2.^,0 



Church. — The Principles of Phyllotaxis. 



In the same way differences of 8 along the ' 8 ' curves will give a numerical 

 value to these members ; and by starting from i, all the meshes, or points, 

 if these are taken, may be numbered up as has been done in the figure 

 (Fig. 35, (5 + 8)). 



Observation of the figure now shows what is really a very remarkable 

 property : all the numerals have been used, and i, a, 3, 4, &c., taken in 

 order, give also a spiral sequence winding to the centre. This is merely 



Fig. 36. Curve-system (6 + 8) : Bijugate type. Contact-cycle as in previous figure. 



a mathematical property of the system {5 -1- 8), in that these numbers are 

 only divisible by unity as a common factor ; but the single spiral thus 

 obtained becomes in a botanical system the genetic-spiral which has been 

 persistently regarded as the controlling factor in the whole system, since 

 if such a construction be elongated sufficiently far, as on a plant-shoot 

 this spiral will alone be left visible. 



The first point to be ascertained in phyllotaxis is the decision as to 



