No. 595] THE MECHANISM OF CROSSING-OVER 



425 



But although these ordinates are, on the average, raised 

 by this amount, each one is not raised equally, for there 

 is less chance that double cross-overs should have the 

 most extreme possible values than medium values. The 

 total addition of .14 units to the curve should hence be dis- 

 tributed among the different possible ordinates according 

 to the relative probabilities that the two points of crossing- 

 over should have been the distance apart represented by 

 these respective ordinates. These various probabilities 

 for the different ordinates, in the case of any specific 

 double cross-over, may be represented in the form of a 

 curve, and the main curve of double cross-over frequency 

 shown in figure 12 is thus really a composite in which these 

 individual curves for each double cross-over have been 

 added together. We may now consider the way in which 

 the individual curves of probability are calculated. 



Let us take the case of the double cross-over that 

 occurred between q l and v and coincidently between s and 

 r. "We have already calculated that the distance between 

 the two points of crossing-over must be somewhere be- 

 tween 8 units and 36 units (see second paragraph above). 

 The curve for this individual double cross-over will there- 

 fore start at 8 on the abscissa and continue to 36. What 

 height shall it have along the ordinates between these 

 points T Let the region c x — v be divided into 8 equal parts 

 — abcdefgh— of two units each, as shown below. 



— ■ — tCOXC'jJ" 8 ^"' ~ 



It will be seen that a double cross-over of 8 to 10 units 

 length (i. e., having 8 to 10 units between its two points of 

 crossing-over) which passes between the factors c, and v, 

 must go between them in the region h, if its other point of 

 crossing-over is to be between s and r. However, any 

 double cross-over of 10 to 12 units length which passes 

 through either g or h will also pass between s and r, and 

 so there is twice as much chance for double cross-overs of 



