English mathematician, biometrician, and eugenicist (1857–1936)
Preface, pp. xii-xiii. Here Pearson refers to Clausius' Ueber die Verdäderungen welche in den bisher gebräuchlichen Formeln für das Gleichgewicht und die Bewegung elastischer fester Körper durch neuere Beobachtungen nothwendig geworden sind, in Poggendorf's Annalen (1849) Vol. 76, pp. 46-67; and to Weber's Königliche Gesellschafl der Wissenschaflen (1835).
My greatest difficulty arose with regard to the rigid line which Dr Todhunter had attempted to draw between mathematical and physical memoirs. Thus while including an account of Clausius' memoir of 1849, he had omitted Weber's of 1835, yet the consideration of the former demands the inclusion of the latter... [with respect to] elastic after-strain. What seemed... needful at... present... was to place before the mathematician the results of physical investigations that he might have some distinct guide to the direction in which research is required. ...I have endeavoured... to abrogate this divorce between mathematical elasticity on the one hand, and physical and technical elasticity on the other. With this aim... I have introduced the general conclusions of a considerable body of physical and technical memoirs in the hope that... I may bring the mathematician closer to the physicist and both to the practical engineer. I trust that in doing so I have rendered this History of value... and so increased the usefulness of Dr Todhunter's... years of patient historical research on the more purely mathematical side of elasticity. In this matter I have kept before me the labours of M. de Saint Venant as a true guide to the functions of the ideal elastician.
The whole early history... is... so intimately connected with the names Galilei, Hooke, Mariotte and Leibniz that I have introduced some account of their work. The labours of Lagrange and Riccati also required some recognition. ...These early writers form the basis... not without interest, whether judged from the special standpoint of the elastician or from the wider footing of... the growth of human ideas. With a similar aim I have introduced throughout the volume... memoirs having purely historical value which had escaped Dr Hunter's notice.
Another class of memoirs which I have inserted are... of mathematical value, omitted apparently by pure accident. For example all the memoirs of F. E. Neumann, the second memoir of Duhamel, those of [P. H.] Blanchet etc. I cannot hope that the work is complete in this respect even now, but I trust that nothing of equal importance has escaped...
I fear that... I may appear to have exceeded the duty of an editor. For all the Articles in this volume whose numbers are enclosed in square brackets I am alone responsible, as well as for the corresponding footnotes, and the Appendix... The principle which has guided me throughout the additions I have made has been to make the work... a standard work of reference for its own branch of science. ...It forms ...the history of a peculiar phase of intellectual development, worth studying for the many side lights it throws on general human progress. On the other hand it serves as a guide to the investigator in what has been done, and what ought to be done. ...[T]he individualism of modern science has not infrequently led to a great waste of power; the same... work has been repeated in different countries at different times, owing to the absence of such histories... [T]he would-be researcher either wastes much of his time in learning the history... or else works away regardless of earlier investigators. ...I have endeavoured to give it completeness (1) as a history of developement, (2) as a guide to what has been accomplished.
We may... be treating merely as physical variations effects which are really due to changes in the curvature of our space; whether, in fact, some or all of those causes which we term physical may not be due to the geometrical construction of our space. There are three kinds of variation in the curvature of our space which we ought to consider as within the range of possibility.
(i) Our space is perhaps really possessed of a curvature varying from point to point, which we fail to appreciate because we are acquainted with only a small portion of space, or because we disguise its small variations under changes in our physical condition which we do not connect with our change of position. The mind that could recognise this varying curvature might be assumed to know the absolute position of a point. For such a mind the postulate of the relativity of position would cease to have a meaning. It does not seem so hard to conceive such a state of mind as the late Professor Clerk-Maxwell would have had us believe. It would be one capable of distinguishing those so-called physical changes which are really geometrical or due to a change of position in space.
(ii) Our space may be really same (of equal curvature), but its degree of curvature may change as a whole with the time. In this way our geometry based on the sameness of space would still hold good for all parts of space, but the change of curvature might produce in space a succession of apparent physical changes.
(iii) We may conceive our space to have everywhere a nearly uniform curvature, but that slight variations of the curvature may occur from point to point, and themselves vary with the time. These variations of the curvature with the time may produce effects which we not unnaturally attribute to physical causes independent of the geometry of our space. We might even go so far as to assign to this variation of the curvature of space 'what really happens in that phenomenon which we term the motion of matter.'
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. ...Shortly before his death he expressed a wish that the book should only be published after very careful revision and that its title should be changed to [our title]. Upon Clifford's death the labour of revision and completion was entrusted to Mr. R. C. Rowe... On the sad death of Professor Rowe... I was requested... to take up the... editing thus left incomplete. ...For the latter half of Chapter III and for the whole of Chapter IV... I am alone responsible. Yet whatever there is in them of value I owe to Clifford; whatever is feeble or obscure is my own. ...With Chapter V. my task has been by no means light. ... I felt it impossible to rewrite the whole without depriving the work of its right to be called Clifford's, and yet at the same time it was absolutely necessary to make considerable changes. ...Without any notice of mass or force it seemed impossible to close a discussion on motion; something I felt must be added. I have accordingly introduced a few pages on the laws of motion [and] since found that Clifford intended to write a concluding chapter on mass. How to express the laws of motion in a form of which Clifford would have approved was indeed an insoluble riddle... because I was unaware of his having written on the subject. I have accordingly expressed... my own views on the subject [i.e.,] a strong desire to see the terms matter and force, together with the ideas associated with them, entirely removed from scientific terminology—to reduce, in fact, all dynamic to kinematic. I should hardly have ventured to put forward these views had I not recently discovered that they have... the weighty authority of Professor Mach... But since writing these pages I have also been referred to a discourse delivered by Clifford at the Royal Institution in 1873, some... of which appeared in Nature June 10, 1880 [pp. 122-123.<nowiki>]</nowiki> Therein it is stated that 'no mathematician can give any meaning to the language about matter, force, inertia used in current text-books of mechanics.' This fragmentary account of the discourse undoubtedly proves that Clifford held on the categories of matter and force as clear and original ideas as on all subjects of which he has treated; only, alas! they have not been preserved.
<small>Footnote: Mr. R. Tucker who... searched Clifford's note books... sends me... the following... in Clifford's handwriting: 'Force is not a fact at all, but an idea embodying what is approximately the fact.'</small>
The rejection of all myth explanation, the reception of all ascertained truths with regard to the relation of the finite to the infinite is what I term freethought or true religious knowledge. ...[T]he freethinker ...possesses more real religion, more of the relation of the finite to the infinite than any mere believer in myth; his very knowledge makes him in the highest sense of the word a religious man.
An imaginary explanation... too often impedes the true explanation when man has attained it. This gives rise to the so-called contests of religion and science or of religion and philosophy—the unintelligible conflicts of "faith" and "reason" which can only arise in the minds of those, who cannot perceive clearly the distinction between myth and knowledge.
The great danger... not content with our real knowledge of the relation of the finite to the infinite, they slur over our vast ignorance by the help of the imagination. Myth supplies the place of true knowledge where we are ignorant of the connection between finite and infinite. Hence... most concrete systems of religion present us with a certain amount of knowledge but a great deal of myth.
[D]efinition... Religion is the relation of the finite to the infinite. ...is the relation. ...[T]here is only one relation, there can be only one religion. ...only so far true as it actually explains the relation of the finite to the infinite. In so far as it builds up an imaginary relation between finite and infinite it is false. ...[S]ince no existing religion lays out before us fully the relation of finite and infinite, all systems of religion are of necessity but half truths. ...not whole falsehoods, for many... may have made... small advance towards the solution...