Now, as I believe that even Mathematics are not much more repugnant than the Talmud to the common apprehension of mankind, and I really love my subject, I shall not quite despair of rousing and retaining your attention for a short time if I proceed to read (as, for greater assurance against breaking down, I shall beg your permission to do) from the pages I hold in my hand.

It is not without a feeling of surprise and trepidation at my own temerity that I find myself in the position of one about to address this numerous and distinguished assembly. When informed that the Council of the British Association had it in contemplation to recommend me to the General Committee to fill the office of President to the Mathematical and Physical Section, the intimation was accompanied with the tranquillizing assurance that it would rest with myself to deliver or withhold an address as I might think fit, and that I should be only following in the footsteps of many of the most distinguished of my predecessors were I to resolve on the latter course.

Until the last few days I had made up my mind to avail myself of this option, by proceeding at once to the business before us without troubling you to listen to any address, swayed thereto partly by a consciousness of the very limited extent of my oratorical powers, partly by a disinclination, in the midst of various pressing private and official occupations, to undertake a kind of work new to one more used to thinking than to speaking (to making mathematics than to talking about them), and partly and more especially by a feeling of my inadequacy to satisfy the expectations that would

be raised in the minds of those who had enjoyed the privilege of hearing or reading the allocution (which fills me with admiration and dismay) of my gifted predecessor, Dr. Tyndall, a man in whom eloquence and philosophy seem to be inborn, whom Science and Poetry woo with an equal spell, and whose ideas have a faculty of arranging themselves in forms of order and beauty as spontaneously and unfailingly as those crystalline solutions from which, in a striking passage of his address, he drew so vivid and instructive an illustration.

From this lotos-eater's dream of fancied security and repose I was rudely awakened by receiving from the editor of an old-established journal in this city, a note containing a polite but peremptory request that I should, at my earliest convenience, favour him with a 'copy of the address I proposed to deliver at the forthcoming meeting.' To this invitation, my first impulse was to respond very much in the same way as did the 'Needy knife-grinder' of the 'Antijacobin,' when summoned to recount the story of his wrongs to his republican sympathiser-Story, God bless you, I have none to tell, Sir!' 'Address, Mr. Editor, I

have none to deliver.'

I have found, however, that increase of appetite still grows with what it feeds on, that those who were present at the opening of the Section last year, and enjoyed my friend Dr. Tyndall's melodious utterances, would consider themselves somewhat ill-treated if they were sent away quite empty on the present occasion, and that, failing an address, the members would feel very much like the guests at a wedding-breakfast

where no one was willing or able to propose the health of the bride and bridegroom.

เ

Yielding, therefore, to these considerations and to the advice of some officially connected with the Association, to whose opinions I feel bound to defer, and unwilling also to countenance by my example the too prevailing opinion that mathematical pursuits unfit a person for the discharge of the common duties of life and cut him off from the exercise of Man's highest prerogative, discourse of reason and faculty of speech divine,'—rather, I say than favour the notion that we Algebraists (who are wont to regard each other as the flower and salt of the earth) are a set of mere calculating-machines endowed with organs of locomotion, or, at best, a sort of poor visionary dumb creatures only capable of communicating by signs and symbols with the outer world, I have resolved to take heart of grace and to say a few words, which I hope to render, if not interesting, at least intelligible, on a subject to which the larger part of my life has been devoted.

The President of the Association, Prof. Stokes, is so eminent alike as a mathematician and physicist, and so distinguished for accuracy and extent of erudition and research, that I felt assured I might safely assume he would, in his Address to the Association at large, take an exhaustive survey, and render a complete account, of the recent progress and present condition and prospects of Mathematical and Physical Science at home and abroad. This consideration narrowed very much and brought almost to a point the ground available for me to occupy in this Section; and as I cannot but be aware that it is as a cultivator of pure mathematics (the subject in which my own researches

have chiefly, though by no means exclusively, lain*) that I have been placed in this Chair, I hope the Section will patiently bear with me in the observations I shall venture to make on the nature of that province of the human reason and its title to the esteem and veneration with which through countless ages it has been, and, so long as Man respects the intellectual part of his nature, must ever continue to be, regarded.†

It is said of a great party leader and orator in the

My first printed paper was on Fresnel's Optical Theory, published in the Philosophical Magazine; my latest contribution to the Philosophical Transactions is a memoir on the 'Rotation of a Free Rigid Body.' There is an old adage, 'purus mathematicus, purus asinus.' On the other hand, I once heard the great Richard Owen say, when we were opposite neighbours in Lincoln's Inn Fields (doves nestling among hawks), that he I would like to see Homo mathematicus constituted into a distinct subclass, thereby suggesting to my mind sensation, perception, reflection, abstraction, as the successive stages or phases of protoplasm on its way to being made perfect in Mathematicised Man. Would it sound too extravagant to speak of perception as a quintessence of sensation, language (i.e. communicable thought) of perception, mathematic of language? We should then have four terms differentiating from inorganic matter and from each other-the Vegetable, Animal, Rational, and Supersensual modes of existence.

Mr. Spottiswoode favoured the Section, in his opening address, with a combined history of the progress of Mathematics and Physics; Dr. Tyndall's address was virtually on the limits of Physical Philosophy; the one here in print is an attempted faint adumbration of the nature of Mathematical Science in the abstract. What is wanting (like a fourth sphere resting on three others in contact) to build up the ideal pyramid is a discourse on the Relation of the two branches (Mathematics and Physics) to, their action and reaction upon, one another, a magnificent theme with which it is to be hoped some future President of Section A will crown the edifice, and make the tetralogy (symbolizable by A+ A', A', A, A.A') complete.

G

House of Lords that, when lately requested to make a speech at some religious or charitable (at all events a non-political) meeting, he declined to do so on the ground that he could not speak unless he saw an adversary before him-somebody to attack or reply to. In obedience to a somewhat similar combative instinct, I set to myself the task of considering certain recent utterances of a most distinguished member of this Association, one whom I no less respect for his honesty and public spirit than I admire for his genius. and eloquence, but from whose opinions on a subject which he has not studied I feel constrained to differ. Goethe has said

*

'Verständige Leute kannst du irren sehn :

In Sachen, nämlich, die sie nicht verstehn.' Understanding people you may see erring-in those things, to wit, which they do not understand.

I have no doubt that had my distinguished friend, the probable President-elect of the next Meeting of the Association, applied his uncommon powers of reasoning, induction, comparison, observation, and invention to the study of mathematical science, he would have become as great a mathematician as he is now a biologist; indeed he has given public evidence of his ability to grapple with the practical side of certain mathematical questions; but he has not made a study of mathematical science as such, and the eminence of his position and the weight justly attaching to his name render it only the more imperative that any assertions proceeding from such a quarter, which may

* Although no great lecture-goer, I have heard three lectures in my life which have left a lasting impression as master-pieces on my memory-Clifford on Mind, Huxley on Chalk, Dumas on Faraday.