

 and 258,570 ; twenty would yield 184,756 and 8,533,606. With 

 thirty-two idants doubling increases the number of combina- 

 tions about 500 fold ^. 



If we now remember that an equal number of idants from 

 each parent meet together during fertilization, and that each 

 of the parental groups of idants represents only one of the 

 numerous combinations which are possible for the species, 

 it is evident that the number of possible variations of germ- 

 plasm which a single pair is capable of producing must be 

 extremely great, for it is a number obtained by multiplying 

 together the maternal and paternal number of combinations. 

 Thus twelve idants yield 8074 x 8074 variations. Although 

 even this large number of combinations does not exclude the 



^ For these figures I am indebted to the kindness of my mathematical 

 friend, Professor Liiroth of Freiburg im Breisgau. 



