6 THE PRESIDENTIAL ADDRESS. 



from the point of view of change of form as the size increases, has not 

 been pursued by botanists with the same perception as zoologists have 

 shown in the study of animals. 



At the back of all problems raised by increasing size stands the well- 

 known principle of similarity, which applies to all structures, inorganic as 

 well as organic. It involves among other consequences that where form 

 remains unaltered bulk increases as the cube, but surface only as the 

 square of the linear dimensions. But in living organisms it is through the 

 limiting surfaces, or ' presentation-surfaces,' as they are called, that 

 physiological interchange is effected. Provided a surface be continuous 

 and its character uniform, it may be assumed that such interchange will 

 be prop.ortional to the area of surface involved. If, then, the form of the 

 growing organism or tissue were retained as at first — for instance, a 

 simple sphere, oval or cylinder — its surfaces of transit would increase at 

 a lower ratio than the bulk which they enclose. There would be with 

 increase in size a constantly decreasing proportion of surface to bulk, and 

 as constantly an approach to a point of physiological inefficiency. But 

 any change from a simpler to a more complex form would tend to uphold 

 the proportion of presentation-surface. Thus, the success of a growing 

 organism might be promoted by elaboration of form. Naturally, other 

 factors than that of size co-operate in determining form. Nevertheless, 

 the recognition of such elaborations of form, whether external or internal, 

 as do tend in point of fact to maintain a due proportion of surface to bulk 

 as growth proceeds, should help to make morphology a rational study. 

 The diffuse form habitual for plants, even the origin of leaves themselves, 

 becomes intelligible from this point of view. 



In the construction of any ordinary vascular plant there are three of 

 these ' presentation-surfaces,' or limiting surfaces of transit, that are of 

 prime importance : (i) the outer contour by which it faces the surrounding 

 medium ; (ii) the sheath of endodermis which envelops the primary 

 conducting tracts ; and (iii) that collective surface by which the dead, 

 woody elements face upon the living cells that embed them, through which 

 water and solutes pass in or out. Each of these may vary independently 

 of the others, and each would be a fitting subject for observation as bearing 

 on this problem of size. But as a test case of the relation between size 

 and form, it is the collective surface where dead wood faces on living cells 

 that will meet our requirements best, for its study can be pursued among 

 fossils almost as well as in living plants. The problem is one not merely 



