No. 593] THE MECHANISM OF CROSSING-OVER 285 



not true, and accordingly it had to be concluded that the 

 length of the loop was variable, or that "crossing-over' 

 did not always occur where the strands crossed. 



Another possibility was that crossings-over were <|uite 

 independent of one another, having an entirely random 

 or chance distribution in the chromosome, with reference 

 to each other. This would mean that when crossing over 

 occurred at one point, another crossing-over would be 

 just as likely to occur coincidently at any other given 

 point— whether this be very near or far away — as when 

 no crossing-over took place at the first point. l>ut this 

 latter scheme would not be that expected on the method of 

 crossing-over proposed by Jannsens and followed by 

 Morgan, for in the stages when Jamisons supposed cross- 

 ing-over to occur the chromosomes are rather loosely 

 twisted, so that loops of very small length do not occur 

 as often as longer ones (thus, very near one point of 

 crossing-over the strands seldom cross hack again). I 

 therefore determined the mathematical relations which 

 would exist between crossing-over frequencies, if cross- 

 ings-over had a chance distribution with reference to one 

 another, in order to compare these figures with those 

 obtained by experiment. On the assumption that sepa- 

 ration between A and B has no influence on separation 

 between B and C, if crossing-over occurs between A and 



