XVII] THE COMPARISON OF RELATED FORMS 1033 



it is possible to inscribe in a net of rectangular coordinates the 

 outline, for instance, of a fish, and so to translate it into a table of 

 numbers, from which again we may at pleasure reconstruct the 

 curve. 



But it is the next step in the employment of coordinates which 

 is of special interest and use to the morpnologist ; and this step 

 consists in the alteration, or deformation, of our system of coordinates, 

 and in the study of the corresponding transformation of the curve 

 or figure inscribed in the coordinate network. 



Let us inscribe in a system of Cartesian coordinates the outUne 

 of an organism, however complicated, or a part thereof: such as 

 a fish, a crab, or a mammalian skull. We may now treat this 

 complicated figure, in general terms, as a function of x, y. If we 

 submit our rectangular system to deformation on simple and 

 recognised lines, altering, for instance, the direction of the axes, 

 the ratio of xjy, or substituting for x and y some more complicated 

 expressions, then we obtain a new system of coordinates, whose 

 deformation from the original type the inscribed figure will precisely 

 follow/ In other words, we obtain a new figure which represents 

 the old figure under a more or less homogeneous strain, and is 

 a function of the new coordinates in precisely the same way as the 

 old figure was of the original coordinates x and y. 



The problem is closely akin to that of the cartographer who 

 transfers identical data to one projection or another*; and whose 

 object is to secure (if it be possible) a complete Correspondence, 

 in each small unit of area, between the one representation and the 

 other. The morphologist will not seek to draw his organic forms 

 in a new and artificial projection; but, in the converse aspect of 

 the problem, he will enquire whether two different but more or less 

 obviously related forms can be so analysed and interpreted that 

 each may be shewn to be a transformed representation of the other. 

 This once demonstrated, it will be a comparatively easy task (in all 

 probability) to postulate the direction and magnitude of the force 

 capable of effecting the required transformation. Again, if such 

 a simple alteration of the system of forces can be proved adequate 

 to meet the case, we may find ourselves able to dispense with many 



* Cf. (e.g.) Tissot, Memoire sur la representation des surfaces, et les projections 

 des cartes geographiques, Paris, 1881. 



