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 stands east and west. See the box-elder shoot, on the left in Fig. 110. One pair does not shade the pair beneath. The leaves are in four vertical ranks.

There are several kinds of alternate arrangement. In the elm shoot, in Fig. 110, the third bud is vertically above the first. This is true no matter which bud is taken as the starting point. Draw a thread around the stem until the two buds are joined. Set a pin at each bud. Observe that two buds are passed (not counting the last) and that the thread makes one circuit of the stem. Representing the number of buds by a denominator, and the number of circuits by a numerator, we have the fraction 1/2, which expresses the part of the circle that lies between any two buds. That is, the buds are one half of 360 degrees apart, or 180 degrees. Looking endwise at the stem, the leaves are seen to be 2-ranked. Note that in the apple shoot (Fig. 110, right) the thread makes two circuits and five buds are passed: two-fifths represents the divergence between the buds. The leaves are 5-ranked.

Every plant has its own arrangement of leaves. For opposite leaves, see maple, box elder, ash, lilac, honeysuckle, mint, fuchsia. For 2-ranked arrangement, see all grasses, Indian corn, basswood, elm. For 3-ranked