A Stndy of Leaves 49 



around the spiral, the seventh will fall on the line with the first 

 and fourth. 



Aloe ciliaris bears the sixth leaf over the first. The distance 

 from leaf to leaf is two-fifths of the way around the spiral. What 

 leaf will come over number three ? The distance from one leaf 

 to the one next younger is called the angle of divergence. Other 

 Aloes have different angles of divergence. Besides the J, -J-, f 

 divergence, the fractions f, —^ ~ wnll represent the arrange- 

 ment of leaves on Proteas and other plants with leaves attached 

 by narrow leaf bases. 



Besides the spiral arrangement, leaves are frequently placed 

 opposite to one another. When the alternate pairs of leaves 

 are at right angles to each other, as in Carissa and Sage, the 

 leaves are said to decussate. Not all opposite leaves are 

 decussate. The Crassulas have opposite leaves, but some have 

 the pairs spirally arranged. 



Making leaf spirals is excellent for very warm or rainy days. 

 On pleasant days find as many plants as possible to illustrate 

 these spirals. 



Phyllotaxy is the word used meaning leaf arrangement. 

 It is sometimes difficult to make out on branches placed hori- 

 zontally, as the leaves borne on the lower side turn so as to 

 face the light. Compare them with upright branches. 



Instead of drawing spirals, long strips of paper, such as 

 telegraph messages are received on, may be coiled and 

 marked into divisions and then pulled out to represent the 

 stem. 



Dr. Kolbe has made an ingenious device for showing 

 phyllotaxy, w^hich he has kindly described and illustrated 

 for us. 



Dr. Kolbe's Phyllotaxy Apparatus. 



" Take a strip of corrugated brown paper, about four inches 

 wide and about three yards long. Roll it up closely, but not 

 too tightly, and paste white paper round the cylinder so formed. 

 From the top the coil will look like this — 



£ 



