Campbell on Differential Geometry

Towards the end of his career J E Campbell's interests turned from continuous groups to differential geometry. He had become fascinated by Einstein's gravitational theory. He had almost completed work on a book on differential geometry at the time of his death in October 1924. The publication of the work was then undertaken by Edwin Bailey Elliott acting as editor. The book, published in 1926, contains a Preface by J E Campbell's son and an Editor's Note by E B Elliot. We give a version of both of these below:

A COURSE OF
DIFFERENTIAL
GEOMETRY

BY THE LATE

JOHN EDWARD CAMPBELL

M.A. (OXON.), HOW.D.BC. (BELFAST), F.R.S.
FELLOW OF HERTFORD COLLEGE, OXFORD

PREPARED FOR THE PRESS WITH
THE ASSISTANCE OF

E. B. ELLIOTT

M.A., F.R.S., EMERITUS PROFESSOR

OXFORD
AT THE CLARENDON PRESS
1926

PREFACE

My father had spent most of his spare time since the War in writing this book. Only two months before his death, while on our summer holiday in 1924, he had brought some of the chapters with him, and sent off the final draft of them to the Clarendon Press. Even on these holidays, which he greatly enjoyed, we were all accustomed to a good deal of work, and it was an unexpected pleasure to find that with these once dispatched to the press he took an unusually complete holiday.

While rejoicing that he was so far able to complete the book, we are sorry that a last chapter or appendix in which he was greatly interested was hardly begun. Apparently this was to deal with the connection between the rest of the book and Einstein's theory. To the mathematical world his interest in this was shown by his Presidential address to the London Mathematical Society in 1920 - to his friends by the delight he took on his frequent walks in trying to explain in lucid language something of what Einstein's theory meant.

We cannot be too grateful to Professor Elliott, F.R.S., an old friend of many years standing, for preparing the book for the press and reading and correcting the proofs. No labour has been too great for him to make the book as nearly as possible what it would have been. And the task has been no light one.

We should like to thank the Clarendon Press for their unfailing courtesy and for the manner in which the book has been produced.

J M H Campbell.
Christmas 1925.

EDITOR'S NOTE

My dear friend the author of this book has devoted to preparation for it years of patient study and independent thought. Now that he has passed away, it has been a labour of love to me to do my best for him in seeing it through the press. As I had made no special study of Differential Geometry beforehand, and was entirely without expertness in the methods of which Mr. Campbell had been leading us to realize the importance, there was no danger of my converting the treatise into one partly my own. It stands the work of a writer of marked individuality, with rather unusual instincts as to naturalness in presentation. A master's hand is shown in the analysis.

Before his death he had written out and submitted to the Delegates of the University Press, nearly all that he meant to say. An appendix, bearing on the Physics of Einstein, was to have been added;. but only introductory statements on the subject have been found among his papers. Unfortunately finishing touches, to put the book itself in readiness for printing, had still to be given to it. The chapters were numbered in an order which, rightly or wrongly, is in one place here departed from, but they stood almost as separate monographs, with only a very few references in general terms from one to another. To connect them as the author would have done in due course is beyond the power of another. The articles, however, have now been numbered, and headings have been. given to them. Also some references have been introduced. The text has not been tampered with, except in details of expression; but a few foot-notes in square brackets have been appended.

E. B. Elliot