APPENDIX. 63 



movement towards the surface of the stem, without the 

 divergence between it and the uppermost leaf upon the 

 helix becoming diminished, until the leaf had arrived at 

 the lateral surface of the stem, and there become perma- 

 nently fixed. It is equally clear that if the rest of the 

 leaves should follow this first at uniform distances, from 

 the turns of the spiral being closer towards the interior, 

 the divergence between the successive leaves would in- 

 crease in proportion as they were situated more internally, 

 and would first acquire the dimension normal for the 

 species at the transit of these leaves over on to the heliacal 

 line. On the other side it is likewise evident that, with- 

 out any alteration of their divergence, the leaves would 

 seem to traverse a spiral, if each of them proceeded to- 

 wards the periphery upon the radius on which it stands 

 at its first origin ; for during the expansion of the axis of 

 the bud, its most external part extends outwards and 

 upwards to become the surface of the stem, the outer 

 end of the spiral running upon this part of the axis, 

 passes, as a continuation of the helix, on to the outer 

 surface of the stem, and the succeeding leaf advances just 

 so much nearer to the end of the spiral line, not because 

 it makes a lateral movement upon it, but because the 

 spiral line is abbreviated in the direction towards the leaf, 

 and its point of transition into the helix advances nearer 

 to the point at which the radius, on which the leaf stands, 

 intersects the circumference of the stem. Which of these 

 processes occurs, whether the leaf actually advances late- 

 rally, or the motion is only apparent, may be decided by 

 investigation whether or not the divergence of the leaves 

 alters. Now I believe that it will be found on examina- 

 tion of the position of the leaves, that they exhibit the 

 same divergence in the terminal bud as on the stem, and 

 that the arrangement of the leaves passes with uniform 

 divergence from the helix into the spiral, and is continued 

 in this ; while, according to Meneghini's idea, the diver- 

 gence must increase in the spiral. The distance from 

 a leaf to its successor on the spiral will naturally be 



