178 SIZE A FACTOR IN STELAR MORPHOLOGY [ch. 



The adult stems and roots of most plants are approximately cylindrical. 

 The same is the case as a rule for their conducting tracts also. The cylinder 

 is one of those solid forms in which the proportion of external surface to bulk 

 is exceptionally low. Any deviation from the cylindrical form, either by 

 external projections or by involutions of surface, necessarily leads to increase 

 in the proportion of surface to bulk. The surface varies only as the square 

 of the linear dimensions, but the bulk as the cube. It follows therefore that 

 in carrying out any of those physiological functions of living organisms 

 which depend upon surface, as do all those of the acquisition and interchange 

 of materials, the actual size of the part which exercises that function is a 

 matter of the greatest moment. It may be assumed that, if other things be 

 equal, such as the structure and quality of the tissues that form the surfaces 

 in question, the rate of interchange by diffusion of soluble gases or salts 

 through a tissue-surface will be directly proportional to the area of the dif- 

 fusing surface. But the demand will probably vary as the bulk enclosed by 

 that surface. If that be so, then for each such function there will be a limit 

 of size beyond which its exercise with sufficient rapidity will become impos- 

 sible if the form be maintained, or if the quality of the surface-tissue through 

 which the transit occurs remains the same. This suggests that the larger the 

 plant is the more dependent it will be upon its form and detailed structure, 

 not only for its stability, but also for the performance of its functions of 

 absorption and transit of liquids and gases. This will apply not only to the 

 external surface, but also to those internal surfaces which limit one tissue- 

 tract from another. Not only the outer surfaces, but also the limiting surfaces 

 of the internal tissue-tracts should then be carefully examined, both as to 

 area, and as to their detailed structure. 



In point of fact stems and roots are only approximately C3dindrical. 

 Fluctuations of size either by increase or by decrease are common. But 

 the most general and the most important of them all is that primary increase 

 of dimensions which is found in the stems of most plants as they pass from 

 the juvenile to the adult state. For the moment only the primary increase 

 is meant : all secondary or cambial increase may be ruled out of this dis- 

 cussion, however interesting its problems may be. Here the intention is to 

 concentrate upon those problems which any land-living plant, having no 

 cambial increase, must face as it passes from the juvenile to the adult state. 

 The facts of ontogenetic development in plants which, like the Ferns, have 

 no secondary growth provide the most cogent evidence of the effect of increase 

 in size upon internal structure. In Ferns the first leaves are small : the later 

 leaves are successively larger. The stem which bears them is relatively 

 small at its base, but as larger leaves are formed the stem which bears them 

 becomes proportionately larger, till the adult size is reached (Fig. 17 1). The 

 same is the case with the stele that lies within. The form of the stem of the 



