98 RELATION OP PHYLLOTAXIS TO MECHANICAL LAWS. 



produces a uniform system of members, it becomes possible to give 

 a mathematically accurate account of the more immediate causes 

 of the phenomena observed, in that the members, as they are 

 formed, fall into a definite spiral system, which by constant 

 repetition produces the subjective effect of " genetic-spiral," " para- 

 stichy " spirals, and so-called " orthostichy " spirals. 



The formal description of phyllotaxis thus becomes restricted 

 within very narrow limitations. As soon as the relative bulk of 

 axis and primordium varies to any considerable extent, changes 

 must ensue in the system, and the phyllotaxis formula becomes 

 altered, and is only again capable of mathematical expression when 

 the ratio once more attains constancy. At the same time it is 

 possible to deduce from these relations the fact that the change, 

 when it does occur in such a mechanically produced system, must 

 normally be a gradual one, while any abrupt transition from 

 one system to another, involving a very considerable alteration in 

 the bulk-ratio, is undoubtedly to be regarded as the expression of 

 an active interference in the working mechanism by the inherent 

 form-determining properties of the protoplasm of the organism. 

 And not only so, but such a violent disturbance of the system 

 must be regarded as the expression of a break in the ontogenetic 

 recapitulation of a phylogenetic change which was originally a 

 gradual progression. Abrupt disturbances in the bulk-ratio, at 

 any given point on a plant axis, thus imply a break in the con- 

 tinuity of a mechanical system of member production, which may 

 be taken as the sign of extreme biological specialisation ; and thus 

 the production of an Aroid spadix (Acorits, Eichardia), or the 

 arrangement of the essential organs in certain flowers (Clematis, 

 Fapaver, Paeonia, Gereus), in which the relative volume of the 

 lateral member with regard to that of the axis is abruptly lowered 

 to a very considerable degree, indicates a highly specialised Line of 

 descent ; and such rapid transition-phases of phyllotaxis cannot be 

 accepted as expressions of the mechanical laws controlling normal 

 phyllotaxis change, but must be considered later, when the rules 

 governing the changes in simpler cases are understood. 



