49 8 LECTURE XXIX, 



theory arbitrarily made, to construct the so-called genetic spiral out of these para- 

 stichies by certain geometrical artifices. But, on the one hand, direct observation 

 shows that these premisses by no means always fit the case, and that nevertheless 

 very fine parastichies arise ; and very often it may be said, on the other hand, that 



when numerous figures or bodies similar 

 to one another are placed close beside one 

 another on a common foundation in any 

 sequence whatever in time, they must 

 necessarily present to the eye viewing 

 them series crossing right and left. Even 



FIG. 33S. — The grbwing-point of a bud of the Larch, 

 seen from above. 



ordinary wall-papers show such parasti- 

 chies, and in the same way the arrange- 

 ment of the scales on the .bodies of fishes, 

 of the hairs on the skin of mammals, and of 

 the tiles on a roof exhibits such parastichies 

 clearly enough. They are particularly well 

 seen in the case of the scales of pine 

 cones, and in the numerous flowers of the 

 capitulum of the Compositse, especially that of Helianthus annuus, or the flowering 

 head of Dipsacus and of the Aroidese, and it was these objects particularly which the 

 supporters of the spiral theory employed by preference, for the purpose of constructing 

 the genetic spiral from the parastichies. Nevertheless it is very easy to show in 

 these very cases how uncertain were the facts on which the spiral theory was often 

 supported. Fig. 336 may serve for the illustration of this. The figure represents 



FIG. 336. — Arrangement of the young fruits on the conical axis of a flower-head of 

 Dipsacus fuUonttm (Fuller's Teazle). * 



the arrangement of the unripe fruits of Dipsacus fullonum closely crowded on the 

 conical floral receptacle, but transferred from the natural curved surface to the plane 

 of the paper : this was attained by blackening the conical flower-head with printer's 

 ink, and subsequently rolling it on the paper. The figure is thus in all essential 

 points quite true to nature. We perceive at once two mutually crossing sytems of 



