D'ALEMBERT.

THE pleasures of a purely scientific life have often been described; and they have been celebrated with very heartfelt envy by those whose vocations precluded or interrupted such enjoyments, as well as commended by those whose more fortunate lot gave them the experience of what they praised; but it may be doubted, if such representations can ever apply to any pursuits so justly as to the study of the mathematics. In other branches of science the student is dependent upon many circumstances over which he has little control. He must often rely on the reports of others for his facts; he must frequently commit to their agency much of his inquiries; his research may lead him to depend upon climate, or weather, or the qualities of matter, which he must take as he finds it; where all other things are auspicious, he may be without the means of making experiments, of placing nature in circumstances by which he would extort her secrets; add to all this the necessarily imperfect nature of inductive evidence, which always leaves it doubtful if one generalization of facts shall not be afterwards superseded by another, as exceptions arise to the rule first discovered. But the geometrician relies entirely on himself; he is absolute master of his materials; his whole investigations are conducted at his own good pleasure, and under his own absolute and undivided control. He seeks the aid of no assistant, requires the use of no apparatus, hardly wants any books; and with the fullest reliance on the perfect instruments of his operations, and on the altogether certain nature of his results, he is quite assured that the truths which he has found out, though they may lay the foundation of further discovery, can never by possibility be disproved, nor his reasonings upon them shaken, by all the progress that the science can make to the very end of time.

The life of the geometrician, then, may well be supposed an uninterrupted calm; and the gratification which he derives from his researches is of a pure and also of a lively kind, whether he contemplates the truths discovered by others, with the demonstrative evidence on which they rest, or carries the science further, and himself adds to the number of the interesting truths before known. He may be often stopped in his researches by the difficulties that beset his path; he may be frustrated in his attempts to discover relations depending on complicated data which he cannot unravel or reconcile; but his study is wholly independent of accident; his

It may be as well to adopt the expression always used on the Continent, to denote the cultivation of mathematical science:-"Ce grand géomètre," is a phrase now universally understood and applied to mathematicians of every description.

reliance is on his own powers; doubt and contestation and uncertainty he never can know; a stranger to all controversy, above all mystery, he possesses his mind in unruffled peace; bound by no authority, regardless of all consequences as of all opposition, he is entire master of his conclusions as of his operations; and feels even perfectly indifferent to the acceptance or rejection of his doctrines, because he confidently looks forward to their universal and immediate admission the moment they are comprehended.

It is to be further borne in mind, that from the labours of the geometrician are derived the most important assistance to the researches of other philosophers, and to the perfection of the most useful arts. This consideration resolves itself into two: one is the pleasure of contemplation, and consequently is an addition to the gratification of exactly the same kind, derived immediately from the contemplation of pure mathematical truth; much, indeed, of the mixed mathematics is also purely mathematical investigation, built upon premises derived from induction. The other gratification is of a wholly different description; it is connected merely with the promotion of arts subservient to the ordinary enjoyments of life. This is only a secondary and mixed use of science to the philosopher; the main pleasure bestowed by it, is the gratification which, by a law of our nature, we derive, from contemplating scientific truth when indulging in the general views which it gives, marking the unexpected relations of things seemingly unconnected, tracing the resemblance, perhaps identity, of things the most unlike, noting the diversity of those apparently similar. This is the true and primary object of scientific investigation. This it is which gives the pleasure of science to the mind. The secular benefits, so to speak, the practical uses derived from it, are wholly independent of this, and are only an incidental, adventitious, secondary advantage. I have fully explained this doctrine in the Preliminary Discourse to the works of the Society for the Diffusion of Useful Knowledge, and in the Introduction to the "Political Philosophy." It never had been stated, as far as I know, before; but it rests on such irrefragable principles, that it has not since been called in question.*

It is an illustration of the happiness derived from mathematical studies, that they possess two qualities in the highest degree, not perhaps unconnected with one another. They occupy the attention, entirely abstracting it from all other considerations; and they produce a calm agrecable temper of mind.

