THE INTERNATIONAL SCIENTIFIC SERIES.

THE

COMMON SENSE

OF THE

EXACT SCIENCES

BY THE LATE

WILLIAM KINGDON CLIFFORD

WITH ONE HUNDRED FIGURES.

'For information commences with the senses but the whole business
terminates in works. . . . The chief cause of failure in work (especially
after natures have been diligently investigated) is the ill determination
and measurement of the forces and actions of bodies. Now the forces
and actions of bodies are circumscribed and measured, either by distances
of space, or by moments of time, or by concentration of quantity, or by
predominance of virtue; and unless these four things have been well
and carefully weighed, we shall have sciences, fair perhaps in theory,
but in practice inefficient. The four instances which are useful in this
point of view I class under one head as Mathematical Instances and
Instances of Measurement.'-Novum Organum, Lib. ii, Aph. xliv.

NEW YORK

D. APPLETON AND COMPANY
1, 8, AND 5 BOND STREET

1885

PREFACE.

IN March 1879 Clifford died at Madeira, six years afterwards a posthumous work is for the first time placed before the public. Some explanation of this delay must be attempted in the present preface.1

The original work as planned by Clifford was to have been entitled The First Principles of the Mathematical Sciences Explained to the Non-Mathematical, and to have contained six chapters, on Number, Space, Quantity, Position, Motion, and Mass respectively. Of the projected work Clifford in the year 1875 dictated the chapters on Number and Space completely, the first portion of the chapter on Quantity, and somewhat later nearly the entire chapter on Motion. The first two chapters were afterwards seen by him in proof, but never finally revised. Shortly before his death he expressed a wish that the book should only be published

A still more serious delay seems likely to attend the publication of the second and concluding part (Kinetic) of Clifford's Elements of Dynamic, the manuscript of which was left in a completed state. I venture to think the delay a calamity to the mathematical world.

after very careful revision, and that its title should be changed to The Common Sense of the Exact Sciences.

Upon Clifford's death the labour of revision and completion was entrusted to Mr. R. C. Rowe, then Professor of Pure Mathematics at University College, London. That Professor Rowe fully appreciated the difficulty and at the same time the importance of the task he had undertaken is very amply evidenced by the time and care he devoted to the matter. Had he lived to complete the labour of editing, the work as a whole would have undoubtedly been better and more worthy of Clifford than it at present stands. On the sad death of Professor Rowe, in October 1884, I was requested by Messrs. Kegan Paul, Trench, & Co. to take up the task of editing, thus left incomplete. It was with no light heart, but with a grave sense of responsibility that I undertook to see through the press the labour of two men for whom I held the highest scientific admiration and personal respect. The reader will perhaps appreciate my difficulties better when I mention the exact state of the work when it came into my hands. Chapters I. and II., Space and Number; half of Chapter III., Quantity (then erroneously termed Chapter IV.); and Chapter V., Motion, were in proof. With these proofs I had only some half-dozen pages of the corresponding manuscript, all the rest having un

fortunately been considered of no further use, and accordingly destroyed. How far the contents of the later proofs may have represented what Clifford dictated I have had no means of judging except from the few pages of manuscript in my possession. In revising the proofs of the first two chapters, which Clifford himself had seen, I have made as little alteration as possible, only adding an occasional foot-note where it seemed necessary. From page 65 onwards, however, I am, with three exceptions in Chapter V., responsible for all the figures in the book.

After examining the work as it was placed in my hands, and consulting Mrs. Clifford, I came to the conclusion that the chapter on Quantity had been misplaced, and that the real gaps in the work were from the middle of Chapter III. to Chapter V., and again at the end of Chapter V. As to the manner in which these gaps were to be filled I had no definite information whatever; only after my work had been completed was an early plan of Clifford's for the book discovered. It came too late to be of use, but it at least confirmed our rearrangement of the chapters.

For the latter half of Chapter III. and for the whole of Chapter IV. (pp. 116-226) I am alone responsible. Yet whatever there is in them of value I owe to Clifford; whatever is feeble or obscure is my own.