GROWTH. 128 



the solution of the problem. Supposing a creature which a 

 year ago was one foot high, has now become two feet high, 

 while it is unchanged in proportions and structure ; what are 

 the necessary concomitant changes that have taken place in 

 it ? It is eight times as heavy ; that is to say, it has to re- 

 sist eight times the strain which gravitation puts on its 

 structure ; and in producing, as well as in arresting, every 

 one of its movements, it has to overcome eight times the 

 inertia. Meanwhile, the muscles and bones have sever- 

 ally increased their contractile and resisting powers in pro- 

 portion to the areas of their transverse sections ; and hence 

 are severally but four times as strong as they were. Thus, 

 while the creature has doubled in height, and while its ability 

 to overcome forces has quadrupled, the forces it has to overcome 

 have grown eight times as great. Hence, to raise its body 

 through a given space, its muscles have to be contracted with 

 twice the intensity, at a double cost of matter expended. This 

 necessity will be seen still more clearly if we leave out the 

 motor apparatus, and consider only the forces required and 

 the means of supplying them. For since, in similar bodies, 

 the areas vary as the squares of the dimensions, and the 

 masses vary as the cubes ; it follows that the absorbing sur- 

 face has become four times as great, while the weight to be 

 moved by the matter absorbed has become eight times as 

 great. If then, a year 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 only just to 

 meet expenditure, and can provide nothing for growth. How- 

 ever great the excess of assimilation over waste, may be dur- 

 ing 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 ba- 

 lances nutrition — a state of moving equilibrium. This, 



