VARIATION AND HEREDITY 29 



measured by de Vries. The lengths are measured 

 horizontally, and the numbers of individuals showing 

 particular lengths of fruit are plotted vertically. 



The species A and C have a characteristic mean size 

 of fruit, and their corresponding curves closely resemble 

 the theoretical curve given above. On the other hand, 

 the third species, represented by the curve B, shows 

 sign of subdivision into two separate groups at least. 

 Had the seeds of all three varieties been classed 

 together, the three curves would have coalesced into 

 one, which would have approached in form the normal 

 curve of simple variation. 



This result not only shows the agreement with the 

 normal type of curve, given by measurement of the 

 individuals of a homogeneous species such as A or C, 

 but also illustrates one of the dangers which accom- 

 pany the use of statistical methods in biological 

 problems. It is often impossible to tell from the 

 data whether a single group or a number of groups 

 are involved. Caution is necessary in the application 

 of a method which is liable to such a fundamental 

 uncertainty. But the need for care does not destrov 

 the usefulness of the theory of variation. Where the 

 individuals concerned are known to be of homogene- 

 ous type, the normal curve will express the variations 

 from the type, and where many different types are 

 present the normal curve will still be found to represent 

 the result, though for somewhat different reasons. 



Where we are dealing with the small, continuous 

 variations, shown by the different individuals of a homo- 

 geneous species, the normal curve will express their 

 distribution. Where discontinuous variations or sports 



