INTERFERENCE 131 



hood of the break, and that this loosens the twisting and 

 prevents another break near by. In regions farther away 

 from the break, the threads would not be so much unrav- 

 elled, so that the greater the distance from the first point 

 of breaking tlie more Avould a second break be likely to 

 occur. That is, interference should grow less at greater 

 distances. But the reappearance of interference at still 

 greater distances seems incompatible with this scheme; 

 thus the actual data favor the first view of crossing over, 

 in which the break occurs during a stage of loose twisting. 

 At any rate, as Weinstein has pointed out, the variation 

 of coincidence with distance must be dependent on other 

 conditions than the mere tension due to the twisting of the 

 chromosomes, and any view which refers the breakage of 

 the threads to the tension of tight twisting must be 

 rejected or supplemented. 



Castle has recently suggested that the difference 

 between the values for a long *^ distance" and summation 

 of short ^^ distances'^ is due to the loci not lying in a 

 straight line but ^ ' out of line. ' ' He suggested that when 

 short steps are taken as the basis for map distance 

 they represent the ^^long way round,'' as, for instance, in 

 passing from one end of a F to the other end, keeping on 

 the line; while when a direct cross is made, giving a 

 shorter ^^ distance," this is a measure of the direct or 

 air-line between the two ends of the F. Such a theory is 

 not in harmony with the following facts. The best data 

 {i.e., data sufficient in amount and free from crossover 

 variations) show that Castle's three dimensional figures 

 reduce to a curved line in a plane. In such a curved line 

 the most distant points are nearer to each other in an ^ ^ air- 

 line" than along the line. Such a graphic representation 

 of the data is possible, but leads to certain inconsistencies. 



If Castle 's procedure is followed it leads to the placing 

 of the same locus in two or more different places on the 

 basis of adequate and comparable data for both positions. 

 The two cases that Castle says furnish the crucial evi- 



