874 



D'ARCY WENTWORTH THOMPSON ON 



diminish rapidly as we pass towards either side, away from the median vertical 

 axis ; and it is probable that they do so according to a definite, but somewhat com- 

 plicated, 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. : — 



x (Oithona) . 

 x (Sapphirina) 



y (Oithona) . 

 y (Sapphirina) 







3 



6 



9 



12 



15 





o 



8 



10 



12 



13 



14 









5 



10 



15 



20 



25 



30 







2 



7 



13 



23 



32 



40 



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 

 little, and is probably nothing, more than a difference of relative magnitudes 

 capable of tabulation by numbers and of complete expression by means of rectilinear 

 co-ordinates. 



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 co- 

 ordinates in which we may inscribe the outline of the lobster becomes a shortened 

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

 line of the carapace in various crabs one with another : and the comparison will he 

 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 variability. 



If we choose, to begin with, such a crab as (jeryon (fig. 18), and inscribe it in 

 our equidistant rectangular co-ordinates, we shall see that we pass easily to forms 

 more elongated in a transverse direction, such as Matuta or Lupa (fig. 19), and 

 conversely, by transverse compression, to such a form as Corystes (fig. 20). In 

 certain other cases the carapace conforms to a triangular diagram, more or les 

 curvilinear, as in fig. 21, which represents the genus Paralomis. Here we can 

 easily see that the posterior border is transversely elongated as compared with that 

 of Geryon, while at the. same time the anterior part is longitudinally extended as 

 compared with the posterior. A system of slightly curved and converging ordinates, 



