No. 595] THE MECHANISM OF CROSSING-OVER 427 



it then proceeds horizontally until a distance from the 

 starting point of the curve equal to the length of the longer 

 section has been passed (above, this was the section 

 c x — v, = 16 ; thus the line proceeded on a level to point 

 8 + 16 = 24 6 ) ; then it falls in a straight line to a point on 

 the abscissa representing the distance between the outer- 

 most factors involved (above, the distance is c t — r, = 36). 

 The height to which the curve rose is determined by the 

 fact that its area (the sum of all the ordinates) must have 

 a value representing the per cent, of total cases in which 

 such a double cross-over occurred (above, each double 

 cross-over must have a curve with an area = .14, since 

 each fly was .14 per cent, of the total count). 



It will be noted that for each individual curve the prob- 

 ability is calculated on a basis of pure chance, no account 

 being taken of possible interference, which, if present, 

 would tend to make the longer distances more likely than 

 the shorter, and so to raise the right end of the curve at 

 the expense of the left. In other words, each bulh-hhml 

 curve represents the frequency with which double cross- 

 overs of different lengths would happen within the partic- 

 ular regions dealt with (in our case above, regions c, — v 

 and s — r), if there were no interference and they had a 

 purely chance distribution, within these regions. The 

 composite curve thus errs rather by showing too little 

 effect of interference than too much. All interference 

 which it does show— that is, all deviation between it and a 

 curve representing an entirely random distribution of 

 double cross-overs— must then be due solely to the way 

 in which the double cross-overs were found to be distrib- 

 uted among the various regions, as no assumption of 

 interference was made in calculating out the curve for 

 each double cross-over. 



The curve representing the proportion of double cross- 

 overs of different lengths which would have been found on 

 an entirely random distribution (no interference) is 



"The discrepancy between this figure (24) and that (26) found by the 

 method of trial used above would disappear if the region c — v had been di- 

 vided infinitely instead of only into eight parts. 



