i8 THE GROWTH OF GROUPS 



a character is obtrusive is not in itself a proof that it 

 arose by accumulation. 



Consider, for example, a structure such as a horn, a 

 foot in length, growing out from the head of a mammalian 

 animal. In terms of the definition it appears as a cha- 

 racter because we know that it may be lost at a step, it 

 may be absent without affecting the rest of the body. 

 But there are several possibilities as to its origin. It 

 may have arisen as a whole at one step, although we should 

 be astonished at the occurrence if we had witnessed it. 

 There is a second possibility. The race with horns a 

 foot in length may have arisen at a step from a race with 

 horns six inches in length. The sudden origin of a 

 breed of cattle called Franquieros, having very large 

 horns, from a race with smaller horns, is mentioned by 

 some writers. It is therefore possible for the final con- 

 dition to be reached by the accumulation of two incre- 

 ments, each a large fraction, a half of the whole, if we 

 may speak of the final state as a whole. And there are 

 of course further possibilities. The final state may have 

 been reached by the accumulation of smaller fractions, 

 i.e. by more numerous and shorter steps. But between 

 each step the various races must have been in a state of 

 stability, unless the animal kingdom of the past was 

 different from that of to-day, when every individual 

 is assignable to its group. 



The several characters which no doubt took part in 

 the building of the horn had, it seems to me, a quantitative 

 relation to one another. We see quantitative characters 

 affecting the total size of the organism or the size of a 

 part in proportion to the whole. 



5. Characters, more especially obtrusive ones, are used 



