whose writings form a standard epoch in the history of the progress of knowledge," and that no further advance was made in the theory of mechanics after his death, until the days of Galileo, who lived eighteen hundred years later.

You will all agree with me, I doubt not, that the man over whose theories and calculations eighteen centuries may fairly be said to have rolled, without obliterating their record, or even impairing their value and their importance, may well be numbered among the fixed stars of Science.

It is a striking fact, that Galileo himself, who may well-nigh be included in the same order of intellects, and who was the first to make any advance or improvement in the condition of science after this long interval, prepared himself for pursuing his own great discoveries by perusing the writings of Archimedes. It was while studying the hydrostatical treatise of the old Syracusan philosopher, that he first conceived the idea of writing an essay on a kindred topic. It was that essay, in illustration of some of the discoveries of Archimedes, which gained for Galileo the favor of a patron (Guido Ubaldi, the brother-in-law of Cardinal del Monte) to whom he afterwards owed most of his worldly success.

Would that this high-priest of the stars, as he has well been denominated, could have caught a little more seasonably something of the noble courage of the brave old Syracusan! Would that, when summoned before the Inquisition "for thinking in astronomy otherwise than the Franciscan and Dominican licensers thought," instead of making an ignominious and humiliating abjuration, he might have been seen boldly asserting to their teeth those eternal truths which had been revealed to him; and accepting, if so it must have been, that crown of martyrdom, which would have come to him "plaited with immortal laurels! I know of no scene in history more derogatory to the character of poor human nature, or more derogatory to the dignity of science, than that of Galileo on his knees before the Inquisitors, recanting that great doctrine of the motion of the earth around the sun which it was his glory to have established; and the sublime exclamation which he is related to have made in a whisper,

* Sir David Brewster's Martyrs of Science.

to a friend at his elbow, as he rose from his knees, "It does move, notwithstanding," only adds a deeper shade to our sense of his humiliation.

We shall have abundant evidence, that he did not derive this unworthy spirit of submission from a study of the life of Archimedes. He might rather be supposed to have caught the idea, that such a stooping to arbitrary power was not inconsistent with the beauty and nobleness of his general character, from the example of that leaning tower of Pisa, upon whose summit Galileo is known to have stood in performing some of his experiments and in taking not a few of his observations, and whose unaccountable deflection from a plumb-line seems to have attracted more admiration in some quarters than even the beauty of its proportions or the purity of its material.

It would be tedious and unprofitable to attempt any detailed account, on such an occasion as this, of the writings of Archimedes. He left many works of a scientific character,- treatises on the quadrature of the parabola, on equilibrium and the centres of gravity, on spirals and spheroids and conoids, on the possibility of numbering even the sands on the seashore, — a treatise in which he is said to have anticipated the modern method of logarithms, — and particularly on the sphere and cylinder, his discovery of the precise ratios of which to each other he evidently regarded as the master-work of his life, when he selected these emblems for that forgotten tombstone which Cicero searched for and found.

All these writings, however, were in the cause of pure, abstract, unapplied science; and had his labors ended here, hist name would have had little claim to the reverence of a Mechanic Association, and his character and career would have had still less interest for a general audience. It was by the application of science to art,-it was by the conversion of the results of his profound investigations and marvellous inventions to the direct advantage of his fellow-men, and to the immediate advancement of his country's welfare, that he earned his chief title to be remembered with admiration and gratitude by the great mass of mankind.

It must be acknowledged, however, at the outset, that there is

too much reason for supposing, that most of what he did in this way was prompted by but little feeling of personal respect for any thing of practical art, and by but little original impulse of philanthropy. He lived at a day when it was not thought quite consistent with the dignity of a philosopher to busy himself with any of the common affairs or common interests of society. Plutarch tells us, that "the first that turned their thoughts to Mechanics, a branch of knowledge which came afterwards to be so much admired, were Eudoxus and Archytas, who thus gave a variety and an agreeable turn to Geometry, and confirmed certain problems by sensible experiments and the use of instruments, which could not be demonstrated in the way of theorem.' "But," he adds, "when Plato inveighed against them with great indignation, as corrupting and debasing the excellence of Geometry, by making her descend from incorporeal and intellectual to corporeal and sensible things, and by thus obliging her to make use of matter, which requires much manual labor and is the object of servile trades, then Mechanics were separated from Geometry, and, being a long time despised by the philosophers, were considered only as a branch of the military art."

