HARDWJCKE' S SCIENCE-GOSSIP. 



manner, the spiral being a continuous one. As 

 example is better than precept, and as in botany 

 practical experience from actual specimens is all im- 

 portant, it will be well to illustrate the subject by the 

 study of the leaf plan of some shrub or tree. Let us 

 take the oak (Qucrcus Robur) as an example. (Should 

 this not be readily obtainable, cherry, poplar, or 

 apple will be equally serviceable.) On careful examina- 



above it, it will be necessary to pass five leaves. And 

 to effect this it will be found that two lines round 

 the stem are made, in order to complete the cycle, as 

 the interval between the leaf and the one immediately 

 above it is termed. Of course it will be noticed that 

 the leaf which terminates one angle also commences 

 the next, and so on. This particular phyllotaxis of 

 the oak, pear, &c, is called the pentastichous [trine, 



Fig. 15. — Phyllotaxial arrangement of 

 lcuf-buds of Wayfaring Tree. 



m 



Fig. 16. — Phyllotaxial arrangement of 

 leaf-buds of Horse- Chestnut. 



n 



Fig. 17. — Phyllotaxial arrangement of 

 leaf-buds of Ash. 



tion it will be found that, starting from any leaf, to 

 arrive at the leaf which is precisely over it, it will be 

 necessary to pass through five leaves in immediate 

 succession to the one chosen at the starting-point. 

 Thus the sixth leaf is exactly over the first. This 

 arrangement is found to be universal with all the 

 leaves. No matter which leaf is selected as the 

 starting-point, before arriving at the one vertically 



five, arixos, row) arrangement. Now it has been 

 found easy to represent this and other plans of 

 alternate phyllotaxis in the form of fractions, the 

 numerator representing the number of turns round 

 the axis, and the denominator the number of leaves 

 in the cycle. Hence, as in the oak there are two 

 turns and five leaves, the fraction § will represent 

 mathematically the phyllotaxis of that tree. It may 



