l8o EXTERNAL CONFORMATION OF PLANTS. 



phyllotaxis have not at present got much further than to ascertain in each sepa- 

 rate case the phenomena preceding and accompanying the origin of a member, as 

 well as those forces which, from their direction, exercise an influence on the point 

 of origin, and to lay down more general laws as the result of comparison in a 

 sufficient number of cases. In these as in all other investigations into organisms, 

 we are always however met at the very outset by a consideration of great im- 

 portance which imposes itself upon us, I mean the /oii/ ensemUe of properties which 

 define the character of the natural group, class, or order. By recognising a plant 

 as a member of a particular class, e. g. Mosses, Ferns, Equisetacese, Rhizocarps, or 

 Phanerogams, &c., an aggregate of properties is ascribed to it, which must be taken 

 into account as such. If we pay special regard to the point of view opened out 

 by the Theory of Descent, we must recognise the law of heredity and of the 

 conformable endowment of the members with definite properties, the difficulty or 

 even impossibility of demonstrating the causes of any morphological phenomenon 

 in any other manner than historically. The organic forms are not the result of 

 combinations of forces and materials given once for all, and always again presented 

 in exactly the same manner, as in the case of a crystal which is first dissolved 

 and then re-crystallised ; but they are the result of combinations which repeat them- 

 selves hereditarily and which at the same time undergo change. To understand 

 these it is necessary to refer to the past, and not only to the immediate present. 



Abundant opportunity will be afforded in the description of the various classes in 

 Book 1 1 for a more exact observation of particular relations of position ; but what has 

 now been said is sufficient as a preliminary. Some additional remarks on the Spiral Theory 

 in the doctrine of phyllotaxis may however find a place here. It has already been 

 shown that the construction required and employed in the spiral theory is not in all cases 

 possible, being in some cases arbitrary and without relation to the history of develop- 

 ment, and in others simply meaningless. Finally, only those cases admit of the applica- 

 tion of the spiral theory without violence, in which the shoot forms three or more rows 

 of leaves distributed singly and uniformly in all directions. The history of development 

 often points to quite different constructions, even in those cases in which the spiral is 

 still geometrically possible. But even in th6se cases in which the union of the leaves 

 according to their order of succession in age by a spiral always running round the 

 stem in the same direction is possible and even apparently useful, there is not in 

 the relations of the history of development any sufficient reason for the hypothesis 

 that the growth of the generating axis itself actually follows a spiral. This was for the 

 first time refuted in detail by Hofmeister in the Bot. Zeitg. 1867, numbers 5, 6, 7, and 

 the refutation is again repeated in his 'General Morphology,' p. 481. With reference 

 to his descriptions it can only be stated that even a short abstract of them would occupy 

 too much space for this text-book. 



Closely connected with the spiral theory, which must be carefully distinguished from 

 the doctrine of phyllotaxis, is another very peculiar mode of expressing the angle of 

 divergence. It is thought, namely, that a natural law was found when it was re- 

 marked that some of the most commonly occurring constant divergences |-, 3-, f , f , 1%, 

 and some of the less common ones, as ^\, \% f i, y\^ \ &c. may be represented as 



^ It must be observed in reference to this that it remains uncertain whether such complicated 

 divergences are ever so formed originally, or whether they are not always consequences of compli- 

 cated displacements, in consequence of which the direct observation of the punctum vegetationis does 

 not give in these cases a certain conclusion. 