Their abstracting and absorbing power is very remarkable, and is known to all geometricians. Every one has found how much more swiftly time passes when spent in such investigations, than in any other occupation either of the senses or even of the mind.

It gave me great pleasure to find it highly approved by my revered friend, Professor Stewart, who regarded it as indeed of more value and originality than I had considered myself. The outline of it had been read many years before (1798) in a literary society at Edinburgh, to which Lord Jeffrey, Dr. Brown, Mr. Horner, and others belonged. See Appendix to this Life.

Sir Isaac Newton is related to have very frequently forgotten the season of meals, and left his food awaiting for hours his arrival from his study. A story is told of his being entirely shut up and disappearing, as it were eclipsed, and then shining forth grasping the great torch which he carried through the study of the heavens; he had invented the Fluxional Calculus. I know not if there be any foundation for the anecdote; but that he continually remained engaged with his researches through the night is certain, and that he then took no keep of time is undeniable. It does not require the same depth of understanding to experience the effects of such pursuits in producing complete abstraction; every geometrician is aware of them in his own case. The sun goes down unperceived, and the night wanes afterwards till he again rises upon our labours.

They who have experienced an incurable wound in some prodigious mental affliction, have confessed, that nothing but mathematical researches could withdraw their attention from their situation. Instances we know of a habit of drinking being cured by the like means; an inveterate taste for play has within my own observation been found to give way before the revival of an early love of analytical studies. This is possibly a cause of the other tendency, which has been mentioned, the calming of the mind. We have seen in the life of Simson, how he would fly from the conflicts of metaphysical and theological science, to that of necessary truth, and how in those calm retreats he ever "found himself refreshed with rest."* Greater tranquillity is possessed by none than by geometricians. Even under severe privations this is observed. The greatest of them all, certainly the greatest after Newton, was an example. Euler lost his sight after a long expectation of this calamity, which he bore with perfectly equal mind; both in the dreadful prospect and the actual bereavement, his temper continued as cheerful as before, and his mind, fertile in resources of every kind, supplied the want of sight by ingenious mechanical devices, and by a memory more powerful even than before. He furnishes an instance to another purpose. Thought

* Vol. i., p. 477.

My late learned and esteemed friend, Mr. Gough, of Kendal, was another example of studies being pursued under the same severe deprivation-but he had never known the advantages of sight, having lost his eyes when an infant, and never had any distinct recollection of light. He was an accomplished mathematician of the old school, and what is more singular, a most skilful botanist. His prodigious memory resembled Euler's, and the exquisite acuteness of his smell and touch supplied in a great measure the want of sight. He would describe surfaces as covered with undulations which to others appeared smooth and even polished. His ready sagacity in naming any plant submitted to his examination was truly wonderful. I had not only the pleasure of his acquaintance, but I have many particulars respecting his rare endow. ments, from another eminent mathematician, who unites the learning of the older with that of the modern school, my learned friend and neighbour, Mr. Slee, of Tirrel. A detailed account of Mr. Gough's case, by

less and superficial observers have charged this science with a tendency to render the feelings obtuse. Any pursuit of a very engrossing or absorbing kind may produce this temporary effect; and it has been supposed that men occasionally abstracted from other contemplations, are particularly dull of temper. But no one ever had more warm or kindly feelings than Euler, whose chief delight was in the cheerful society of his grandchildren, to his last hour, and whose chief relaxation from his severer studies was found in teaching these little ones.

