RELATIVE POSITIONS OF LATERAL MEMBERS. 
20I 
always however met at the very outset by a consideration of great importance which 
imposes itself upon us, I mean the /ouf ensemhle 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. Muscinese, Filices, Equisetacese, Rhizocarpese, Phanerogamia, 
&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 in the law of heredity and the physiological adaptation 
of organs, the difficulty or even impossibility of demonstrating the causes of any 
morphological phenomenon in any other manner than genetically. Organic forms 
are not the result of combinations of forces and materials given once for all, 
and always again reproduced in exactly the same manner, as in the case of 
a crystal which is first dissolved and then re-crystallised, but of combinations 
which repeat themselves hereditarily and which at the same time undergo change. 
To understand these it is necessary to refer to the past, and not merely to the im- 
mediate present. 
Abundant opportunity will be afforded in the description of the various classes in 
Book II. 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 this theory is not in all cases 
possible, being sometimes arbitrary and without relation to development, and at other 
times simply meaningless; and that, finally, only those cases admit of the application 
of this theory without violence, where 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 v^^hich the spiral is still 
geometrically possible. But even where the connection of the leaves in order of suc- 
cession in age by a spiral running round the stem in the same direction is possible and 
even apparently useful, there is not in the phenomena connected with development 
any sufficient reason for the hypothesis that the growth of the generating axis itself 
actually follows a spiral ^. 
Closely connected with the spiral theory, which must be carefully distinguished from 
the doctrine of phyllotaxis, is another very peculiar law connected with the angles of 
divergence. It was thought, namely, that a kind of natural law was found when it was 
discovered that some of the most commonly occurring constant divergences ^, |, f, 
and some of the less common ones, as /j-, &c.^, may be represented as succes- 
sive convergents of the continued fraction 
2 + 1 
I + I 
Were it possible- to combine all kinds of phyllotaxis without exception in this manner 
into one single continued fraction, we should actually have a kind of natural law, in which 
there would be no relation of cause and effect, and which would hence stand out as an 
^ See on this point Hofmeister, Bot. Zeitg. 1867, nos. 5, 6, 7, and Allgemeine Morphologie, 
p. 481. 
2 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 growing point does 
not give in these cases a certain conclusion. 
