THE MATHEMATICAL AND

OTHER WRITINGS

OF

ROBERT LESLIE ELLIS, M.A.

LATE FELLOW OF TRINITY COLLEGE, CAMBRIDGE.

EDITED BY

WILLIAM WALTON, M.A.

TRINITY COLLEGE; MATHEMATICAL LECTURER AT

MAGDALENE COLLEGE, CAMBRIDGE.

With a Biographical Memoir

BY

THE VERY REVEREND HARVEY GOODWIN, D.D.

DEAN OF ELY.

CAMBRIDGE:

DEIGHTON, BELL, AND CO.

LONDON: BELL AND DALDY.

DEDICATORY LETTER.

DEAR LADY AFFLECK,

Having undertaken with your sanction the publication of the writings of your lamented brother in a collected form, I may be permitted to address to you a few observations on the principles by which I have been guided in the fulfilment of an act of piety to the memory of a friend of many years, whom I shall ever remember with affection and veneration.

The greater part of the writings contained in this volume had previously appeared in Scientific Journals, and Reports, some few in Educational Treatises. I have had no scruple whatever in reprinting these works, since their publication had already taken place by the author's own act or permission.

The question of the publication of manuscripts presented to my mind greater difficulty. During his long years of suffering he was in the habit of dictating to his friends various speculations in adaptation to their different tastes and pursuits, evidently for the most part not intended for the press. A great many mathematical investigations, which may be described as interesting problems, communicated to me on numerous occasions either by dictation or by letter, are in my possession. Out of these manuscripts I have ventured to publish only two, the one on the Retardation of Sunrise, and the other a new Solution of a Problem in the First Book of Newton's Principia. All the manuscripts entrusted to me by you, classical, philological, botanical, and mathematical, works of a more elaborate character, I have not hesitated to include in this volume, from a conviction that they will be interesting to many readers, and