PHANEROGAMIA : FOLIAR ORGANS. 263 



arising from the axis in the same plane, scattered leaves (f. spar so). 

 These three positions of the leaves upon the axis are, most un- 

 doubtedly? the primary ones occurring in the plant. We find the 

 first in the cotyledon of the Monocotyledons ; the second in the 

 cotyledons of the Dicotyledons. But if we disregard, in the Mo- 

 nocotyledons, the character of embracing the stem, only looking to 

 the fact that one leaf alone is formed at one level on the stem 

 if we trace the further development of the leaves of Monocoty- 

 ledons, and of those of most Dicotyledons, since in the latter it is 

 only in a few groups that the later leaves are formed in whorls, 

 we find that the great majority of plants have scattered leaves. 

 If every vegetable axis be regarded as a cylinder, the bases of 

 the leaves must admit of being connected by a spiral line. More 

 minute investigation, then, shows that the distances of the bases of 

 the leaves on this spiral are not without law ; but a certain regu- 

 larity may be observed, and, in fact, the angle (angle of divergence) 

 made by two planes, passing through the middle of the axis and 

 the bases of two adjacent leaves, which angle therefore is the 

 measure of the distance of these leaves from each other, is on an 

 average 137 30' 28", consequently a number bearing no ratio to 

 the circumference of the stem (360) ; so that no two leaves ever 

 can be exactly in the same vertical line. In the course of the 

 entire axis the distances of the turns of the spiral alter, but always 

 regularly, sometimes even on account of accidental influences ; and 

 thus from the simplest fundamental condition proceeds an infinite 

 multiplicity of modes of manifestation, even when the various forms 

 of the axis do not interfere. Compare but the rosette of leaves of 

 Sempervivum tectorum, the stalk of Lilium Martagon, a shoot of 

 Populus dilatata, a cone of Abies excelsa, and the fruit peduncle 

 of Heliantlius annuus, which latter exhibits the regular position 

 of the leaves even through its fruit which originate from axillary 

 buds. 



The study of the position of leaves has recently occupied so many 

 excellent labourers, that it indeed cannot be attributed to the want of 

 talent or applied industry if the results obtained are at present so little 

 satisfactory or certain. Rather have we to seek the cause in the inac- 

 curate methods, and, secondly, in our as yet so imperfect knowledge of 

 the nature of plants generally, especially of the laws of their morpho- 

 logical development. In reference to the first point, it must be remarked 

 that observation and research have been restricted wholly to isolated, 

 determinate conditions of the developed plant, when the abortion of 

 particular parts has so frequently already destroyed the regularity of the 

 rudiment, while at the same time the recognition of this fact has opened 

 the door to fancy, so that when the phenomena would not exactly suit 

 themselves to a preconceived hypothesis, this has been supported by a 

 supposed abortion of the parts. Two very opposite paths have been 

 struck out, one by the Germans, Schimper and Braun, the other by the 

 French, the brothers Bravais. Schimper arid Braun examined a count- 

 less multitude of cases, sought by the most accurate measurements 

 possible to obtain a series of results, which they used as a basis for an 



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