DISTRIBUTION OF THE GREEN LEAVES ON THE STEM 399 



the circumference of the stem by the leaves situated vertically above one another. 

 The two lines are opposite, or, what comes to the same thing, they are separated 

 from one another by half the circumference of the stem. This arrano-ement of the 

 leaves, which may be observed, for example, on the branches of elms {Ulmus) and 

 limes (Tilia), is called the one-half phyllotaxis. 



Second case. Three leaves are developed in one story, each at a definite height, 

 an under, a middle, and an upper leaf. In a horizontal direction two of the leaves 

 following one another in age are always shifted from one another through a third 

 part of the circumference (see fig. 99 2 ). If the point of insertion of the lower leaf 

 is connected with that of the middle leaf, and this again with that of the upper 

 leaf by a line, and this line is continued to the beginning of the next story, a single 

 spiral is thus formed surrounding the stem. Now above the story just described, 

 which we will call the lowest, a second follows, which is again provided with three 

 leaves arranged in exactly the same way. The lower leaf of the second story is 

 situated vertically above the lower leaf of the first story, the middle above the 

 middle, and the upper above the upper leaf, and the same arrangement is continued 

 through all the stories. In this manner three rectilineal lines, or orthostichies, 

 arise on the circumference of the stem from the leaves situated above one another, 

 and each of the lines is separated from the other two by ^ of the circumference. 

 This arrangement, which is to be found on the upright branches of alders, hazels, 

 and beeches, is called the one-third phyllotaxis. 



Third case. Five leaves originate in each story, which are designated according 

 to age as the first, second, third, fourth, and fifth, the lowest being the oldest, the 

 highest the youngest. These five leaves give place to one another in a horizontal 

 direction, and the shifting, i.e. the horizontal distance between two leaves next in 

 age, amounts to f of the circumference of the circle (see the plan, fig. 99 3 ). If 

 the five leaves are joined together in succession according to their age, a spiral 

 line is obtained consisting of two revolutions, and the " genetic spiral " consequently 

 forms two circuits round the stem. If a stem, whose leaves are arranged in this 

 manner, is built up of two or several stories, then the similarly numbered leaves 

 are situated in straight lines above one another, the first (lowest) leaves of all the 

 stories form together one straight line (orthostichy); in the same way the second, the 

 third, ^:c. Thus five lines are developed on the circumference of the stem by the 

 leaves situated one above the other, and each line is separated from another by 

 i of the circumference. This arrangement, which is found in oaks, round-leaved 

 willows, and in many buckthorns, is designated the two-fifths phyllotaxis. 



Fourth case. Eight leaves are to be found in each story, which may again be 

 numbered from one to eight according to their age. Any two successive leaves are 

 separated from one another horizontally by f of the circumference (see fig. 99 4 ). 

 If a line be drawn starting from the first and lowest leaf, joining all the eight leaves 

 of the story in the order of their ages, this forms a spiral line, or " genetic spiral ", 

 which traverses the stem three times. In a stem consisting of several such stories, 

 the leaves named by the same numbers are placed in straight lines above one 



