PHYLLOTAXY. 



83 



angle of divergence is T 5 j, which is easily found by counting the very obvious 



secondary spirals to right and left. We have only alluded to the most obvious 



secondary spirals ; but it will readily be understood 



that there are many others, some more, some less 



oblique than these, and that every numerical series 



having the same relative differences between them 



would be a spiral. The secondary spirals are 



especially visible in Pine cones, the axis of which 



is much longer than that of the Houseleek, and 



in which they form very distinctly marked parallel 



series. 1 



Begin by numbering as 1 one of the outer leaves 

 of the rosette, or of the lower scales of the cone, 

 and regard it as the first of a secondary spiral 

 turning from left to right. To find No. 2 on it, re- 

 member that the numbers of a secondary spiral must 

 be separated by a space equal to the number of the 

 secondary spirals of which this forms a part ; and 

 as there are five parallel left-to-right spirals, the 

 second leaf or scale must be numbered 6, the third 

 11, and so on to the top of the cone, or centre of 

 the rosette. Having thus numbered all the scales 

 or leaves of one of the five parallel secondary left- 

 to-right spirals, these numbers may serve as start- 

 ing-points from which to number all the other 

 scales or leaves of the cone or rosette. We know 

 that each of the numbered scales or leaves of 

 the secondary left-to-right spiral equally forms 

 one in the series of the right- to-left spirals, and we 

 may number all the leaves or scales from any 

 starting-point, by adding 5 when turning to the right, and 8 when turning to 

 the left. 



Let us take, for example, No. 32 ; this number in the left-to-right spiral would 

 (adding 5) lead us to No. 37, 37 leads to 42, and so on; but since No. 32 also 

 enters into one of the eight secondary right- to-left spirals, the leaf or scale succeed- 

 ing it in this spiral should be numbered 32 + 8, i.e. 40 ; and following this spiral, by 

 .additions of 8, we should have 40, 48, 56, 64, 72, &c. 



To obtain in the same spiral the numbers below 32, we must deduct the number 

 8, which we had before added, and we shall have successively 32, 24, 16, 8. 



If, in starting from the same No. 32, we descend the secondary spiral which 

 turns from left to right, we must take 5 from 32, when we shall have successively 

 27, 22, 17, 12, 7, 2, &c. 



All the leaves or scales of the rosette or cone being numbered, their succession 



1 Nothing is easier than to observe this, by numbering the scales of a ripe cone of the Maritime Pine. 



02 



459 d. Cone of Maritime Pine, with the scales 

 numbered according to their relative heights. 

 The most obvious secondary spirals are formed 

 to the right by the series of numbers in fives ; 

 to the left by the series of numbers in eights. 



