210 MATHEMATICAL MODES OF 



the sliell was formed by the soft parts of the animal — 

 those parts, though not possessed of the rigidity of tlie 

 outer shell, yet, if we measured their textures, tlieir relative 

 proportions and rates of increase, we should also find that 

 they were formed according to a mathematical law. It was im- 

 possible, therefore, they should ]iot form a general harmony ! 

 How rapidly science advances ! A few years ago it was sup- 

 posed that the capillary vessels would model anything, and 

 that parts were formed by the extremities of these. But if we 

 admitted absorption, and the death of precise parts, we might 

 expect to ascertain the mathematical law of the body. The 

 period was not far distant when this subject would embrace a 

 much greater number of mathematical rules. No subject could 

 better employ those possessed of mathematical talents than 

 the application of modern analysis to organised bodies. They 

 must begin with the Mollusca. Professor j\Ioseley had exa- 

 mined only the turbinated and discoid shells. The logarithmic 

 curves varied in different shells. But it would come to this 

 at last, that instead of the naturalist describing these bodies 

 by a long roundabout enumeration of their colours, sizes, etc., 

 he would just give the mathematical curves which indicated 

 them. This was already done in crystallography, where crystals 

 were classified according to certain geometrical relations. 



By Professor Moseley's investigations matter had been 

 added to the stock, and something had been done towards 

 the investigation in this manner of animals and vegetables. 

 Professor Moseley, by mathematics, had ascertained that a 

 process must go on, which other naturalists had not discovered 

 — namely, by the revolution which the operculum of the 

 shell must make. It was easily conceived that the oper- 

 culum made a revolution round its axis. The mouth was ot 

 a particular figure. Cut any part in a certain direction (the 

 direction of the plane of its axis), and every section would 

 give a form exactly similar to the form of the mouth. The 