It has been alleged, and certainly has been somewhat found by experience to be true, that the habit of contemplating necessary truth, and the familiarity with the demonstrative evidence on which it rests, has a tendency to unfit the mind for accurately weighing the inferior kind of proof which alone the other sciences can obtain. Once finding that the certainty to which the geometrician is accustomed cannot be attained, he is apt either to reject all testimony, or to become credulous by confounding different degrees of evidence, regarding them all as nearly equal from their immeasurable inferiority to his own species of proof-much as great sovereigns confound together various ranks of common persons, on whom they look down as all belonging to a different species from their own. In this observation there is, no doubt, much of truth, but we must be careful not to extend its scope too far, so as that it should admit of no exceptions. The following life affords one of the most remarkable of these; as far as physical science went, Laplace afforded another; in several other branches he was, perhaps, no exception to the rule.*

The hold which their favourite studies have, and keep over geometricians is not the least remarkable proof of the gratification which they are calculated to afford.-I well know, to take one instance within my own observation, that my learned and esteemed friend, the present Lord Chancellor, a most successful student of the mathematics in his earlier years, reverted to the pursuits in which he had so often found delight, long after he had held the highest offices and been engaged in the most dissimilar discussions. As late as 1838, when I was engaged in preparing my Analytical Review of the Principia, I found that, by an accidental coincidence, he was amusing his leisure with the calculus long intermitted; and I am sure that he could have furnished as correct and more

Mr. Slee and Professor Whewell (a pupil of his), would be most curious and instructive. Euler's memory was such, that he could repeat the Eneid, noting the words that begin and end each page. Mr. Gough also was an excellent classical scholar.

* It is said that when the Emperor asked him why he had left out the consideration of a Supreme Intelligence in his speculations, he answered that he conceived he could explain the phenomenon without that hypothesis. But when we look to his demonstration of the high improbability of the system having been formed without an intelligent cause, (above four millions of millions to one he proves it in his Calcul de Probabilité,) we cannot lend much faith to this Paris anecdote.

elegant analytical demonstrations of the Newtonian theorems than I had the fortune to obtain in composing that work.

I have thought it a useful thing to consider the personal history with the scientific achievements of a very great geometrician, with a view to the illustration of these remarks-and I have chosen D'Alembert in preference to Euler or to Clairaut, the two other illustrious analysts of their age, because we have more ample materials for the study. Whatever of peace and comfort he enjoyed, D'Alembert owed to geometry, and confessed his obligations. Whatever he suffered from vexation of any sort, he could fairly charge upon the temporary interruption of his mathematical pursuits. In both portions of his history, therefore, it is likely to prove instructive, and to enforce the doctrine which I have laid down.

Jean le Rond d'Alembert was born on the 17th of Nov. 1717, being a foundling exposed near the church of St. Jean le Rond in Paris, and thus called by the name of the parish, as is usual in most countries. The commissary of the district, before whom the infant was carried, perceiving its feeble and almost dying condition, instead of sending it to the hospital gave the charge to the wife of a poor but honest glazier in the neighbourhood, living in the Rue Michel-le-Comte, for he was acquainted with the good woman's respectability. In a few days the father, M. Destouches, commissary of artillery, came forward to own the child, and made provision for its support. The general belief is, that the exposition had been concerted with the police. But if so, a very needless risk was unaccountably incurred by exposing so tender an infant in a winter's night, when the parties might have sent it at once to the place where it was destined to be brought up. It is more likely that the mother, afraid of discovery, if not of the burden to be thrown upon her, caused the exposure before the father was apprised of the birth having happened, and that as soon as he knew of what had been done, he hastened to send after the person who had been entrusted with the charge. The mother was an unmarried lady, sister to Cardinal Tencin, Archbishop of Lyons, and she was afterwards well known in the circles of Paris as a person of rare talents and accomplishments. Marmontel, in his Memoirs, calls her Madame de Tencin, she having probably in her old age passed by that name; and he relates some of her sayings, of which one is singular in relation to the life of her celebrated son. "Wo to him," she said, "who depends for his subsistence on his pen! The shoemaker is secure of his wages; the bookmaker is not secure of any thing." She was wont also to give the result of her experience of men, by recommending persons who lacked friends to prefer choosing them among women, as they are far more zealous to serve those they wish well to; but then, she added, "You must be their friend, and not their lover." She was the author of a novel, " Les Mémoires du Comte de Cominges," of which a good judge, Baron Grimm, says, "Il est en possession de faire pleurer." After giving an account of the plot, he adds, "11

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