In another place, in speaking of some of the great machines which Archimedes invented, he says, "Yet Archimedes had such a depth of understanding, such a dignity of sentiment, and so copious a fund of mathematical knowledge, that though in the invention of these machines he gained the reputation of a man endowed with divine rather than human knowledge, yet he did not vouchsafe to leave behind him any account of them in writing. For he considered all attention to Mechanics, and every art that ministers to common uses, as mean and sordid, and placed his whole delight in those intellectual speculations, which, without any relation to the necessities of life, have an intrinsic excellence arising from truth and demonstration only."

The old Greek biographer, indeed, seems disposed even to apologize for the great Geometrician, by representing him, in his mechanical inventions, as yielding reluctantly to the importunity of his royal relative. "He did not think the inventing of them (says he) an object worthy of his serious studies, but only reckoned them among the amusements of Geometry. Nor had he

gone so far, but at the pressing instance of King Hiero, who entreated him to turn his art from abstracted notions to matters of sense, and to make his reasonings more intelligible to the generality of mankind by applying them to the uses of common life."

Thus, according to Plutarch's account, it is King Hiero who deserves the credit of having originally prompted that "application of Science to Art," which is to be the subject of your Lectures, and which is the great secret and source of the wonderful inventions and improvements of modern times. And a brave and noble fellow this Hiero certainly was, Hiero the Second, King of Syracuse, who, during a reign of more than half a century, devoted himself to promoting the arts of peace, adorning the city over which he reigned with numberless works of public utility as well as of great magnificence, while he ruled his people with an almost republican simplicity, and with much of the substance, and not a few of the forms, of a free constitutional government.

A modern commentator on the character of Archimedes * seems to think that Plutarch "confounded the application of geometry to mechanics with the solution of geometrical problems by mechanical means," and that he is mistaken in representing Archimedes as despising all mechanical contrivances and practical inventions. I would gladly believe that this is a true theory, but I confess to a good deal of distrust for these corrections of history eighteen hundred years after it was written, and in regard to points, too, upon which no new facts or new testimony have been, or can be, procured.

But whatever may have been the circumstances under which Archimedes originally turned his mind and his hand to mechanical inventions, and in whatever estimation he may himself have held the practical arts and sciences, the noble use to which he afterwards applied them, no less than the wonderful effects which he afterwards produced with them, will be enough to secure him an everlasting remembrance among men.

There is no more characteristic anecdote of this great philosopher, than that relating to his detection of a fraud in the com

*Professor Donkin of Oxford.

position of the royal crown. Nothing, certainly, could more vividly illustrate the ingenuity, the enthusiasm, and the complete concentration and abstraction of mind with which he pursued whatever problem was proposed to him.

King Hiero, or his son Gelon, it seems, had given out a certain amount of gold to be made into a crown, and the workman to whom it had been entrusted, had at last brought back a crown of corresponding weight. But a suspicion arose that it had been alloyed with silver, and Archimedes was applied to by the King, either to disprove or to verify the allegation. The great problem, of course, was to ascertain the precise bulk of the crown in its existing form; for gold being so much heavier than silver, it is obvious that if the weight had been in any degree made up by the substitution of silver, the bulk would be proportionately increased. Now it happened that Archimedes went to take. a bath, while this problem was exercising his mind, and, on approaching the bath-tub, he found it full to the very brim. It instantly occurred to him, that a quantity of water of the same bulk with his own body must be displaced before his body could be immersed. Accordingly, he plunged in; and while the process of displacement was going on, and the water was running out, the idea suggested itself to him, that by putting a lump of gold of the exact weight of the crown into a vessel full of water, and then measuring the water which was displaced by it, and by afterwards putting the crown itself into the same vessel after it had again been filled, and then measuring the water which this, too, should have displaced, the difference in their respective bulks, however minute, would be at once detected, and the fraud exposed. "As soon as he had hit upon this method of detection (we are told), he did not wait a moment, but jumped joyfully out of the bath, and running naked towards his own house, called out with a loud voice that he had found what he had sought. For, as he ran, he called out in Greek, 'Eureka, Eureka!""

No wonder that this veteran Geometer, rushing through the thronged and splendid streets of Syracuse, naked as a pair of his own compasses, and making the welkin ring with his triumphant shouts, no wonder that he should have rendered the phrase, if not the guise, in which he announced his success,