The publication of the preceding section concludes the essential 

 part of a memoir commenced in November 1900 and submitted, 

 unsuccessfully, to the Linnffian Society in May 1901. Since that 

 time sections including suggestions on floral construction have 

 been added in order to place the subject on a wider basis, and 

 many additional figures have been included in the text, but 

 publication has been delayed for lack of funds. The first two 

 parts were published by the author in 1901-2, and the assistance 

 of a grant from the Eoyal Society (August 1904) has admitted of 

 the completion of the present volume. 



Grateful acknowledgment is here made of the suggestions and 

 assistance of many mathematical friends who have been perhaps 

 more interested in the subject than botanists, and especially to 

 Mr H. Hilton of Magdalen College and to Mr E. H. Hayes of 

 New College, without whose interesting discussion of the curves 

 the subject would have remained in a rudimentary phase. 



A. H. C. 



