THE CHROMOSOMES 169 



sometime be found to have exchanged places in the 

 pair of chromosomes. Such interchange of genes is 

 due to variations in the strength of the specific 

 forces attracting each back to its place in the 

 original series, and is supposed to occur in a specific 

 proportion of cases, which is different for different 

 pairs of genes. The insufficiency of this hypothesis 

 becomes evident when we remember that whole 

 sections of the linear series are interchanged bodily, 

 a single pair of genes never interchanging alone. 

 There is the further point that after crossing over 

 has taken place the same percentage of interchange 

 is found in the next generation as occurred previ- 

 ously, a condition which is the reverse of that which 

 would result on Goldschmidt's hypothesis. 



Castle's suggestion that the genes are arranged in 

 a three dimensional manner was arrived at by 

 combining Hnkage results obtained in different 

 experiments. It is well known that such results 

 are not strictly comparable. When data from a 

 single experiment involving many loci at once are 

 used, all tlie linkages of the factors are most nearly 

 represented by the distances of points in a curved 

 line lying in a single plane, instead of in three 

 dimensions. Further analysis shows that the curva- 

 ture of this line is due to multii)lc crossovers, which 

 have been omitted from the calculation of the 

 longer distances. When thes(» corrections are made 

 the curved line of course resolves itself into a straight 

 line. Castle has now withdrawn his hypothesis of 

 three dimensional arrangement. 



