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 linkage 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 the 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 multiple crossovers, which 
have been omitted from the calculation of the 
longer distances. When these corrections are made 
the curved line of course resolves itself into a straight 
line. Castle has now withdrawn his hypothesis of 
three dimensional arrangement. 
