20 



VARIATION 



but will never reach it, because definite number is discontinuous. 

 This is why we can never accurately measure continuity except 

 by a line, and this is why we cannot express in numbers the 

 growth of an animal or plant, except approximately in terms of 

 discontinuity. 



All chemical compounds are made up of elements in definite 

 proportion. They are therefore discontinuous. We have H 2 O 

 and H 2 O 2 , but no intermediate is possible, this again for numer- 

 ical reasons. Plants and animals generally are dimorphic, the one 

 form being male, the other female : this is discontinuity. Some 

 species are trimorphic or even polymorphic. The ant is either 

 male, female, worker, or soldier, and though they all belong to 

 the same species there are no connecting 

 links in this discontinuous chain. 



Dimorphism without respect to sex oc- 

 curs in many beetles, and is exceedingly 

 marked in the common earwig, 1 as shown 

 in the accompanying diagram. 



The shape of this curve shows clearly 

 that here are two distinct forms of male, 

 a large and a small one, living together 

 and arising naturally out of the common 

 mass, yet showing almost no intermediates, 

 nounced, but there are Students of breeding familiar with the 

 almost no intermediates, older types of Hereford will recall that the 

 breed was almost dimorphic in that two dis- 

 tinct types tended to appear with singular perverseness, refusing 

 either to blend or to undergo modification. There was the old, 

 large, solid-bodied, thick-meated, deep-ribbed type, ideal except 

 as to lateness of maturity ; then there was also the pony-built 

 tv P e short in the barrel and lacking in depth behind, though 

 well proportioned in front. 



The shorthorns are almost polymorphic in possessing not one 

 but a variety of types, each standing out with extreme distinct- 

 ness and not readily merged. 



The more the matter is examined the more it will be seen that 

 strange and unaccountable gaps are found everywhere. Many a 



1 Bateson, Materials for the Study of Variation, pp. 36-42. 



FIG. i. Dimorphism illus- 

 trated : two types of the 

 common earwig. B is 



