172 THE PHILOSOPHY OF BIOLOGY 



exactness with which it applies to the growth of the 

 crystal. We might spend a lifetime growing tablets 

 of cane-sugar, but in all cases we should find that the 

 mass of any crystal was proportional to the cube of a 

 length of a diameter : there would be a strict relation 

 between mass and geometrical form. But this strict 

 relation does not hold in the case of a series of organ- 

 isms belonging to the same species but differing in 

 size. If we measure, for instance, the lengths of a 

 great number of fishes of the same species, we should 

 find that we must describe the law of growth, not by 

 the simple equation M=aP, but by an empirically 

 evaluated expression of the form M=a+bl+cl 2 +dl* + 

 . . . and that the constants in this equation would 

 vary with the species studied and with the conditions 

 in which it is living — that is, the organism changes in 

 form as it increases in size. This is inconceivable in 

 the case of purely physical growth by the accretion 

 of molecules, and we find again that the characters 

 of the organism depend not only on what it is but also 

 upon what it has been — that is, upon its duration. 

 Growth, then, in plants and animals implies variability 

 in form, in general cumulative variability, leading to 

 an indefinite departure from the typical form. 



The organism, therefore, does not grow simply by 

 the accretion of material, but, having attained a 

 certain limit of size, it divides or reproduces. In the 

 lowest plants and animals this process of division is 

 simple : either the organism (unicellular or multi- 

 cellular) divides itself into two approximately equal 

 parts or it divides into a number of such parts. The 

 first process is represented by the reproduction of a 

 bacterium or an Amoeba, or by the division of a 

 Planarian worm ; the second is represented by the 

 division (in many Protozoa, for instance) of the whole 



