XVII] THE COMPARISON OF RELATED FORMS 777 



recondite methods of comparison and analysis, leading doubtless to 

 very much more complicated results. In this last case, of Diodon 

 and the sunfish, we have seen that the vertical expansion of the 

 latter as compared with the former fish, increases rapidly as we 

 go backwards towards the tail ; but we can by no means say that 

 the lateral compression increases in like proportion. If anything, 

 it would seem that the said expansion and compression tend to 

 vary inversely ; for the Diodon is very thick in front and greatly 

 thinned away behind, while the flattened sunfish is more nearly 

 of the same thickness all the way along. Interesting as the whole 

 subject is we must meanwhile leave it alone ; recognising, however, 

 that if the difficulties of description and representation could be 

 overcome, it is by means of such co-ordinates in space that we 

 should at last obtain an adequate and satisfying picture of the 

 processes of deformation and of the directions of growth*. 



* There is a paper on the mathematical study of organic forms and organic 

 processes by the learned and celebrated Gustav Theodor Fechner, which I have 

 only lately read, but which would have been of no little use and help to our 

 argument had I known it before. (Ueber die mathematische Behandlung organ- 

 ischer Gestalten und Processe, Berichte d. k. sdchs. GeseUsch., Math.-phys. CI., 

 Leipzig, 1849, pp. 50-64.) Fechner's treatment is more purely mathematical 

 and less physical in its scope and bearing than ours, and his paper is but a short 

 one; but the conclusions to which he is led differ little from our own. Let me 

 quote a single sentence which, together with its context, runs precisely on the 

 lines of the discussion with which this chapter of ours began. " So ist also die 

 mathematische Bestimmbarkeit im Gebiete des Organischen ganz eben so gut 

 vorhanden als in dem des Unorganischen, und in letzterem eben solchen oder 

 aquivalenten Beschrankungen unterworfen als in ersterem ; und nur sofern die 

 unorganischen Formen und das unorgaiiische Geschehen sich einer einfacheren 

 Gesetzlichkeit mehr nahem als die organischen, kann die Approximation im 

 unorganischen Gebiet leichter und weiter getrieben warden als im organischen. 

 Dies ware der ganze, sonach rein relative, Unterschied." Here in a nutshell, in 

 words written some seventy years ago, is the gist of the whole matter. 



An interestmg little book of Schiaparelli's (which I ought to have known long 

 a.go)— Forme organiche naturali e forme geometrlche pure, Milano, Hoepli, 1898 — 

 has likewise come into my hands too late for discussion. 



