98 



THE AMEBIC AN NATURALIST 



[Vol. LIV 



for purposes of argument, to be in the chromosomes) are 

 linear, is that "it is doubtful . . . whether an elaborate 

 organic molecule ever has a simple string-like form." 

 This argument is therefore based upon the unique as- 

 sumption that the whole chromosome (or that part of it 

 containing the genes) consists of one huge molecule. 

 Later, he speaks still more explicitly of this "chromo- 

 some molecule" and says, "the duplex linkage systems 

 of a germ cell at the reduction division must be . . . twin 

 organic molecules, ' ' so that ' 1 a purely mechanical theory 

 [of crossing over] seems inadequate to account for inter- 

 change of equivalent parts between them." The argu- 

 ment may therefore be paraphrased as follows: since (1) 

 the whole group of genes is but a single organic molecule, 

 and since (2) an organic molecule can not be linear, then 

 it must follow that (3) the group of genes is not linear, 

 and that the theory of crossing over is therefore erro- 

 neous. Although the premises of this argument are both 

 entirely gratuitous, it must be admitted that there is no 

 flaw in the reasoning, once the premises are admitted. 



2. The second argument brought forward against the 

 linear arrangement of genes is that, in the linear maps, 

 the distances between widely separated loci are not 

 strictly proportional to the per cents of crossing over 

 actually found, being relatively too large, in comparison 

 with the per cents of crossing over. This he terms a 

 "discrepancy" in the map, which has required the "sub- 

 sidiary hypothesis" of double crossing over, in order to 

 harmonize it with the theory of linear linkage. The 

 answer to this is that it has never been claimed, in the 

 theory of linear linkage, that the per cents of crossing 

 over are actually proportional to the map distances: 

 what has been stated is that the per cents of crossing 

 over are calculable from the map distances— or, to put 

 the matter in more mathematical terms, that the per 

 cents of crossing over are a function of the distances of 

 points from each other along a straight line. As Avill be 

 shown presently, this circumstance alone is sufficient to 



