18 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



to a central ideal line, suggests most clearly that no orthostichy is 

 really possible until the "ideal angle" is reached; that is to say, 

 only at infinity wiU a leaf be found exactly on the same radius as 

 1. The series in the specimen is bounded by a few leaves, and so 

 No. 22 is near enough for practical purposes, and the phyllotaxis 

 is usually given as ^ ; but there is no proof of its position over 

 No. 1 ; on the contrary, a very strong presumption against the 

 acceptance of any orthostichies at all. 



2. Braun's Method of Determining Paeastichies. 

 (Pinus Pinea.) 



The ripened carpellary cones of Pinus afford useful permanent 

 examples of spiral phyllotaxis. The large cone of P. Pinea, 5J 

 inches by 3, is especially suitable for observation, and the smooth 

 scales are large enough to be clearly numbered. 



Such a cone is observed to consist of obliquely intersecting rows of 

 scales (fig. 6-7), of which eight long curves intersecting thirteen 

 shorter ones are the most obvious. 



Since the cone may be regarded as built up of a certain nimiber 

 of oblique rows winding left, or again of a certain number of rows 

 winding right, a complete cycle may be regarded as formed by 

 taking one member from each of the two series. Thus in the case 

 figured (fig. 7), the structure may be regarded as built up of — 



I., of oblique rows of the type 1, 9, 17, etc., of which eight can be 

 counted going all round the cone. 



II., of rows 1, 14, 27, etc., of which thirteen can be counted. 

 III., of rows of the type 1, 22, 43, etc., of thich there are twenty- 

 one. 



In the first case, the scales will differ by eight, the number of 

 the curves, in the second by thirteen, and in the third by twenty- 

 one. 



A simple method thus follows for numbering the scales in the 

 serial order of their development {genetic spiral). By taking any 

 given scale as one, the number of each one adjacent to it may be 

 determiued by counting round the cone the number of curves in 



