pendence was gratified; and by his frugality and the profits of his works he was enabled to redeem his little estate from some original incumbrances. With this turn of mind it is not to be wondered at that he was led into some singularities in his dress. He completely wore out his clothes; and his wig, which was of a reddish-brown colour, lasted him the greater part of his life. He usually dispensed with a waistcoat, and had his shirt made to button behind, whilst the two lower buttons of his coat were kept in constant requisition. When the brim of his hat began to droop with age and service, he applied the shears to its superfluous parts, and if he did not restore it to its original beauty, he brought it, at least, to its pristine utility.

It has been said that Mr. Emerson, though he had acquired a deep knowledge of all the branches of mathematics and physics, was destitute of genius. If to invent whole sciences at a time, as Newton did the method of fluxions, or to discover such universal and extensive truths as the theory of the universe by the same great man, be necessary to entitle a man to that character, Mr. Emerson was not possessed of genius; but if this is to be the test, there are fewer men of genius than the most censorious amongst us have usually imagined. But if genius* is that intellectual power which can make proficiency in science, as contrasted with dulness in its various degrees from idiotism up to common sense, and, I may say too, common talent, then Mr. Emerson was possessed of it in a very eminent degree, and he gave as unequivocal proof of it as any reasonable man could desire. It would, no doubt, be rather unpleasant to the author of such insinuations to anticipate a similar character after death; but he certainly has exhibited less decisive proofs of genius than Mr. Emerson has done. Mr. E.'s works are eharacterised by industrious research, accurate reasoning, and concentration of thought. They are deservedly esteemed, and will not lose their rank in the public estimation by any cavils which may be raised against their author. Had he been a little more complying, he might have been handed down to posterity with an F. R.S. attached to his name; but this is an honour of which he was not solicitous, and which we are justified in asserting that he despised. He knew that a set of initials could not increase the merits of the man, or the value of his works; he knew too that his writings would be equally esteemed by men of science without these marks of distinction, and he wished to avoid the foolish admiration of those who could be dazzled with an author because he had three letters affixed to his name.

He had enjoyed a very good state of health, with the exception of some slight attacks of the stone, till about 1780. His disorder, however, then

The following definitions by Doctors Hartley and Johnson, will at least appear as good authorities:

"Genius is the art of producing new beauties in works of imagination, and new truths in matters of science."

"The true genius is a mind of great mental powers, accidentally determined to some particular direction:- that quality, without which judgment is cold, and knowledge is inert; that energy which collects, combines, amplifies, and animates; always inves tigating; always aspiring; in its widest researches still longing to go forward ; always something greater than it knows; always endeavouring more than it can do."

began to grow upon him to an alarming degree. He therefore disposed of the whole of his library to a bookseller in York, and quietly rested from his labours. He died May 29th, 1782, in the 81st of his age. year

Mr. Emerson's character has had to contend with the malevolent forgeries of envy and ignorance, in a variety of forms. But of all the accounts which have been published of him, perhaps there is none which has had so exten sive a circulation, and is at the same time so far from the truth, as that of the late Rev. David Simpson, of Macclesfield, in his "Plea for Religion and the Sacred Writings." He is there placed as the fourth of his twelve grand instances of the effects of infidelity; called a rude, vulgar, and immoral man; it is stated that both intoxication and profane language were familiar to him; and that he drew up his objections to the Scriptures much in the same way as Thomas Paine. That when afflicted very dreadfully with the stone, he would crawl about the room on his hands and knees, sometimes swearing, and sometimes praying, just as the humour took him.

Now, Mr. Editor, these are heavy charges, and they ought not to be brought against a man without the clearest proof; and even then the minister of mercy(and such a Christian minister should ever be) would cast the veil of oblivion over them, or at least apologise for them by referring to the weakness of human nature, rather than triumph over the frailty of his brethren. But so far is this from being the case, that after making the most diligent enquiry, I cannot find even the shadow of a fact to justify the assertions of Mr. Simpson; on the contrary, every thing concurs to disprove them. But the author seems to have received his account of Mr. Emerson's character from those who were his determined enemies, and who, with the utmost effrontery, have charged him with every vice of which human nature is capable.

