No. 631] FACTORS OF HEREDITY 



115 



rection of the line joining them. A given distance then 

 no longer represents a given frequency. 



6. It has been shown in the above two sections that a 

 single figure will not represent accurately, by propor- 

 tionate distances, the various linkage frequencies actu- 

 ally found in experiments involving many factors at 

 once. If, on the other hand, it had been attempted to 

 combine into one map the absolute frequencies obtained 

 in a series of different experiments with two factors at a 

 time, as Castle claims to do, the number and extent of 

 discrepancies irreconcilable with any possible geomet- 

 rical figure would have been much greater still. For, 

 since the absolute frequencies found in different exper- 

 iments necessarily have all sorts of irregular relation- 

 ships to each other, it follows that it would be even less 

 possible to show in one solid model separation frequencies 

 which were obtained in this way. One such irrecon- 

 cilable value has already been recognized by Castle- 

 namely, the frequency y B. He is forced to represent 

 this frequency by a curved wire in his model, because it 

 is longer (being 47) than the longest distance possible 

 (41) between these two points in any figure founded on a 

 proportionate representation of the other frequencies. 

 Of course, if distance on the model is to have any mean- 

 ing, it cannot arbitrarily be represented along a straight 

 line in some instances, and along lines having various 

 degrees of curvature in other instances. In this one case, 

 then, Castle is compelled to assume that the wrong value 

 has been obtained, owing to experimental error, even 

 though in all other cases- he has assumed that it is quite 

 legitimate to combine the results of different exper- 

 iments. It would have been strange if, in making a model 

 of this sort representing the separation frequencies ot 

 so manv combinations of factors. Castle had not encoun- 

 tered more of these refractorv cases. He does not men- 

 tion any more, but it is noticeable that several other 

 curved lines appear in his model. Moreover there is a 

 conspicuous absence in the model of the factor lethal 2. 



