1056 THE THEORY OF TRANSFORMATIONS [ch. 



ratio. If, instead of seeking for an actual equation, we simply 

 tabulate our values of x and y in the second figure as compared with 

 the first (just as we did in comparing the feet of the Ungulates), 

 we get the dimensions of a net in which, by simply projecting the 

 figure of Oithona, we obtain that of Sapphirina without further 

 trouble, e.g.: 



In this manner, with a single model or type to copy from, we 

 may record in very brief space the data requisite for the production 

 of approximate outlines of a great number of forms. For instance, 

 the difference, at first sight immense, between the attenuated body 

 of a Caprella and the thick-set body of a Cyamus is obviously httle, 

 and is probably nothing more than a difference of relative mag- 

 nitudes, capable of tabulation by numbers and of complete expression 

 by means of rectihnear coordinates. 



The Crustacea afford innumerable instances of more complex 

 deformations. Thus we may compare various higher Crustacea 

 with one another, even in the case of such dissimilar forms as 

 a lobster and a crab. It is obvious that the whole body of the 

 former is elongated as compared with the latter, and that the crab 

 is relatively broad in the region of the carapace, while it tapers off 

 rapidly towards its attenuated and abbreviated tail. In a general 

 way, the elongated rectangular system of coordinates in which we 

 may inscribe the outhne of the lobster becomes a shortened triangle 

 in the case of the crab. In a little more detail we may compare 

 the outline of the carapace in various crabs one with another : and 

 the comparison will be found easy and significant, even, .in many 

 cases, down to minute details, such as the number and situation 

 of the marginal spines, though these are in other cases subject to 

 independent variabihty. 



If we choose, to begin with, such a crab as Geryon (Fig. 513, 1) 

 and inscribe it in our equidistant rectangular coordinates, we shall 

 see that we pass easily to forms more elongated in a transverse 

 direction, such as Matuta or Lupa (5), and conversely, by transverse 

 compression, to such a form as Corystes (2). In certain other cases 



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