732 A NOTE ON POLYHEDRA [ch. 



such an hypothesis, after being dethroned and repudiated, has now 

 fought its way back and claims a right to be heard, so it may be 

 also in biology. We begin by an easy and general assumption of 

 specific properties, by which each organism assumes its own specific 

 form ; we learn later (as it is the purpose of this book to shew) that 

 throughout the whole range of organic morphology there are innu- 

 merable phenomena of form which are not pecuhar to living things, 

 but which are more or less simple manifestations of ordinary physical 

 law. But every now and then we come to deep-seated signs of 

 protoplasmic symmetry or polarisation, which seem to lie beyond 

 the reach of the ordinary physical forces. It by no means follows 

 that the forces in question are not essentially physical forces, more 

 obscure and less familiar to us than the rest; and this would seem 

 to be a great part of the lesson for us to draw from Lehmann's 

 beautiful discovery. For Lehmann claims to have demonstrated, 

 in non-living, chemical bodies, the existence of just such a deter- 

 minant, just such a "Gestaltungskraft," as would be of infinite help 

 to us if we might postulate it for the explanation (for instance) of 

 our Radiolarian's axial symmetry. Further than this we cannot 

 go; such analogy as we seem to see in the Lehmann phenomenon 

 soon evades us, and refuses to be pressed home. The symmetry 

 of crystallisation, which Haeckel tried hard to discover and to reveal 

 in these and other organisms, resolves itself into remote analogies 

 from which no conclusions can be drawn. Many a beautiful 

 protozoan form has lent itself to easy physico-mathematical ex- 

 planation ; others, no less simple and no more beautiful prove harder 

 to explain. That Nature keeps some of her secrets longer than 

 others — that she tells the secret of the rainbow and hides that of 

 the northern hghts — is a lesson taught me when I was a boy. 



A note on Polyhedra. 



The theory of Polyhedra, Euler's doctrina solidorum, is a branch 

 of geometry which deals with the more or less regular solids; and 

 the rudiments of the theory may help us to study certain more or 

 less symmetrical organic forms. Euler, a contemporary of Lin- 

 naeus, is the most celebrated of the many mathematicians who 

 have carried this subject beyond where Pythagoras, Plato, Euclid 

 and Archimedes had left it. He drew up a classification of poly- 



