XVII] THE COMPARISON OF RELATED FORMS 1041 



represented as radiating from a point or "focus," while the other 

 set are transformed into circular arcs cutting the radii orthogonally. 

 These radial coordinates are especially apphcable to cases where 

 there exists (either within or without the figure) some part which 

 is supposed to suffer no deformation ; a simple illustration is afforded 

 by the diagrams which illustrate the flexure of a beam (Fig. 497). 

 In biology these coordinaites will be especially applicable in cases 

 where the growing structure includes a "node," or point where 

 growth is absent or at a minimum; and about which node the rate 

 of growth may be assumed to increase symmetrically. Precisely 



Fig. 498. 



such a case is furnished us in a leaf of an ordinary dicotyledon. 

 The leaf of a typical monocotyledon — such as a grass or a hyacinth, 

 for instance — grows continuously from its base, and exhibits no 

 node or "point of arrest." Its sides taper off gradually from its 

 broad base to its slender tip, according to some law of decrement 

 specific to the plant; and any alteration in the relative velocities 

 of longitudinal and transverse growth will merely make the leaf 

 a little broader or narrower, and will effect no other conspicuous 

 alteration in its contour. But if there once come into existence 

 a node, or "locus of no growth," about which we may assume 

 growth — which in the hyacinth leaf was longitudinal and trans- 

 verse — to take place radially and transversely to the radii, then we 



