XVII] THE COMPARISON OF RELATED FORMS 1085 



with a rectilinear axis in a man's skull, but what is a straight line 

 in the one has become a certain definite curve in the other. 



Mr Heilmann tells me that he has tried, but without success, 

 to obtain a transitional series between the human skull and some 

 prehuman, anthropoid type, which series (as in the case of the 

 Equidae) should be found to contain other known types in direct 

 linear sequence. It appears impossible, however, to obtain such a 

 series, or to pass by successive and continuous gradations through 

 such forms as Mesopithecus, Pithecanthropus, Homo neanderthalensis, 

 and the lower or higher races of modern man. The failure is not 

 the fault of our method. It merely indicates that no one straight 

 line of descent, or of consecutive transformation, exists; but on 

 the contrary, that among human and anthropoid tjrpes', recent and 

 extinct, we have to do with a complex problem of divergent, rather 

 than of continuous, variation. And in like manner, easy as it is to 

 correlate the baboon's and chimpanzee's skulls severally with that 

 of man, and easy as it is to see that the chimpanzee's skull is much 

 nearer to the human type than is the baboon's, it is also not difficult 

 to perceive that the series is not, strictly speaking, continuous, and 

 that neither of our two apes lies precisely on the same direct line 

 or sequence of deformation by which we may hypothetically connect 

 the other with man. 



After easily transforming our coordinate diagram of the human 

 skull into a corresponding diagram of ape or of baboon, we may 

 effect a further transformation of man or monkey into dog no less 

 easily; and we are thereby encouraged to believe that any two 

 mammalian skulls may be compared with, or transformed into, one 

 another by this method. There is something, an essential and 

 indispensable something, which is common to them all, something 

 which is the subject of all our transformations, and remains invariant 

 (as the mathematicians say) under them all. In these transforma- 

 tions of ours every point may change its place, every line its 

 curvature, every area its magnitude; but on the other hand every 

 point and every hne continues to exist, and keeps its relative order 

 and position throughout all distortions and transformations. A series 

 of points, a, 6, c, along a certain line persist as corresponding points 

 a', h\ c\ however the line connecting them may lengthen or bend; 

 and as with points, so with lines, and so also with areas. Ear, 



