SECT, viii.] INTRODUCTION. 37 



that though no two individuals are identical, there are many which 

 in the aggregate of their characters nearly approach each other, 

 constituting thus a normal, from which comparatively few differ 

 widely. In such a species the magnitude of these differences is 

 proportional to the rarity of their occurrence. Now this, which is 

 a matter of common experience, has been shewn by Galton to be 

 actually true of several quantities which in the case of Man are 

 capable of arithmetical estimation. In the cases referred to it has 

 thus been established that these quantities when marshalled in 

 order give rise to a curve which is a normal curve of Frequency of 

 Error. Taking for instance the case of stature, Galton's statistics 

 shew that for a given community there is a mean stature, and the 

 distribution of the statures of that community around the mean 

 gives rise to a Curve of Error. In this case the individuals of that 

 community in respect of stature form one group. Now in the case 

 of a collection of individuals which can be separated into two 

 species, there is some character in respect of which, when arranged 

 by their statistical method, the individuals do not make one group 

 but two groups, and the distribution of each group in respect of 

 that character cannot be arranged in one Curve of Error, though 

 it may give rise to two such curves, each having its respective 

 mean. For example, if in a community tall individuals were 

 common and short individuals were common, but persons of medium 

 height were rare, the measurements of the Stature of such a 

 community when arranged in the graphic method would not form 

 one Curve of Error, though they might and probably would form 

 two. There would thus be a normal for the tall breed, and a 

 normal for the short breed. Such a community would, in respect 

 of Stature, be what is called dimorphic. The other case, in which 

 the whole community, grouped according to the degrees in which 

 they display a given character, forms one Curve of Error, may 

 conveniently be called monomorphic in respect of that character. 

 By considering the possible ways in which such a condition of 

 dimorphism may arise in a monomorphic community, one of the 

 uses of the term Discontinuity as applied to Variation will be 

 made clear. 



Considering therefore some one character alone, in a species 

 which is monomorphic in respect to that character, individuals 

 possessing it in its mean form are common while the extremes 

 are rare ; while if the species is dimorphic the extremes are 

 common and the mean is rare. Now the change from the mono- 

 morphic condition to the dimorphic may have been effected with 

 various degrees of rapidity : for the frequency of the occurrence of 

 the mean form may have gradually diminished, while that of the 

 extremes gradually increased, through the agency of Natural 

 Selection or otherwise, in a long series of generations ; or on the 

 other hand the diminution in the relative numbers of the mean 

 individuals may have been rapid and have been brought about in 



