WINTER CONDITION OF SHOOTS AND BUDS 69 



adjacent pairs. The alternate leaves are arranged in a spiral 

 on the stem; i.e., a line drawn around the stem from left 

 to right and passing over the leaf scars would form a spiral. 

 The arrangement, whether on the opposite or alternate plan, is 

 probably the result of natural causes in the origin of the leaves 

 on the small growing point of the stem, where they are much 

 crowded. The origin in some such regular order whether on 

 the opposite or alternate plan, permits a large number in a given 

 space. Either of these arrangements, however, gives the leaves 

 a better light relation, as will be seen in the study of leaves, 

 than if the leaves were arranged promiscuously, or all in a line 

 one above another. The influence of light therefore may have 

 had some influence through inheritance of a favorable position 

 for the leaves. 



114. In the case of the elm shoots, if the end of a cord is 

 pinned on a leaf scar near the base of the last year's growth, 

 and wound around the stem from left to right, passing over the 

 successive leaf scars, it will pass once around the stem for every 

 two scars. This arrangement is represented by the fraction , the 

 numerator denoting the number of turns around the stem, and 

 the denominator indicating the number of leaf scars traversed 

 in order to reach another leaf scar directly above the one at the 

 starting point. In the sedges and in the American white helle- 

 bore (Veratrum viride} there will be one turn for every three 

 leaves, and this is represented by . In the butternut, oak, etc., 

 there will be two turns of the spiral for every three scars or 

 leaves, and this is represented by . Now we find this curious 

 relation. If we add together the numerators and denominators of 

 the first two fractions, the result is as follows: i + 5 = f . Now 

 if we add together the last two fractions in a similar way it gives 

 a fraction which represents another plan of arrangement possessed 

 by many shoots, thus \ % f = f . In like manner $ J f = -fg, 

 which represents another, and so on for several other known 

 systems. 



