EPILOGUE 



I N the beginning of this book I said that its scope and treatment 

 were of so prefatory a kind that of other preface it had no need; 

 and now, for the same reason, with no formal and elaborate con- 

 clusion do I bring it to a close. The fact that I set little store by- 

 certain postulates (often deemed to be fundamental) of our present- 

 day biology the reader will have discovered and I have not 

 endeavoured to conceal. But it is not for the sake of polemical 

 argument that I»have written, and the doctrines which I do not 

 subscribe to I have only spoken of by the way. My task is finished 

 if I have been able to shew that a certain mathematical aspect of 

 morphology, to which as yet the morphologist gives little heed, is 

 interwoven with his problems, complementary to his descriptive 

 task, and helpful, nay essential, to his proper study and com- 

 prehension of Growth and Form. Hie artem remumque repono. 



And while I have sought to shew the naturalist how a few mathe- 

 matical concepts and dynamical principles may help and guide him, 

 I have tried to shew the mathematician a field for his labour — a field 

 which few have entered and no man has explored. Here may be 

 found homely problems, such as often tax the highest skill of the 

 mathematician, and reward his ingenuity all the more for their 

 trivial associations and outward semblance of simplicity. Haec utinam 

 excolant, utinam exhauriant, utinam aperiant nobis Viri mathematice 

 docti*. 



That I am no skilled mathematician I have had little need to 

 confess. I am "advanced in these enquiries no farther than the 

 threshold"; but something of the use and beauty of mathematics 

 I think I am able to understand. I know that in the study of 

 material things, number, order and position are the threefold clue 

 to exact knowledge ; that these three, in the mathematician's hands, 

 furnish the "first outlines for a sketch of the Universe"; that by 

 square and circle we are helped, like Emile Verhaeren's carpenter, 

 to conceive "Les lois indubitables et fecondes Qui sont la regie et 

 la clarte du monde." 



For the harmony of the world is made manifest in Form and 



* So Boerhaave, in his Oratio de Usu Ratiocinii Mechanici in Medicina (1703). 



