Church. — ^The Principles of Phyllotaxis. 



239 



retical generalizations of the mathematical conception of uniform growth, 

 and would be at the same time in closest agreement with the facts of 

 observation ; while no other mathematical scheme could be drawn which 

 would include primordia arranged in such contact relations and at the 

 same time give an orthogonal construction. If, that is to say, the quasi- 

 circle can be established as the mathematical representative of the 

 primordium of a lateral appendage, the orthogonal construction, which 

 is the one point most desired to be proved, will necessarily follow. 



Fig. 41. Quasi-circles of the systems (a + 2), (i + 1) and (i + 2) arranged for illustration in the 

 plane of median symmetry. C, C", C", the centres of construction of the respective curves. 

 (After E. H. Hayes.) 



It remains therefore now to discuss the nature of the curves denoted 

 by the term quasi-circles ; their equations may be deduced mathematically, 

 and the curves plotted on paper from the equations. These determinations 

 have been made by Mr. E. H. Hayes. Thus a general equation for the 

 quasi-circular curve inscribed in a mesh made by the orthogonal inter- 



