GENERAL OBSERVATIONS. 21 



cylindrical stem for a distance of 3-4 feet or more before the end 

 tapers to the inflorescence. Old flowering stems, cut in September 

 or October, when all the leaves have been shed, afford the best^ 

 material. On these cylindrical stems, owing to the absence of 

 winter-bud formation, the alternation of the seasons is shown by the 

 alternating approximation and separation of the leaf-scar cycles ; 

 the sears being closer together in autumn and fairly scattered in 

 spring. The figure (fig. 8) represents a continuous portion of a 

 stem A, B, C, D, E, cut into four sections for convenience of illustra- 

 tion. By using the method of parastichies on the spring area (A), 

 rhombs are readily noted formed by (3-1-5) intersecting curves, 

 pointing to a | phyllotaxis ; but the top member of the rhomb (9) 

 is not on the same vertical line as the bottom one, and the fraction 

 may therefore be higher. On another piece (B, C) the same 

 rhombs are conspicuous, but another set may be marked out form- 

 ing (5 -f- 8) curves of a j^g phyllotaxis, but the top member of the 

 rhomb is again not vertically superposed to the bottom one. On a 

 third piece (C, D) the same rhombs may be traced, or a steeper 

 series due to (8-|-13) curves of ^j- type. The top member is again 

 not in vertical series. The stem is erect and contains little wood, 

 there is no sign of torsion on it, but the phyllotaxis, as defined by 

 the observation of orthostichies, seems ever elusive. In the same 

 way still steeper curves may be located, as in D, E, where 13-f-21 

 point to a ^| system, and, given a long cylinder, they may be made 

 as steep as one likes ; as soon as the eye becomes accustomed to one 

 set, a still steeper may be seen. It becomes clear that the curves 

 may be carried the whole length of the stem before the series comes 

 to a compulsory end. This range was short in the Pine cone ; in the 

 cylinder it becomes indefinitely prolonged, a leaf accurately super- 

 posed to No. 1 being, in fact, only reached at some quite indefinite 

 station, although a nearer approach is gained at every rise of the 

 phyllotaxis series. Thus the actual expression given becomes a 

 convention, since the ever-steepest curves pass beyond the limit of 

 observation. These are the facts, but what do they mean ? 



It is clear that the phyllotaxis fraction, whatever numerical 

 value is given to it, rises in the series as the axis is telescoped, 

 and falls as it is lengthened. In fact, if a high phyllotaxis be 



