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 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 superseded by another, as exceptions arise to the rule first discovered.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

* 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.

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 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 impor tant 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 plea

sure 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

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 myself considered it. 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 Life of Robertson, vol. ii.

another. They occupy the attention, entirely abstracting it from all other considerations; and they produce a calm agreeable 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. 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 are well known 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. Thoughtless 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 grand-children, to his last hour, and whose chief relaxation from

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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 endowments, 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 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.