GENERAL MORPHOLOGY. 137 



second order, as in young shoots. Hugo Mohl* has collected many in- 

 teresting facts with reference to this, but as yet we have not been able 

 to deduce any results from them. 



76. A form that frequently occurs in the plant, and which 

 appears to be especially characteristic, is the spiral, most constantly 

 and normally appearing as a thickening layer, in the vital processes 

 of the individual cell (see above, 18.); also in the arrangement of 

 the chlorophyll in Spirogyra, Chara ; again in the spiral position 

 of the nodose thickening of the cell-wall (see 17.), in the very 

 frequently evident spiral arrangement of appendicular parts rounii 

 an axis; and, finally, in the spiral twistings of elongated parts, 

 as tendrils and twining plants. 



The facts adduced in the above paragraph are indisputable, and 

 decidedly indicate a certain connection between a spiral direction and 

 some peculiarity inherent in the nature of plants ; but we must beware of 

 overrating the importance of these facts, since they present much that is 

 but vague and uncertain. In tendrils and twining plants, the phenomenon 

 admits of a different explanation, for every filiform part, when wound 

 round a stick, must form a spiral, which no one would seek to explain 

 from the nature of an iron wire or a hemp cord. With respect to the 

 spiral position of appendicular organs, appearance, or even strict mathe- 

 matical measurement, may in many cases confirm the view of the existence 

 of this peculiarity, as, for instance, in the cones of Coniferce, in the warts of 

 Mammillarice, and in the fruits of the sun-flower; but it cannot be denied, 

 at the same time, that in most of these cases the leaves decidedly do not 

 form any mathematical spiral, and that it can only be proved that the law 

 discovered for the spiral may be tolerably well applied to the arrange- 

 ment of leaves, when only we bring the leaves a little into order. It 

 seems to be entirely forgotten here, that all the points scattered upon a 

 cylinder (and a stem is seldom or never a mathematical cylinder) may be 

 united by a spiral, if we consider the distances of all the points from the 

 base as fractional parts of the length of the cylinder, and assume that the 

 common measure of these fractional parts is the distance between every 

 two windings of the spiral. We ought, however, only to assume that there is 

 the spiral indicated in the arrangement of the points when the distance 

 between the two points is everywhere equal. But this requirement is only to 

 be fulfilled by an arbitrary pushing aside of the points (the places at which 

 the leaves are inserted), or by the assumption of an abortion, which we 

 cannot find in nature. This view will acquire a true significance in the 

 observation of the vegetable organism when we are able to show from 

 what property of the plant a spiral arrangement must necessarily result, 

 and the laws on which the individual irregularities depend. The two 

 opposite views of Schimper and the brothers Bravais plainly demonstrate 

 how arbitrary every thing is that has reference to the subject. I shall 

 have occasion to revert to this when I come to speak of the leaves of the 

 Phanerogamia. The spiral arrangement of the thickening layer in the 

 cell seems evidently the most certain, but even in this we have the mere 

 naked fact, and not a single idea how it maybe methodically derived from 

 the nature of the cell of the plant. It is manifest that the comparisons 



* Hugo Mohl, Ueber die Symmetric der Pflanzen. Tiibingen, 1838. 



