37 



If his view were correct, all these were connected together by one 

 common law, so that if one element were given the rest could be 

 deduced. The required data were the amounts and proportion of two 

 forces whose nature he did not yet attempt to define, the one tending 

 to lengthen the stem and its offshoots, the other tending to separate 

 the wood fibres laterally, the two energies holding much the same 

 relation to each other as the centrifugal force and that of gravity did 

 to each other in the planetary system. If the first force predominated, 

 the tree would be tall and narrow ; if the latter, it would be wide- 

 spreading. The ratio of the two gave a constant fraction, which 

 might be called the " co-efficient of ramification," and from which the 

 whole outline of the tree might perhaps be calculated, just as a curve 

 might be traced from its equation. 



The size of the first limb was doubtless determined by some in- 

 herent law, as trees of the same species showed a striking uniformity 

 in this respect, but he was not able even to imagine its nature. He 

 knew, however, that the proportion of the limb to the stem once fixed 

 was preserved throughout, and that every shoot bore the same propor- 

 tion to its parent as the first branch to the primitive stem. The size 

 of the barrel above the limb was far easier of determination. Its 

 sectional area, added to that of the limb, alvvays gave the sectional 

 area of the trunk from which they sprung, and this was equally true 

 where the division was into three or more branches. Thus, if from a 

 trunk 37in. in circumference two limbs, measuring respectively i8in. 

 and I2in. round, forked off, the resulting stem would measure 3oin. in 

 circumference, whether the two branches were at one point or separate, 

 or, in other words, the sum of the squares of i8, 12, and 30 equalled 

 the square of 37, nearly. This law, which held good, without ex- 

 ception, in every tree and every twig, settled a most important 

 question, showing us that limbs were not off-shoots or lateral growths, 

 but actual divisions of the stem from which they sprung ; and this 

 being so, we were led to infer that the whole of the leaf stalks on a 

 tree, if united in one bundle, would make up the thickness of the main 

 trunk, a conclusion as startling as it was inevitable. 



This result might be illustrated by binding together, say, a hun- 

 dred twigs, afterwards dividing them into ten, and these successively 

 into fives, twos, and ones. The effect would be, that a fair model of 

 a tree would be produced, in which the ultimate divisions evidently 

 made up the bulk of the parent stem. If such a bundle were cut 



