82 



OKGANOGRAPHY AND GLOSSOLOGY. 



same direction, and include within their course the points of insertion of all the 

 leaves. 



If, on the other hand, starting from No. 1, we examine its relations with No. 6, 

 on the radius next to the right, we find between them a difference of five ; and 

 similarly with 6 and 11, 11 and 16, &c. ; and between Nos. 2 and 7, and Nos. 12, 

 17 and 22, and along the series commencing with 4 and 5. Here again, from left 

 to right, the number expressing the difference corresponds to that of the series. 

 Each of these series may be shown more clearly by means of a curved line uniting 

 all the leaves which compose it, and we shall then have five segments of a spiral 

 turning symmetrically from left to right, and passing through the insertions of all 

 the leaves. These segments of the spiral have been termed secondary spirals, to 

 distinguish them from the primitive spiral, also termed generating spiral. Now it 

 will be remarked that the secondary spirals proceeding from right to left are three 



459 6. Rosette forming two cycles of eight leaves, 

 of which the angle of divergence U J. 



4.W <. Rosette forming a cycle of thirteen leaves, of 

 which the angle of divergence is /, ; the axis A, where 

 they are In.-ci U*l, tn-uni live turns of the spiral, show- 

 ing the point of insertion of each leaf. 



in number, which number is the numerator of the fraction ; and that the sum of 

 these three, and of the five going from left to right, is eight, or the denominator of 

 the fraction. If therefore it is possible to count the secondary spirals to left and 

 right, of rosettes, involucral bracts, or scales of Pine cones, in all of which the 

 primitive spiral is obscured by the closeness of the parts, we may assume that the 

 smaller number represents the numerator, and the sum of the two numbers the 

 denominator of the desired fraction ; which again gives the angle of divergence, the 

 number of leaves in the cycle, and the number of turns of the spiral which they 

 occupy. 



This crowding of the leaves, which we have illustrated by Sedum, is frequent 

 amongst plants with radical leaves, in many of which the cycle of the leaves is 

 indicated by the fraction $ (Common Plantain, fig. 459 6). 



The number of secondary spirals to right and left being known, it is easy to 

 number each leaf in the primitive spiral. Take, for example, the rosette (fig. 459 c), 

 which represents a Houseleek, or the cone of the Maritime Pine (6g. 459 d). Their 



