CHAPTER X 



A PARENTHETIC NOTE ON GEODESICS 



We have made use in the last chapter of the mathematical principle 

 of Geodesies (or Geodetics) in order to explain the conformation 

 of a certain class of sponge-spicules ; but the principle is of much 

 wider appHcation in morphology, and would seem to deserve atten- 

 tion which it has not yet received. The subject is not an easy one, 

 and if we are to avoid mathematical difficulties we must keep within 

 narrow bounds. 



Fig. 346. Annular and spiral thickenings in the walls of plant-cells. 



Defining, meanwhile, our geodesic hne (as we have already done) 

 as the shortest distance between two points on the surface of a 

 soUd of revolution, we find that the cyhnder gives us some of the 

 simplest of cases. Here it is plain that the geodesies are of three 

 kinds: (1) a series of annuh around the cyhnder, that is to say, a 

 system of circles, in planes parallel to one another and at right 

 angles to the axis of the cylinder (Fig. 346, A); (2) a series of 

 straight lines parallel to the axis; and (3) a series of spiral curves 

 winding round the wall of the cyhnder (B, C). These three systems 



