60 THE COMICAL GROWTH OF TREES. 



point taken below the terminal bud, it is only necessary to 

 count the number of sets of bud-rings on the exterior bark, 

 or of years' rings visible in the wood on the cross-section 

 of the axis, as both numbers will be found to correspond 

 invariably with each other. To make this plain to the 

 reader, the diagram shows not only the relative position 

 and number of the several conical growths, but their re- 

 spective lengths and breadths at the same time, the latter 

 being visible at the bottom of the diagram in the form of 

 a corresponding number of circular and concentric woody 

 layers or strata. 



The following simple geometrical consideration will, we 

 hope, aid the reader in obtaining an approach to a proper 

 conception of the relation subsisting between growth in 

 length and increase in breadth among the branches of trees. 

 If he regards the diagram attentively for a few moments, 

 he will see that the two sides of the innermost cone, esti- 

 mated from the point immediately below the terminal bud 

 marked '53, form, with the diameter or breadth of the cone 

 at its base, an isosceles triangle. Now, supposing the base 

 of this triangle to remain constant and its two sides to vary, 

 it is plain that the angle of acumination formed at the apex 

 of the triangle will be a function of its sides, for this angle 

 will become greater or smaller, in proportion as we suppose 

 the apex of the triangle to approach to or recede from its 

 base, and its . two sides to shorten or elongate. For the 

 shorter and more abbreviated the axis of the cone, the more 

 relatively enlarged is its base, and the more clearly is it 

 conical; but the more its axis is lengthened, so much the 

 more do the two sides of the cone approach to a state of 

 parallelism, and the axis tend to a cylindrical form. 



These considerations prove that the following law will ex- 

 press the relation subsisting between the two dimensions of 

 length and breadth ; the branches are more cylindrical the long- 

 er they are, and more conical in proportion as they are shorter. 



As examples of well-marked conical growth we may men- 

 tion those extremely abbreviated, or more properly speaking, 

 abortive shoots, called thorns, of which (Cratceguscrus-galli) 

 the Cockspur thorn furnishes us with an admirable instance. 



