peculiar {134} and specialised functions that of cell-multiplication tends to fall into abeyance[173]. It would seem to follow, as a natural consequence, from what has been said, that we could without much difficulty reduce our curves of growth to logarithmic formulae[174] akin to those which the physical chemist finds applicable to his autocatalytic reactions. This has been diligently attempted by various writers[175]; but the results, while not destructive of the hypothesis itself, are only partially successful. The difficulty arises mainly from the fact that, in the life-history of an organism, we have usually to deal (as indeed we have seen) with several recurrent periods of relative acceleration and retardation. It is easy to find a formula which shall satisfy the conditions during any one of these periodic phases, but it is very difficult to frame a comprehensive formula which shall apply to the entire period of growth, or to the whole duration of life. But if it be meanwhile impossible to formulate or to solve in precise mathematical terms the equation to the growth of an organism, we have yet gone a very long way towards the solution of such problems when we have found a “qualitative expression,” as Poincaré puts it; that is to say, when we have gained a fair approximate knowledge of the general curve which represents the unknown function. ―――――――――― As soon as we have touched on such matters as the chemical phenomenon of catalysis, we are on the threshold of a subject which, if we were able to pursue it, would soon lead us far into the special domain of physiology; and there it would be necessary to follow it if we were dealing with growth as a phenomenon in itself, instead of merely as a help to our study and comprehension of form. For instance the whole question of _diet_, of overfeeding and underfeeding, would present itself for discussion[176]. But without attempting to open up this large subject, we may say a {135} further passing word upon the essential fact that certain chemical substances have the power of accelerating or of retarding, or in some way regulating, growth, and of so influencing directly the morphological features of the organism. Thus lecithin has been shewn by Hatai[177], Danilewsky[178] and others to have a remarkable power of stimulating growth in various animals; and the so-called “auximones,” which Professor Bottomley prepares by the action of bacteria upon peat appear to be, after a somewhat similar fashion, potent accelerators of the growth of plants. But by much the most interesting cases, from our point of view, are those where a particular substance appears to exert a differential effect, stimulating the growth of one part or organ of the body more than another.