120 PHYSICAL BASIS OF HEKEDITY 



ence of & to c and c to d. Four points arranged in a 

 straight line still fulfill the relations here found. I know ■ 

 of no other geometric configuration that covers all these 

 results — perhaps there is none. When we add more 

 and more linked genes to the series, and find the same 

 predictable relations continue to hold, the theory of 

 the linear arrangement becomes firmly established'. Per- 

 haps the best proof of the linear order is found in the 

 opportunity it gives for prediction; for, when the rela- 

 tion of d to b and to a is known its relation to a can be 

 foretold accurately. 



It has been found when there is a large amount of cross- 

 ing over between two factors used in an experiment, that 

 the crossover value is not the same as the value deter- 

 mined by adding together the crossover values of inter- 

 mediate points between the two factors in question. What 

 appears here to be a contradiction proves, when under- 

 stood, to be one of the best pieces of evidence in support 

 of the theory of the linear order. 



A few examples will serve to illustrate the point at 

 issue. When a fly with yellow wings and bar eyes is mated 

 to a wild-type fly, the amount of crossing over in the Fj 

 female between yellow and bar (as determined by back- 

 crossing) is 43.6 per cent., but if the crossing over between 

 yellow and bar is calculated by adding up the crossover 

 values obtained by using intermediate points {ab + be, 

 etc.) the value is about 57 per cent. The apparent incon- 

 sistency is at once cleared up by arranging the experiment 

 so that, while obtaining the data for yellow and bar, 

 there are also obtained data showing what is happening in 

 theregion between them. It is found that a large amountof 

 double crossing over occurs, and, when the correction for 

 this is made, the "discrepancy" disappears. If crossing 

 over may take place at any level, it is obvious that it might 

 occur at two points at the same time, and experience 



