2 
Proceedings of the Royal Society of Edinburgh. [Sess. 
masses, and their relation to the physiological functions which they 
perform. So far, however, the principle of similar structures has not been 
applied in botanical science as freely as its importance would justify. An 
attempt will be made in this address to show how the principle has 
affected the internal morphology of the Vascular System of Plants. The 
most marked illustrations will be taken from the Ferns, a class of plants 
in which the vascular system has always attracted attention by reason 
of the complexity and peculiarity of its details. But further evidence 
will be brought to show that it has its application in other types of 
plants as well. 
The 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, 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 a 
living organism which depend upon surface, as do all those of the 
acquisition and interchange of material, 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 diffusing 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 impossible 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 cylindrical. 
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 
