Gibb : The Study of a Fircone. 409 



pectively, and manage to shew a little strip of their base running 

 to the centre of the cone. If we strip off i, 2 and 3, the result 

 will be that 4, 5 and 6 will be left clear, 7 and 8 will be overlapped 

 on one edge only, and three new scales will peer between as did 

 6, 7 and 8. In short, the old order will instantly ^be restored 

 with a general shift round ; and we may continue to strip the 

 cone with the same result (like turning a wheel) to the end. 



Here again the phyllotaxian numbers are met in a new way. 

 The thyee free scales, the five which form the whorl, the eight 

 which complete the series of the secondary spirals — these are 

 our old friends shewing themselves in the very heart of the cone. 

 The ring of five scales which encircles the bottom of the cone 

 is the starting point of the five secondary spirals running to the 

 right or left, as the case may be. Each one of these five scales 

 is the origin of a spiral, and it will now be easy to see how these 

 coils are formed, and how we may correctly number each scale 

 upon the cone. It is necessary here to make the preliminar}^ 

 remark that the object of the spiral arrangement of leaves 

 being to secure as much light and air as possible for each, a 

 corkscrew-like progression is not the plan adopted, and 2 will 

 not be found next to i (as may easily be seen upon consulting 

 the diagrams), the coil making a sweep of one-third around the 

 stem before the second scale finds its place, a similar one before 

 the third is placed, and then with two more sweeps dropping 

 4 between i and 2, and 5 between 2 and 3. When this first 

 circle is finally disposed, the sixth scale is invariably placed next 

 to I, either on its right or left, according to which way the five 

 secondary spirals are to proceed ; 7 will be in the same position 

 with regard to 2, and so on ; and the five secondary spirals 

 are started. Having marked one of the three free scales at the 

 bottom as No. i, we could now correctly number the whole 

 cone without difficulty, so as to shew the course of the invisible 

 central spiral. If the one chosen has eight spirals to the right 

 and five to the left, the numbers of the first five scales from left 

 ■to right will run i, 4, 2, 5, 3 ; and following the spirals to the 

 left which are started respectively by each of these, every 

 scale must be marked with a number five in advance of the 

 preceding one ; i, 6, 11, 16 and so on. If the cone has five 

 spirals to the right and eight to the left, the numbers of the first 

 five scales will be the same, only running from right to left, and 

 the resulting spirals to the right will be numbered in the same 

 way. 



1909 Dec. I. 



