1058 THE THEORY OF TRANSFORMATIONS [ch. 



just the Qonverse of this. While the carapace of these crabs presents 

 a somewhat triangular form, which seems at first sight more or less 

 similar to those just described, we soon see that the actual posterior 

 border is now narrow instead of broad, the broadest part of the 

 carapace corresponding precisely, not to that which is broadest in 

 Paralomis, but to that which was broadest in Geryon; while the 

 most striking difference from the latter Hes in an antero-posterior 

 lengthening of the forepart of the carapace, culminating in a great 

 elongation of Ihe frontal region, with its two spines or "horns." 

 The curved ordinates here converge posteriorly and diverge widely 

 in front (Fig. 513, 3 and 6), while the decremental interspacing of 

 the abscissae is very marked indeed. 



We put our method to a severer test when we attempt to sketch 

 an entire and compHcated animal than when we simply compare 

 corresponding parts such as the carapaces of various Malacostraca, 

 or related bones as in the case of the tapir's toes. Nevertheless, up 

 to a certain point, the method stands the test very well. In other 

 words, one particular mode and direction of variation is often (or 

 even usually) so prominent and so paramount throughout the entire 

 organism, that one comprehensive system of coordinates suffices to 

 give a fair picture of the actual phenomenon. To take another 

 illustration from the Crustacea, I have drawn roughly in Fig. 514, 1 

 a little amphipod of the family Phoxocephalidae (Harpinia sp.). 

 Deforming the coordinates of the figure into the curved orthogonal * 

 system in Fig. 514, 2, we at once obtain a very fair representation of 

 an alhed genus, belonging to a different family of amphipods, namely 

 Stegocephalus. As we proceed further from our type our coordinates 

 will require greater deformation, and the resultant figure will usually 

 be somewhat less accurate. In Fig. 514, 3 I shew a network, to 

 which, if we transfer our diagram of Harpinia or of Stegocephalus, 

 we shall obtain a tolerable representation of the aberrant genus 

 Hyperia'f, with its narrow abdomen, its reduced pleural lappets, its 

 great eyes, and its inflated head. 



* Similar coordinates are treated of by Lame, Lemons sur les coordonnees curvilignes, 

 Paris, 1859. 



t For an analogous, but more detailed comparison, see H. Mogk, Versuch einer 

 Formanalyse bei Hyperiden, Int. Rev. d. ges. Hydrobiol., etc., xiv, pp. 276-311, 

 1923; xvn, pp. 1-98, 1926. 



