ECCENTRIC GROWTH. 273 



the cause or the effect of the unequal growth, may also be placed 

 on one side. 



The log. spiral hypothesis, based on the laws of uniform growth, 

 which so readily established the connection between spiral 

 (asymmetric) and whorled (symmetrical) centric leaf arrangement, 

 is equally readily applicable to the case of eccentric growth-systems. 

 The eccentricity involves the whole growth-system of axis and 

 appendages (leaves), and the mathematical properties of the quasi- 

 square systems remain unaffected, the only alteration produced 

 being a co-ordinated change in the form of the whole shoot-system ; 

 just, for example, as in the case of an unequally developed Pine- 

 cone, every scale on the cone is affected, and takes its share in the 

 structural eccentricity. 



Just as uniform centric growth is a definite mathematical 

 conception, the geometrical properties of which may be readily 

 investigated by drawing suitable log. spiral constructions on a 

 groundwork of a circular meshwork of quasi-squares, and the 

 geometrical properties of such constructions may be deduced 

 before making any further observation of the plant ; so it is well 

 to put together the general facts of the homologous cases of 

 eccentric growth, in order to see what phenomena will be char- 

 acteristically expected, before any attempt is made to bring plant 

 constructions into line with such a hypothesis. 



The difficulties in the way of getting a satisfactory geometrical 

 construction for an eccentric growing system, in which, that is to 

 say, the eccentricity is progressive, and becomes more marked as 

 growth proceeds, although it may not be visible to the eye to 

 begin with, are naturally considerably greater than in the first- 

 studied simple case of centric distribution (fig. 24) ; since all the 

 periclinal curves in the most general case would cease to be circles, 

 and become complicated ovoid curves very much of the type 

 observed in typical starch grains, while the diagonal construction 

 lines cease to be log. spirals, although all the lines may still 

 be regarded as derivatives of these curves. A useful figure 

 which appears to combine all the essential facts of eccentricity, 

 together with a simple geometrical method of construction, in 

 that it is wholly constructed in terms of orthogonally intersect- 



