ON THE THEORY OF VEGETABLE SPIRALS. 359 



which grow, for instance, on the north side of a tree, or all those 

 belonging to a given spiral which rise above a circle drawn 

 round the axis of growth. The two modes of resolution give, 

 as we shall see, similar results ; but we shall set out from the 

 first. If we were to take off all the leaves on the north side of 

 a tree, those left could not be arranged in spiral order at all, 

 except in particular cases : but there is always one mode in 

 which spirals may be divided by means of two azimuths, so that 

 the essential principle of the spiral remains untouched. This 

 will be clear from the figure .which, like all the other figures, 



Fig. i. 



represents a spiral in a state of development, that is, as if un- 

 wound from the cylindrical axis on which it grew, so that the 

 right-hand and left-hand sides of the xectangle are in reality one 



