XVII] THE COMPARISON OF RELATED FORMS 1087 



separately described and accounted for. We see that the chief 

 essential differences in plan between the dog's skull and the man's 

 lie in the fact that, relatively speaking, the former tapers away in 

 front, a triangular taking the place of a rectangular conformation; 

 secondly, that, coincident with the tapering off, there is a progressive 

 elongation, or pulling out, of the -whole forepart of the skull; and 

 lastly, as a minor difference, that the straight vertical ordinates of 

 the human skull become curved, with their convexity directed for- 

 wards, in the dog. While the net result is that in the dog, just as 

 in the chimpanzee, the brain-pan is smaller and the jaw^s are larger 

 than in man, it is now conspicuously evident that the coordinate 

 network of the ape is by no means intermediate between those which 

 fit the other two. The mode of deformation is on different Hnes; 

 and, while it may be correct to say that the chimpanzee and the 

 baboon are more brute-like, it would be by no means accurate to 

 assert that they are more dog-like, than man. 



In this brief account of coordinate transformations and of their 

 morphological utility I have dealt with plane coordinates only, and 

 have made no mention of the less elementary subject of coordinates 

 in three-dimensional space. In theory there is no difficulty what- 

 soever in such an extension of our method; it is just as easy to refer 

 the form of our fish or of our skull to the rectangular coordinates 

 X, y, z, or to the polar coordinates ^, rj, ^, as it is to refer their plane 

 projections to the two axes to which our investigation has been 

 confined. And that it w^ould be advantageous to do so goes w^ithout 

 saying, for it is the shape of the sohd object, not that of the mere 

 drawing of the object, that we want to understand; and already 

 we have found some of our easy problems in solid geometry leading 

 us (as in the case of the form of the bivalve and even of the univalve 

 shell) quickly in the direction of coordinate analysis and the theory 

 of conformal transformations. But this extended theme I have not 

 attempted to pursue, and it must be left to other times, and to other 

 hands. Nevertheless, let us glance for a moment at the sort of simple 

 cases, the simplest possible cases, with which such an investigation 

 might begin; and we have found our plane coordinate systems so 

 easily and effectively applicable to certain fishes that we may seek 

 among them for our first and tentative introduction to the three- 

 dimensional field. 



