360 THE REV. H. MOSELEY ON THE GEOxMETRICAL FORMS 



curve, will be certain increments of the capacity of the shell ; and it appears from the 

 following mathematical investigation of the properties of conchoidal surfaces (see 

 equation 19.), that the increments of the capacity of the shell, thus taken, will be in a 

 constant ratio to the then existing whole capacities of the shell. The increment of 

 the animal's bulk corresponding to each of these increments of the shell must then be 

 in a constant ratio to its then existing bulk ; that is, the animal's growth correspond- 

 ing to a given increment, A 0, in the angle described by the generating curve of its 

 shell, is proportional always to its existing growth. 



Let us now suppose that the physical living energies of the animal (those by which 

 it grows), at any time, are proportional to its then existing growth ; and therefore that 

 its growth in any increment of time is proportional to its growth up to that time (a 

 supposition which possesses an independent probability). From the conclusion be- 

 fore arrived at, and from this supposition, it follows that the growth of the animal 

 corresponding to a given increment, A 0, in the angle of revolution of the generating 

 curve, and the growth corresponding to a given increment of time, are each propor- 

 tional to the animal's whole then existing growth, and therefore to one another; and, 

 since they begin together, that the whole angle, 0, of revolution of the generating 

 curve of the shell, is proportional to the whole corresponding time of the animal's 

 growth, and therefore that the whole number of whorls, and parts of whorls, is pro- 

 portional to its whole age : a conclusion which, like the supposition whence it is de- 

 duced, possesses an independent probability. 



The separate probability of each of the two suppositions, *• that the physical energies 

 of the Mollusk, as developed in its growth in a given increment of time, are propor- 

 tional to its whole then existing growth*, and that its age is always proportional to 

 the whole angle which, in the construction of the shell, it has then described round 

 its axis," is greatly increased by the necessary relation which is here shown to obtain 

 between them ; a relation, by reason of which, either supposition being made, the other 

 becomes a conclusion. 



The form of the Mollusk being supposed to remain geometrically similar to itself, 

 the surface of its mantle, by which organ it deposits its shell, of necessity varies as 

 the square of its linear dimensions, whilst the whole bulk of the animal varies as the 

 cube of its linear dimensions. But, as its whole bulk, varies its active living and 

 growing energy, and therefore the amount of the deposition of its shell in a given 

 time ; this last, then, varies as the cube of its linear dimensions ; but the surface of 

 the depositing organ (the mantle) varies only as the square of the same linear dimen- 

 sions. Besides, then, the organic increase of the surface of the mantle, there must 

 be an increased functional activity of all its organs, varying as its simple linear di- 

 mensions. 



This increased functional activity of the surface of the depositing organ, varying 



* May not this law of the growth of a Mollusk have its analogy in other forms of animal life, and perhaps 

 in vegetable life ? 