Mr. Simpson's credulity is as proverbial as his industry, and indeed he appears to have been more desirous of saying a great deal, and telling us what books he had read, than of informing us which parts of them were well attested, and which were not. He loved quotations too well to reject any thing which gave him the appearance of a man of extensive information. In this instance, he has been talking without any authority whatever.-After the most diligent enquiry and extensive information, I feel confident that Mr. Emerson was neither a drunkard, a common swearer, nor an infidel; but a man whose character was of the most respectable kind.

D.

Mathematical Repository.

AN ESSAY ON THE USEFULNESS OF MATHEMATICAL LEARNING.

[Concluded from page 231.]

IF we consider to what perfection we now know the courses, periods, distances, and proportions of the several great bodies in the universe that fall

within our view, we shall have cause to admire the sagacity and industry of mathematicians, and the power of numbers and geometry.

With respect to light, how unsuccessful are inquiries about this glorious body without the help of geometry. Those versed in this science have discovered that it has two remarkable properties, the reflection and refraction of its beams; and from these have invented the noble sciences of optics, catoptics, and dioptries. They have also demonstrated the causes of several celestial appearances that arise from the inflection of its beams, both in the heavenly bodies themselves, and in other phenomena, as the perhelia, the iris, &c. Of air and water we know little but what is owing to mechanics and geometry. The two chief properties of air, its gravity and elastic force, have been discovered by mechanical experiments. From thence the decrease of the air's density, according to the increase of the distance from the earth, has been demonstrated by geometers, and confirmed by experiments of the subsidence of the mercury in the Torricellian experiment. From this likewise, by the assistance of geometry, the height of the atmosphere has been determined. Here also mathematicians consider the different pressures, resistances and celerities of solids in fluids; from whence they explain many appearances of nature that are unintelligible to those who are ignorant of geometry.

;

In the animal kingdom, we see the brightest strokes of divine mechanics and whether we consider the animal economy in general, either in the internal motion and circulation of the juices, forced through the several canals by the motion of the heart, or their external motions, and the instruments with which these are performed, we must reduce them to mechanical rules, and confess the necessity of the knowledge of mechanics, either to understand them ourselves, or to explain them to others. But if we consider not only the animal-economy in general, but also the wonderful structure of the different sorts of animals, according to the different purposes for which they were designed, the various elements which they inhabit, the several ways of procur ing their nourishment, and propagating their kind, the different enemies they struggle with, and the accidents they are subject to, here is still a greater need of geometry:

As to the two other kingdoms, mathematics have been applied to explain the nature of vegetation, to fossils and other parts of natural history. And I shall only add, that, if we consider motion the great instrument of the action of bodies upon one another, its theory is entirely owing to the geometers, who have demonstrated its laws, both in hard and elastic bodies ; showed how to measure its quantity, how to compound and resolve the severa forces by which bodies are agitated, and to determine the lines which those compound forces make them describe: of such force is gravity, being the most constant and uniform, that it affords a great variety of useful knowledge in considering the several motions that happen upon the earth; as the free descent of heavy bodies, the curve of projectiles, the descent and weight of heavy bodies, when they lie on inclined planes, the theory of the motion of pendulums, &c.

The usefulness of mathematics in several other arts and sciences is fully as plain. Every body knows that chronology and geography are indispen

VOL. II.

Q ૧

sable preparations for history; a relation of a matter of fact being very imperfect, without the circumstances of time and place. To have a true idea of any city or country, we ought to know the relation it bears to any other place, its climate, heat, cold, length of days, &c.

Nobody, I think, will question the interest which mathematics have in painting, music, and architecture. With respect to painting, perspective and the rules of lights and shadows are owing to geometry and optics. If mathematics had not reduced music to a regular system, it had been no art, but enthusiastic rapture, left to the roving fancy of every practitioner. This appears by the extraordinary pains taken by the ancients to fit numbers to three sorts of music, the diatonie, chromatic, and enharmonic: but music had been still imperfect, had not arithmetic stepped in once more, and Guido Aretinus, by inventing the temperament, and making the fifth false, by a certain determined quantity, taught us to intermix all the three kinds of the ancients, to which we owe all the regular and noble harmony of our modern music. As for civil architecture, there is hardly any part of mathematics but what is someway subservient to it: geometry and arithmetic, for the due measure of a building; for plans, models, computation of materials, time and charges; for ordering right its arches and vaults, that they may be both firm and beautiful: mechanics for its strength and firmness, transporting and raising materials; and optics for the beauty and symmetry of the whole. It must however be owned that he, that should pretend to draw, without any other knowledge of the art, than the geometrical rules of perspective, or compose music merely by his skill in harmonical numbers, would produce very awkward performances. Since all these arts, besides the stiffness of rules, require fancy, genius, and habit. Yet nevertheless, these arts owe their being to mathematics, as laying the foundation of their theory, and affording them precepts, which, being once invented, are securely relied on "by the artist.

