76 GROWTH AND WORK OF PLANTS 



others, as the horse chestnut, lilac, etc. In these examples each 

 pair is at right angles to the pair above and below, so that looking 

 down the axis of the stem there are seen four rows of leaves. 



127. Whorled or verticillate leaves. Leaves are whorled 

 where three or more arise at the same level, or node, on the stem, 

 and they are usually equidistant around the circumference of 

 the stem. The Joepye-weed (Eupatorium) is an example. 



128. Alternate leaves. By far the larger number of plants 

 have alternate leaves. There is but one leaf at the same level 

 or node. Not only do the majority of plants have alternate 

 leaves, but there is a great variety in their arrangement, though 

 they all are arranged spirally around the stem. The simplest 

 arrangement of alternate leaves is seen in such an example as the 

 elm, iris, corn, etc. There are two rows of leaves, one each on 

 opposite sides of the stem. If a pin is thrust through the end of 

 a string and then stuck at the point of attachment of a leaf, or 

 in a leaf scar, and the string is wound around the stem in a spiral, 

 passing across each successive leaf scar or point of attachment, 

 the string will cross two leaf scars for each complete revolution 

 around the stem. This gives us the law or plan of arrangement 

 of alternate leaves of the elm type which is expressed in the form 

 of a fraction, the numerator being the number of revolutions the 

 string makes around the stem until it reaches a leaf directly 

 above the leaf at the starting point, while the denominator is 

 represented by the number of leaf scars, or points of attach- 

 ment, over w r hich the string passes in making the same number 

 of revolutions, not counting the leaf scar which served as the 

 starting point. In the case of the elm, therefore, the plan of 

 arrangement is expressed by the fraction \ which represents also 

 the angle of divergence of successive leaves from each other 

 around the stem. This is the two ranked arrangement. The 

 next higher arrangement is the three ranked, shown in the 

 sedges, the Veratrum or American white hellebore (Veratrum 

 viride) in swamps and damp woods. The leaves are in three 

 rows, and the arrangement is expressed by the fraction J. The 

 five ranked arrangement is shown in the apple, poplar, etc. Here 



