162 



spirals (p = a e ), intersecting everywhere at right angles. Indeed, 

 in two-dimensional space the logarithmic spiral is the only curve, 

 in which one part differs from the other only in size, but not in 

 shape, a property which brings out very strikingly the essential 

 character of such curves as lines of growth. 



If it be kept in mind that the primordial cells will be greater as 



a. 





Fig. 1290 and b. 



they are older, Church gives the following constructions of the spiral 

 arrangements in the first zone of growth. As symbols of the emer- 

 gences based on lateral members of cell-aggregates, he takes, like 



De Candolle (loco cit. p. 52), 

 circles of different diameter 

 packed closely together in the 

 way of the most closely packed 

 "cubic" arrangements (fig. 12 pa 

 and b, and in both principal 

 directions (cf. fig. 121), as well 

 laterally (fig. i2pa) as diago- 

 nally (fig. i2<?b) oriented along 

 the radii of all-sided growth. 

 The "diagonal" arrangement 

 corresponds to the special sup- 

 position that a new member 



takes its place precisely in the cavity left between two members 

 already present. The radial arrangement is in agreement with the 

 radial direction of transversal growth (De Candolle, loco cit. p. 29). 

 Now the concentric circles indicating the successive zones, are 

 substituted by a logarithmic spiral as "genetic" line, "like the line of 

 current in a spiral vortex", and the radii likewise substituted by pa- 

 rastichies of the same shape wound in one or in the opposite direction. 



Fig 130. 





