512 PATTEN— COOPERATION AS A FACTOR IN EVOLUTION. 



IV. 



Let us consider a few special cases that may serve to make our 

 meaning clearer. We shall have space to refer to a few of the more 

 important points only. 



Let us assume that equal units or cells are growing under uniform 

 conditions, suspended in a medium from which they draw their 

 varied supplies. Such units will tend to form a solid sphere, in- 

 creasing in volume till its radius is nearly equal in length to the 

 longest line of conveyance requisite for metabolism (Fig. i. A). 

 The sphere might enlarge beyond that point, but if it did, an ever 

 larger central space would be formed, filled with fluid, or non-living 

 materials and the thickness of its living walls could not be greater 

 than the longest line of effective conveyance through protoplasm, 

 nor less than the one necessary for structural stability, or cohesion. 



Growth in a spherical form beyond either of these limits, would 

 be impossible. But since there are more such lines of exchange, in 

 a cylinder or disc, with two or three unlike axes, than in a sphere of 

 equal volume, as fast as all of the possible lines of conveyance are 

 occupied, the spherical body, of necessity, assumes a more and more 

 discoidal or cylindrical form, C, E. This change of form cannot 

 be regarded as an extraneous " variation " to accommodate growth ; 

 it is the inevitable result of growth attaining its fullest expression. It 

 marks the successive steps in the attainment of the maximum length 

 of the lines of conveyance, the attainment of the maximum number 

 of such lines, and the accumulation of the products of growth along 

 the lines of least resistance. 



When the cylindrical, or discoidal, body has reached its limits of 

 growth, still further increase would be possible by opening up the 

 interior, D. But here again the increased dimensions attainable by 

 this improvement in conveyance are limited, for the walls could not 

 exceed a definite thickness without the formation of a new barren 

 area (coelomic cavity) between the inner and outer surface of the 

 walls, and when that limit was reached, growth should again cease. 



But the inevitable effects of these changes, even if we assume that 

 no minor complications arose, would be very great. They would 

 tend : ( i ) to orient the cylindrical, or disc-shaped body to the chief 



