38 



across, a very different spectacle was produced from that seen in the 

 cross section of a forest tree. In the latter we saw a series of cor- 

 centric rings traversed by radiating lines, known as " medullary rays ;" 

 in the former, a collection of circles, which, under extreme com- 

 pression, might assume the hexagonal form. But this dissimilarity 

 vanished on closer inspection and a more careful consideration of the 

 manner in which trees grow. If we surrounded one twig by a circle 

 of others, and subjected the whole to uniform pressure, we should find 

 that the outer twigs, if sufficiently compressible, would form one con- 

 tinued ring, wherein each separate piece had the wedge-form produced 

 by intersecting radii. Ring after ring might be thus formed, and the 

 whole section of an aged tree satisfactorily imitated. 



It would be noticed that in the fancied model each medullary 

 wedge was connected with one twig and one only ; and it might be 

 asked whether he considered such to be the order of actual tree- 

 growth ? To this he answered that his illustration was but an illustra- 

 tion, and was intended to prove nothing ; but the supposition was quite 

 possible, though he knew nothing whatever concerning its truth. The 

 angle of ramification was very uniform in trees of the same species, 

 and was readily explained on the principle to which he wished to 

 draw their attention. 



Every student of dynamics knew that if two forces acting on or 

 from one point be graphically represented by two lines of equivalent 

 length and direction, the diagonal of the parallelogram so indicated 

 would give the length and direction of their resultant, and vice versa. 

 So if we knew the longitudinal and lateral forces at any given fork, we 

 should be able to trace the angle at which each division would leave 

 the point of separation. As these data were not forthcoming, another 

 means of investigation must be found. It was manifest that a force 

 tending to separate any pair of fibres must vary in total amount 

 directly as the number of fibres present ; and as these together made 

 up a limb, it followed that the amount of pressure tending to cause 

 any two limbs to diverge from the original direction would be in direct 

 proportion to the sectional area ot the limbs themselves. On the 

 other hand, there was primd facie reason to suppose that which he 

 hoped to establish by another line of reasoning : that the tendency to 

 longitudinal extension was at its greatest at the commencement, and 

 decreased according to the amount of work done, or according to the 

 distance from the root . On such a supposition we readily deduced a 



