BOTANICAL GAZETTE. 



H5 



stem. This cycle then is? rep- „ 



^ 26 



resented by 2 (1-2) -2 (3)= 

 1-6. (Fig. 9.) In like manner 

 it may be shown that the next 21 

 cycle, in which the 6th pair of 

 leaves stands directly over the is 

 first pair, is represented by 2 

 (l)-2(5)=2-10. And it will 

 be found that the cycles of 

 opposite leaves are represent- 

 ed by the series, 0-2, 1-4, 1-6, 

 2-10, 3-16, 5-26, 8-42, &c. 



24. The following table ex- 

 hibits the number and direc- 

 tion of all the orders of spirals 

 belonging to each cycle of op- 



27 



27 



26 



26 



25 



24 



24 



23 



22 



23 



21 



20 



20 



19 



18 



19 



16 



14 



13 



17 



12 



16 



16 



14 



13 



17 



12 



15 



11 



11 



10 



10 



FiL'. 10. 



posite leaves, as far as the 13-68 cycle. 



TABLE III. 25. Exceptional cones of Pine and 



Fir are to be met with, which belong 

 to the higher cycles of opposite leaves. 

 Fig. 10 is a cone of Black Spruce, in 

 which the cycle is 5-26. The c^'^cle of 

 such a cone is to be determined in the 

 same way as one belonging to the al- 

 ternate system (16.), except that in 

 numbering the scales the common dif- 



ference is found by taking half the 



Hi number of spirals in each order. It 

 will be found that two sets of numbers are necessary to mark all the 

 scales of the cone. 



26. In like manner cycles of verticillate leaves when there are 

 three leaves at each node will fall into the series 0-3, 1-6, 1-9, 2-15, 

 &c. When there are four leaves at each node the series will be 0-4, 

 1-8, 1-12, 2-20, &c. 



TABLE IV. 27. There is authority for ex- 



amples t)f cycles in systems other 

 than the common one. 



Table IV exhibits three systems 

 of cycles and the number and di- 

 rection of their different orders of 



