THE RELATION IX SIZE AND FORM y\ PLANTS < 



bud .md branches only occasionally, as in Ferns and Palms : th< 

 takes a conical form as a consequence oi cambial thickening Fig. 5). 

 Here there is profuse branching with numerous relatively small 



distal buds, as in forest trees. When young the two types do not 

 seem to differ essentially from one another : but as greater dimensii 

 are reached they tend to diverge, not only in external form but also 

 internally. 



Principle of Similarity. 



Galileo's Principle of Similarity applies to all structures, gri 

 and small, living or not living. In accordance with it, if the form of 

 an enlarging solid body remains unaltered, its bulk increases as the 

 cube, but its surface only as the square of the linear dimension 3. 

 In living organisms it is through limiting surfaces, whether external 

 or internal, that physiological interchange is effected. It may be 

 assumed that, other things being equal, the amount of substance 

 transferred will be proportional to the area involved. Hence the 

 importance of the principle here applied to obconical plants of 

 primary development : for provided any surface of transit be con- 

 tinuous, it would increase at a lower ratio than the bulk that it 

 encloses ; and if its character remains unchanged during growth 

 there would be a constant approach to a point of functional in- 

 efficiency. A remedy may, however, be found in change of form as 

 the growth proceeds : and this is actually to be seen in most spore- 

 lings. Any elaboration of so simple a contour as the inverted cone would 

 tend to uphold the surface-volume ratio. 



Examples and Illustration 



The mouldings that occur in individual development of the primary plant- 

 body, as it advances onwards from the spore or the zygote, may appear 

 either externally or internally. A few examples will show how, by-elaboration 

 of form, certain difficulties that arise from increasing si/e have actually been 

 met in Nature. Obconical sporelings present relatively simple methi 

 For instance in the green Alga, FritschieUa (Fig. .\\:) the germinal filament 

 first enlarges upwards, and then branches profusely, forming .1 <list.il brush. 

 The bulk of each thread equals approximately th.it .>t the first, though 

 their collective bulk is great. By this elaboration <>t form the propor- 

 tion of surface-exposure of the whole tends to be maintained. A fern 

 prothallus (Fig. 391), or a young Fucus (Figs. 2 )), widens into a thin 



expanse with flattened sides : this tends by a different method to uphold 

 the surface-volume ratio. In the tissue of a young growing BporeKng of 

 Riccia, clefts appear in the enlarging upward growth, and these open 

 B.B. 2 1' 



