XVII] THE COMPARISON OF RELATED FORMS 1093 



to begin with, and within my own recollection it was confidently 

 believed, that the broad lines of descent, the relation of the main 

 branches to one another and to the trunk of the tree, would soon 

 be settled, and the lesser ramifications would bp unravelled bit 

 by bit and later on. But things have turned out otherwise. We 

 have long known, in more or less satisfactory detail, the pedigree of 

 horses, elephants, turtles, crocodiles and some few more; and our 

 conclusions tally as to these, again more or less to our satisfaction, 

 with the direct evidence of palaeontological succession. But the 

 larger and at first sight simpler questions remain unanswered; for 

 eighty years' study of Darwinian evolution has not taught us how 

 birds descend from reptiles, mammals from earlier quadrupeds, 

 quadrupeds from fishes, nor vertebrates from the invertebrate stock. 

 The invertebrates themselves involve the selfsame difficulties, so 

 that we do not know the origin of the echinoderms, of the molluscs, 

 of the coelenterates, nor of one group of protozoa from another. 

 The difficulty is not always quite the same. We may fail to find 

 the actual links between the vertebrate groups, but yet their re- 

 semblance and their relationship, real though indefinable, are plain 

 to see; there are gaps between the groups, but we can see, so to 

 speak, across the gap. On the other hand, the breach between 

 vertebrate and invertebrate, worm and coelenterate, coelenterate 

 and protozoon, is in each case of another order, and is so wide that 

 we cannot see across the intervening gap at all. 



This failure to solve the cardinal problem of evolutionary biology 

 is a very curious thing; and we may well wonder why the long 

 pedigree is subject to such breaches of continuity. We used to be 

 told, and were content to believe, that the old record was of necessity 

 imperfect — we could not expect it to be otherwise; the story was 

 hard to read because every here and there a page had been lost or 

 torn away, like some hiatus valde deflendus in an ancient manuscript. 

 But there is a deeper reason. When we begin to draw comparisons 

 between our algebraic curves and attempt to transform one into 

 another, we find ourselves limited by the very nature of the case 

 to curves having some tangible degree of relation to oner another; 

 and these "degrees of relationship" imply a classification of mathe- 

 matical forms, analogous to the classification of plants or animals 

 in another part of the Systema Naturae. 



