A Study of Leaves 5 1 



of the way 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 di- 

 vergence. Besides the ^, \^ | divergence, the fractions |, y%, ^y 

 will represent the arrangement on Proteas and other plants with 

 leaves attached by narrow bases. Still other arrangements may 

 be found. 



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 be decussate. Not all opposite leaves are 

 decussate. The Crassulas have opposite leaves, but some have 

 the pairs spirally arranged. 



Making leaf spirals is excellent work for very warm or rainy 

 days. On pleasant days find as many plants as possible to il- 

 lustrate 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 phyl- 

 lotaxy, which 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 (Fig. 58) — 



" On the outside of the white paper, divide the circumference 

 into fifths, eighths, etc., as far as you want to show the fractions 



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