SEGREGATION OF HOMOLOGOUS CHROMOSOMES 455 



sented by the formula 2" in which n represents the number of 

 chromosomes in the reduced series; that is, the number of pairs 

 of homologues. In this instance n = 4 since we are consider- 

 ing only the accessory and the three heteromorphic tetrads. 

 Then 2>, or 16, is the possible number of combinations of these 

 chromosomes in the gametes of this individual. While the 

 number of morphologically different gametes formed as a result 

 of the segregation of any given three is 8 (2=), of any given two 

 is 4 (2^) of a given one 2 (2v). The occurrence of any combi- 

 nation is shown by the coefficients of the expanded binomial 

 raised to the nth power in which case n again represents the num- 

 ber of homologous pairs. In this instance the series of coeffi- 

 cients is 1-4-6-4-1. 



From the two formulae given above we should expect to find 



Any given 4 V's in y$ of the gametes Any 4 V's in j^ of the gametes 



Any given 3 V's in £ of the gametes Any 3 V's in fa of the gametes 



Any given 2 V's in I of the gametes Any 2 V's in fa of the gametes 



Any given IV in £ of the gametes Any 1 V in fa of the gametes 



and V in j^ of the gametes and V in n of the gametes 



The difference — it will be noted — between these two series is 

 in regard to any one, two or three as opposed to a given one, 

 two or three; that is, in the latter case, we must distinguish 

 between the V's with which we are dealing. A given V (as the 

 accessory) would be found in one-half of the gametes, but, on 

 the other hand, one-quarter of the gametes would contain only 

 one V. 



Perhaps both may be better shown graphically. Let A, B, C, 

 D, represent the V-shaped homologues and the accessory and 

 a, b, c, d, the rod-shaped homologues of the tetrads and the 

 absence of any homologue in the case of the accessory. There 

 are then the foregoing sixteen combinations any one of which is 

 equally probable ; all four V's together, e.g., A B C D, one-six- 

 teenth of the time; any three, as in the second division, four- 

 sixteenths of the time; any given three, e.g., A, B, C,« two- 

 sixteenths of the time; any two, as in the third division, six- 

 sixteenths of the time; any given two, four-sixteenths of the 

 time; while any given one occurs eight-sixteenths of the time 

 and only one four-sixteenths of the time. 



