230 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 1, 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 1, 2, 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 + 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 
