152 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



account of the phenomena when the construction remains constant for 

 a period sufficient to give hy recapitulation the appearance of definite 

 contact-parastichies ; an unequal number of intersecting curves means 

 asymmetrical construction, an equal number implies true symmetry. 



The slightest deviation from absolute symmetry produces an 

 apparent spiral effect, just as the failure of a circle to come round 

 on itself in the smallest degree would produce a spiral curve, 

 and the subjective effect, as judged by the eye and interpreted in 

 terminology, is quite disproportionate to the cause. 



Thus the parastichies of wall-papers and tiles on a roof, quoted 

 by Sachs, are as clearly the expression of a symmetrical con- 

 struction as the vertical and horizontal lines of the pattern. 

 Equally good examples are often seen in the arrangement of 

 imbricating ovules in an ovary (Asclepias) or scale-emergences on 

 fruits, etc. (Raphia, Acorn-cup); so long as the construction is 

 regular, the secondary " parastichies " present an equal number in 

 either direction ; but the slightest deviation from strict regularity 

 at once renders these curves unequal or irregular, and a spiral 

 system is the result. Thus in the Sago-Ealm fruit {Raphia, fig. 

 72), the emergences are relatively very large, and when regularly 

 formed they fall into series giving symmetrical curves (6-f 6), 

 (7 + 7); but any trifling irregularity in formation spoils these 

 rows, and thus (6 + 7) is equally common: the secondary spiral 

 appearance thus produced does not imply that the scales constitute 

 a phyllotaxis system, or that the members are leaves, although 

 regarded merely as adult structures the resemblance is very 

 striking ; the suggestion that this similitude in lateral appendages 

 of different value morphologically may be the outcome of a 

 common law of growth is very obvious. 



The phyllotaxis phenomena of whorls and spirals observed on 

 the plant are thus merely the outward expression of the distinc- 

 tion between symmetrical and asymmetrical construction. In the 

 primary system, seen in Zone I., when the original lateral contacts 

 are maintained, the most obvious sign of the mode of growth is 

 the equality or inequality of the diagonal construction lines 

 (parastichies), these being more readily checked by the eye than 

 the complementary lines of construction, which may be circles or 



