48 introduction to Botany. 



the number of vertical rows is to stick pins or dissecting 

 needles into each leaf scar perpendicular to the tangent at 

 that point, passing spirally up the stem, omitting none of 

 the scars, until the scar is reached which stands immedi- 

 ately above the initial scar, that is, the one with which the 

 start was made. When the twig is now held in front of 

 the observer, parallel to the line of vision, the number of 

 vertical rows of leaf scars may easily be counted and the 

 angular divergence of the rows determined. The angular 

 divergence of a leaf from the one next above or below it is 

 now to be determined. 



Suppose that in counting the scars it is found that in 

 passing once around the stem the fifth scar is immediately 

 above the initial scar; then it is plain that the angular 

 divergence of the leaves from each other is one fifth of 

 360, or 72. But suppose the five leaves are distributed 

 over two turns of the stem ; then it is evident that they are 

 twice as far apart as in the first case, that is, their angular 

 divergence is now twice 72, or 144. If examples of this 

 sort were multiplied, it would be seen that the angular 

 divergence of the leaves would be that fraction of 360 

 whose numerator is the number of times the circumference 

 of the stem is passed over, and whose denominator is the 

 number of intervals traversed in passing spirally from the 

 initial scar to the one directly above it. Of what use is a 

 definite angular divergence of the leaves ? 



64. Study in like manner cottonwood and lilac. 



65. Make thin cross sections of a one-year-old stem of 

 Aristolochia, and treat with phloroglucin and chlor-zinc- 

 iodide, or double stain with cyanin and erythrosin (see 

 page 384). Examine with a simple lens or with the low 

 power of the compound microscope. ^ On the outside is 

 the epidermis, a (Fig. 19). Within this is a zone of tissues 



