188 THE SECOND-CHROMOSOME GROUP 



was started in each case. A few of these cultures failed, and the total 

 data in the separate experiments are consequently not in equal amounts. 

 The balance is for this reason not perfect, though such partially bal- 

 anced results are far better than an equal amount of data secured from 

 only one of the four possible types of experiment. Additional cultures 

 could have been raised until a balance was reached, and such a practice 

 has been followed in other cases, for example, the vermilion sable 

 forked case reported by Morgan and Bridges (1916). A summary 

 of these complementary crosses appears in table 42, from which the 

 following balanced cross-over values are calculated: black purple 

 6.4, purple vestigial 10.8, and black vestigial 16.3. 



COINCIDENCE. 



Another and very important advantage of these more complex 

 crosses is that the process of double crossing-over can be examined. 

 Thus there were 23 double cross-overs, or 0.46 per cent of the total 

 flies. If the proportion of double cross-overs were determined by 

 chance alone the percentage should have been 6.4 per cent of 10.8 per 

 cent or 0.69 per cent of the total. The observed per cent of coincident 

 cross-overs (0.46) is only 61 per cent of the theoretical per cent (0.69). 

 This percentage, 61, is called the " coincidence" for black purple 

 vestigial. This index can be more conveniently calculated directly 

 from the back-cross numbers as follows (see Weinstein, 1918) : 



No. of doubles X Total flies X 100 23 X 5001 X 100 



Total firsts X Total seconds 322 x 539 



-=61.3 



THE RELATION BETWEEN COINCIDENCE AND MAP-DISTANCE. 



The coincidence of 61 observed in this case is relatively very high. 

 A coincidence under 5 is expected for cases in the first chromosome 

 where similar map-distances are involved. This higher coincidence 

 may mean that for some reason the freedom of crossing-over is much 

 less in this region of the second chromosome than it is in the first 

 chromosome. The 17.5 units of map-distance between black and 

 vestigial may correspond to as great a length of actual chromosome 

 as is involved in cases in the first chromosome where the coincidence 

 is the same, but the map-distances are nearly three times as great. On 

 the other hand, instead of the higher coincidence being due to a lower 

 "coefficient of crossing-over/' it may be due to a relatively short 

 " average internode." The length of chromosome represented by a 

 given map-distance may be the same in the two regions compared, 

 but in the second chromosome the mechanism of double crossing-over 

 may not require so long a section of chromosome between successive 

 cross-overs. If the average length of the internode was shorter 

 because of this closer spacing of doubles, then a greater proportion of 

 doubles would occur in the given region from black to vestigial, and 

 coincidence would be correspondingly higher. However, the interest 



