44 RELATION OF PHYLLOTAXIS TO MECHANICAL LAWS. 



whole area, but only at the periphery, and the construction by 

 circles in arithmetical progression is therefore the expression of 

 peripheral growth, since if all the cells continued to grow equally, 

 they would form a series in geometrical progression and no new 

 radial walls would be laid down. 



The several cases of symmetrical and asymmetrical construction 

 in an apex presenting uniform growth may now be considered in 

 order, commencing with the symmetrical forms, since these present 

 the simplest diagrams. 



Eestrieting the diagram to a plane expression, it is clear that a 

 circular-vortex wUl be represented by concentric and radial series 

 of similar figures ; a spiral- vortex by similar figures arranged along 

 intersecting logarithmic spirals. 



If orthogonal figures ("squares") are used in the circular con- 

 struction, they will also be represented by " square " areas bounded 

 by log. spirals in the spiral-vortex. 



The curves (" circles ") inscribed in these areas, which approach 

 true circles as the " squares " approach true squares, may be repre- 

 sented by inscribed circles, the difference being within the error of 

 drawing when the angle subtended is small. 



