224 HEREDITARY TRANSMISSION [CH. 



characters A and B is mated with one bearing a and b, the 

 majority of the gametes of the offspring also transmit A 

 and B or a and b, yet absolute coupling is very rarely, if 

 ever, found. Nearly always some gametes bearing A and b 

 or a and B are also produced, the relative frequency of these 

 exceptional combinations varying greatly in different pairs. 

 The American investigators call these exceptional combina- 

 tions cross-overs, since in the combinations Ab and aB, A and 

 a are regarded as having crossed over from their normal com- 

 binations and to have exchanged places. In respect of any 

 pair of characters, the number of cross-overs is on the average 

 fairly constant, ranging from less than I per cent, in some 

 pairs of characters to as much as 40 per cent, in others. 

 If there were 50 per cent, of cross-overs there would of course 

 be no coupling, and the characters would be transmitted 

 independently of each other. The relative number of cross- 

 overs is thus a measure of the intensity of the coupling, 

 a high intensity being synonymous with a low ratio of cross- 

 overs. It is further found that when there are in a coupled 

 group several characters A, B, C, D. . ., they can be arranged 

 in a series in such a way that the ratio of cross-overs between 

 the extremes is approximately equal to the sum of the ratios 

 between the characters placed next to each other; for 

 example, if there is I per cent, of crossing over between A 

 and B, 30 per cent, between B and C, and 3 per cent, between 

 C and Z), then there will be about 31 per cent, between A 

 and C, 33 per cent, between B and Z), and 34 per cent, 

 between A and D. These numbers are only approximately 

 realised in practice, but are sufficiently close to enable at least 

 a rough forecast to be made of the intensity of coupling 

 between two characters, if the intensity of their coupling 

 with a third character is already known 1 . 



1 In a case described by STURTEVANT (Journ. Exp. Zool. xiv. p. 48) on 



