48 



PHTLLOTAXT, OR LEAF ARRANGEMENT, 



case of the subsequent development of the branch, as often occurs in the Berb- 

 eris and laroh, their spiral arrangement becomes manifest In the pines the fas- 

 aides have fewer leaves, their number being definite and charaoteriatic of the species. 

 Thus P. strobus, the white pine, has 5 leaves in each fascicle, P. palustris, the long- 

 leaved pine, has 3, P. inops, 2. 



226. The opposite leaved type is also spiral. The leaves in each circle, 

 whether two or more, are equidistant, dividing the droumference of the stem into 

 equal arcs. The members of the second circle are not placed directly above those 

 of the first, but are turned, as it were, to the right or left, so as to stand over the 

 intervening' spaces. Hence there may be traced as many spirals as there are leaves 

 in each whorl. 



227. DEOtrssATE leaves result from this law, as in tlie motherwort 

 and all the mint tribe, where each pair of opposite leaves crosses in di- 

 rection the next pair, forming four vertical rows of leaves. Therefore, 

 it is 



228. An established law that the course of development in the 

 growing plant is universally spiral. But this, the formative cycle as it 

 is called, has several variations. 



' 92, 93, 94, showing the course of the spiral threiitl .ind the order of the leaf-succession in the 

 axes of elm, alder, and cherry. 95, axis of Osage-orange with a section of tlie barit peeled, dis- 

 playing the order of the leaf-scars (cycle |). 



229. The elm cycle. Inthestrictly alternate arrangement (elm, linden, grasses) 

 the spiral thread makes one complete circuit and commences a new one at the third 

 leaf The third leaf stands over the first, the fourth over the second, and so on, 

 forming two vertical rows of leaves. Here (caUing each complete circuit a cych) 

 we observe 



230. First, That this cycle is composed of two leaves ; second, that the angu- 

 lar distance between its leaves is J a cycle (180°); third, if we express this cycle 

 mathematically by J, the numerator (1) will denote the turns or revolutions, the de- 

 nominator (2) its leaves, and the fraction itself the angular distance between the 

 leaves(Jof360o). 



