446 - : LAWS OF MULTIPLICATION. 



under the common title of Chordata, are included in the same 

 phylum with the Vertebrata, then it may firstly be replied 

 that those types which have no vertebra cannot properly be 

 called Vertebrata, and secondly that if, as being Chordata, 

 they must be recognized, then the exception which they pre- 

 sent further illustrates the truth that agamogenetic multi- 

 plication occurs only in creatures small in size, or low in 

 structure, or both. 



337. Such are a few leading facts serving to show how 

 deduction is inductively verified, in so far as the antagonism 

 between Growth and Asexual Genesis is concerned. In 

 whatever way we explain this opposition of the integrative 

 and disintegrative processes, the facts and their implications 

 remain the same. Indeed we need not commit ourselves to 

 any hypothesis respecting the physical causation. It suffices 

 to recognize the results under their most general aspects. 

 "We cannot help admitting there are at work these two anta- 

 gonist tendencies to aggregation and separation; and we 

 cannot help admitting that the proportion between the aggre- 

 gative and separative tendencies, must in each case determine 

 the relation between increase in bulk of the individual and 

 increase of the race in number. 



The antithesis is as manifest a posteriori as it is necessary 

 d priori. While the minutest organisms multiply asexually 

 in their billions; while the Infusoria thus multiply in their 

 millions; while the small compound types next above them 

 thus multiply in their thousands; while larger and more 

 compound types thus multiply in their hundreds and their 

 tens; the largest types do not thus multiply at all. Con- 

 versely, those which do not multiply asexually at all, are a 

 billion or a million times the size of those which thus mul- 

 tiply with greatest rapidity; and are a thousand times, or a 

 hundred times, or ten times the size of those which thus 

 multiply with less and less rapidity. Without saying that 

 this inverse proportion is regular, which, as we shall here- 