I proceed, now, to show the immediate usefulness of mathematics in civil affairs. To begin with arithmetic: it would be an endless task to relate its several uses in public and private business. If we should feel the want of it in the easiest calculations, how much more should we want in those that are something harder, as interest, discounts, annuities, &c., in which it is incredible how much the ordinary rules and tables influence the dispatch of business. Arithmetic is not only the great instrument of private commerce; but by it are or ought to be kept the public accounts of a nation, in regard to the number and fruitfulness of its people, the increase of stock, and the improvement of lands and manufactures; the balance of trade, public revenues, coinage, military power by sea and land, &c. In short numbers are applicable even to such things as seem to be governed by no rule; I mean such as depend on chance; in which the degree of probability, and its proportion in any two proposed cases, is as much a subject of calculation as any thing

else.

The several uses of geometry are not much fewer than those of arithmetic. It is necessary for measuring distances, laying down plans and maps of countries, for ascertaining of property both in planes and solids, or in surveying and guaging. By the help of this science, land is sold by the measure as well as cloth; workmen are paid the due price of their labour, according to

the superficial or solid measure of their work; and the quantity of liquors may be easily determined, for a due regulation of their price and duty.

From astronomy we have the regular disposition of our time, in a due succession of years which are kept within their limits, as to the return of the seasons, and the motion of the sun. This is of no small advantage to our public, private, military, and country affairs. The adjusting of the moon's motion to that of the sun is required for the celebration of the church-feasts and fasts, according to the ancient custom and primitive institution; and likewise for knowing the time for the ebbing and flowing of the tides, the the spring and neap tides, currents, &c. Besides, without a regular chrono logy there can be no certain history.

Mechanics have produced so many useful machines, that it would be too great a task to enumerate them. If we consider such only as are invented for raising weights, and employed in building, and other great works, in which no impediment is too great for them; or hydraulic engines for raising water; or such as by making wind and water perform works which would require a great number of hands, or those invented by mankind to give delight by imitating the motions of animals, &c. we shall have reason to extol so excellent an art. How admirable are those invented to measure time, as clocks, watches, sun-dials, &c. or those for ascertaining the changes in the air, as thermometers, barometers, &c. To this sort of engines, ought to be referred spheres, globes, astrolabes, projections of the sphere, the orrery, &c., by which we are able in our closets to judge of the celestial motions, and to visit the most distant parts of the earth without the fatigue and danger of voyages; to determine their distances, situations, and climates, the nature of their seasons, the length of their days, and their relation to the celestial bodies. To these may be added, those instruments invented by mathematicians for the execution of their own precepts, for making observations either at sea or land, surveying, guaging, &c.

Catoptrics and dioptrics furnish us with a variety of inventions, by which sight the great instrument of our perception is so much improved, that neither the distance, nor the minuteness of the object, are, any longer, impediments to it: they have produced a heat inimitable by our hottest furnaces, and have furnished infallible, easy, cheap, and safe remedies for the decay of sight, commonly arising from old age, and for pur-blindness.

Again, mathematics are highly serviceable to a nation in military affairs, which take in number, space, force, distance, time, &c. as in tactics, castrametation, fortifying, attacking, and defending. The modern method of fortification is built on geometry, by which the lines and angles of a fortification, that contribute most to its strength, are determined. But there is another much harder piece of geometry, which gun-powder has given us occasion to improve, and that is the doctrine of projectiles, on which the art of gunnery is founded. Here the geometers have invented a beautiful theory, and rules and instruments that have reduced the casting of bombs to great is so

exactness.

Lastly, Navigation, which is made up of astronomy and geometry," noble an art, and to which mankind owe so many advantages, that upon this single account those excellent sciences deserve most of all to be studied, and