412 RELATION OF aUANTITY TO iESTHETIC SENTIMENT. 



numbers. In trees such as tlie bircli, we liave one main trunk send- 

 ing out branches at equal distances ; and each side branch, in its 

 turn, becomes a central axis, sending out comparatively small branches. 

 Examine the leaf, and we shall find one central vein sending out 

 its veins on either side ; and these, in like manner, sending out other 

 smaller veins at equal distances. In trees such as the sycamore, we 

 see more clearly the relation of numbers to this arrangement. The 

 sycamore, at the height of eight or ten feet, sends out all at once a 

 cluster of five branches ; and in correspondence with this, its long 

 leaf is divided into five mid-veins. The horse-chestnut sends forth, 

 from the top of a bare trunk, seven branches, and the leaf is divided 

 in exact correspondence with this. So in herbaceous plants : we find 

 triplet stalks corresponding with triplet leaves. 



In the arrangement of the leafy appendages of plants, there occurs 

 a curious series of numbers: 1, 2, 3, 5, 8, 13, 21, 34, 55, &e. Here 

 it will be observed that any two numbers of the series give the suc- 

 ceeding one. Of this arrangement, the cone of the fir-tree furnishes 

 the most apparent illustration. In the cone we have a well-defined 

 spiral arrangement, by which the scales are arranged round its axis. 

 We take its most common form, in which two of these spirals are 

 visible ; though in reality there are four spirals — the governing one, 

 by which the scales are arranged round the axis, and one other run- 

 ning in the same direction, and two others running in the opposite 

 direction. The two sets of visible spirals intersecting each other form 

 a series of figures, consisting of two equilateral triangles on the sur- 

 face of the cone. These diamond-shaped figures have definite angles. 

 Those above and below approximate to 120°; those on the sides to 

 60°. These well-defined and beautifully proportioned rhomboidal 

 figures on the surface, give to the cone its peculiar beauty and har- 

 mony of shape. This arrangement also necessitates a series of 

 figures spread over the surface of the cone : one of the rhomboidal 

 protuberances occupies the centre, with four others corresponding — 

 one at each angle : these give the figure known in gardening as the 

 "quincunx." 



In the spirals themselves we have a definite and special arrange- 

 ment of numbers. They are, as we have seen, in two sets : one run- 

 ning from right to left, the other from left to right. The parts or 

 numbers of each set, seen in the section of a cone — which Dr. 

 McCosh has called threads — are arranged in numbers corresponding 



