100 



the position of the curviseriate leaves treated of; both are of 

 such extent and go so deeply into the minutiae, that we must 

 here content ourselves with communicating the results which 

 the authors themselves have drawn from then* observations. 



At the commencement of the first chapter the following sup- 

 positions are made before entering into a more accurate ex- 

 position of the question relating to the multiple spires : the 

 point of the insertions forms a cylinder : the secondary spires 

 are geometrical helices : the coils are all parallel to each 

 other and equidistant. In the resume it is further stated, 

 that it frequently happens that the spires of an aggregation 

 of leaves or of vital nodes are raised or depressed, and cease 

 in consequence to be spirals in the most rigorous acceptation 

 of the word. Nevertheless this arrangement can hardly be said 

 to invalidate the results ? 



It is quite certain that some unknown cause at times disturbs 

 in a greater or less degree the uniformity of the successive in- 

 ternodes ; but this does not destroy the divergence. Just as 

 the most depressed spires, for instance the primitive spires, are 

 the most favourably disposed to allow of our appreciating by 

 means of their deviations, the least variation in the vertical 

 heights of the insertions, in the same way the most elevated 

 spires, those approaching most to the vertical, being placed 

 under quite opposite circumstances, will also be most advanta- 

 geously situated to allow us to appreciate the least change in 

 the secondary divergences, as these variations of different kinds 

 occur in each of the two cases in the direction of a line which 

 is almost perpendicular to the spiral. Now we find as a con- 

 stant fact of observation, that the more the spires are of a higher 

 order, the more regular are their forms and directions. When 

 an insertion is driven out too much to the right or to the left 

 by some alteration in the vegetative power it is only a local fact, 

 an apparent deviation from the law, and the succeeding in- 

 sertions do not generally participate in this displacement. 

 Let us suppose that the place of the insertions is no longer a 

 cylinder but a conical surface, which is even more conformable 

 to nature, the secondary spires become Archimedean spirals 

 on the plane of convolution. But it may also happen that the 

 spires do not exactly follow the law of the spiral above ex- 

 pressed, they may either be too much raised or too much 



