152 THE INDUCTIONS OF BIOLOGY. 



ago, the absorbing surface could take up twice as much 

 nutriment as was needed for expenditure, thus leaving one- 

 half for growth, it is now able onl}^ just to meet expenditure, 

 and can provide nothing for growth. However great the 

 excess of assimilation over waste may be during the early 

 life of an active organism, we see that because a series of 

 numbers increasing as the cubes, overtakes a series increasing 

 as the squares, even though starting from a much smaller 

 number, there must be reached, if the organism lives long 

 enough, a point at which the surplus assimilation is brought 

 down to nothing — a point at which expenditure balances 

 nutrition — a state of moving equilibrium. The only way in 

 which the difficulty can be met is by gradual re-organization 

 of the alimentary system ; and, in the first place, this entails 

 direct cost upon the organism, and, in the second place, indi- 

 rect cost from the carrying of greater weight : both tending 

 towards limitation. There are two other varying 



relations between degrees of growth and amounts of expended 

 force; one of which conspires with the last, while the other 

 conflicts with it. Consider, in the first place, the cost at 

 which nutriment is distributed through the body and effete 

 matters removed from it. Each increment of growth being 

 added at the periphery of the organism, the force expended 

 in the transfer of matter must increase in a rapid progression 

 — a progression more rapid than that of the mass. But as 

 the dynamic expense of distribution is small compared with 

 the dynamic value of the materials distributed, this item in 

 the calculation is unimportant. ISTow consider, in the second 

 place, the changing proportion between production and loss 

 of heat. In similar organisms the quantities of heat gene- 

 rated by similar actions going on throughout their substance, 

 must increase as the masses, or as the cubes of the dimen- 

 sions. Meanwhile, the surfaces from which loss of heat 

 takes place, increase only as the squares of the dimensions. 

 Though the loss of heat does not therefore increase only as 

 the squares of the dimensions, it certainly increases at a 



