LEAVES, THEIR FORM AND MOVEMENT 83 



4. ARRANGEMENT OF LEAVES. 



130. The arrangement of leaves on the stem seems to follow 

 certain definite laws, and, barring accidents, is always the same 

 for a given species. 



131. Opposite leaves. Leaves are opposite on the stem 

 when two arise at the same level, or node, but on opposite sides. 

 The milkweed (Asclepias] is a good example, but there are many 

 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. 



132. 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. 



133. 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. 



Formula for the arrangement of alternate leaves. In the simplest type 

 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 attach- 

 ment, 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 denomi- 

 nator is represented by the number of leaf scars, or points of attachment, 

 over which 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 



