SELECT PAPERS ON VARIOUS SUBJECTS, READ BEFORE A LITERARY SOCIETY IN LONDON. No. V. ON THE ADVANTAGES TO BE DERIVED FROM THE BY MR. YOSEPH DEAN*. I IN all ages and countries where Learning hath prevailed, the Ma thematical Sciences have been justly looked upon as the most considerable branch of it; but, notwithstanding their excellence and reputation, they have neither been taught nor studied so universally as some of the rest; which has probably arisen in a great degree from one or all of the following causes: 1. The aversion of the majority of mankind to serious attention and close investigation ; 2. not comprebending sufficiently their great utility in other parts of learning ; 3. tbe want of public encouragement, and of able masters. For these and perhaps other reasons, this study hath been regarded only by a few persons, whose happy genius or curiosity have prompted them to it; or by some others who have been forced upon it by its evident and immediate subserviency to some object of their pursuit . In the present age of experiment and deduction, the custom of trying events by the standard of truth is becoming more general, and of course the Mathematical Sciences are much more studied now than formerly ; an endeavour, therefore, to point out the advantages derived from them to mankind, will, I conceive, afford considerable pleasure. I shall then briefly attempt to shew their obvious tendency, ist, To beget a babit of attention ; zdly, To furnish a method of close and demonstrative reasoning ; by which, in the 3d place, tbe mind may be delivered from prejudice, credulity, and superstition. And, First, that the Mathematics beget a habit of attention is certain; and this is accomplished by employing the mind on a variety of truths, which are delightful, and at length evident, although not at first obvious. Truth is so amiable, that the discovery of it must always be attended with the most exquisite pleasure; no other method of enquiring after it can in any degree be compared with Mathematical reasoning, the conclusions drawn from hence being infallibly true : In most of the other sciences, consisting only of probable inferences, the mind hath no where to fix itself, and thus wanting sufficient * The Editor believes this Gentleman to be a Teacher of the Mathematics in King's-Head Court, Gough Square, and Mathematical Master at the Grey Coat Hospital. grounds upon which to pursue its researches, gives them over as impossible ; but, in mathematical investigations, the truth, after diligent enquiry, may always be obtained ; and the difficulties which present themselves in the pursuit generally operate as a stimulus to arrive at the end proposed. Secondly, From the study of the Mathematics is obtained a method of close and demonstrative reasoning. Example is more powerful than precept: this universal maxim applies equally in the art of reasoning as in the inferior arts of singing, dancing, &c. By accustoming ourselves to reason closely about quantity (the object of the Mathematical Sciences) we acquire a habit of doing so in other things, and the method of Geometricians, in their analyses, is the model upon which we must form ourselves, in order to make a decisive progress in any object of enquiry; for the way in which Mathematicians arrive at the truth, is by means of definitions of words before agreed upon, self-evident truths, and propositions that have been previously demonstrated; and this is practical in other subjects, although not to the same extent; the natural want of evidence in the things themselves not always allowing it. Permit me to add, that one accustomed to the systems of truth, which Geometricians have reared in the several branches of those sciences which they have respectively cultivated, can hardly bear with the confusion and disorder of many of the other sciences, but will endeavour, as far as he can, to reform them. Thirdly, Mathematical knowledge adds a manly vigour to the mind, and frees it from prejudice, credulity, and superstition. This desirable end it accomplishes in two ways : first, by accustoming us to examine, and not to take things upon trust; 2dly, By giving us a more clear and extensive knowledge of the system of the world, which, while it excites in us a most profound reverence of the almighty and wise Creator, frees us from the mean and narrow thoughts which ignorance and superstition always generate. — The Mathematician asks, Could the Being whose mind projected such a stupendous whole, and whose power enabled him to execute it-He who diffused so many blessings over the whole earth, and clothed her surface with such a variety of good—could he intend that a river, or an arm of the sea, should be the limit of man's goodwill to his fellow-man, or that an unessential difference of opinion should teach men to hate each other? –The philosopher rejects the grovelling idea, passes the narrow boundary of his own country, and emphatically feels and ardently acknowledges the honest man of every region of the world to be his brother. In former times the wily politician, aided by priest-craft, succeeded in causing the Mathematics to be considered as enemies to religion. To the barbarous system of tyranny which they so long and impiously miscalled religion, the Mathematical Sciences were indeed most powerful adversaries : but can that pursuit whose aim is truth, and in the investigation of which a steady adherence to right is es sential, be inimical to morality ? Certainly not. On the contrary, the Mathematical Sciences must ever be the friends of true religion, inasmuch as they calm the passions, restrain the impetuosity of the imagination, and purge the mind from error and prejudice. Having briefly endeavoured to shew how essentially the Mathematics contribute toward the acquirement of a sound and vigorous constitution of mind, I shall next proceed to shew their general, and then their more inmediate practical importance towards the benefit of social life. Every production of nature is in number, weight, and measure, and these are the objects of mathematical pursuit; in order, therefore, to consider them, we should know Arithmetic, Geometry, and Statics. If we consider the degree of knowledge we have now acquired, of the distances, courses, periods, order and proportions of the several great bodies of the universe, we shall have cause to admire the sagacity and persevering industry of Mathematicians, and the power of numbers and geometry. Unassisted by this latter science, how insufficient would be our enquiries about light! But those versed in this science have discovered the two remarkable properties of light, the reflection and refraction of its beams, and hence has been derived the noble science of Optics: they have also demonstrated the causes of several appearances, arising from the inflexion of its rays, both on the heavenly bodies and in other phenomena, as the parrhælia, the iris, &c. Of air and water we know little, but what is owing to Geometry and Mechanics. The two chief properties of air, its gravity and elastic force, were discovered by mechanical experiments. Here, also, Mathematicians consider the different pressures, resistances, and celerities of solids in fluids, whence they explain many of those appearances of nature unintelligible to persons who are ignorant of geometry. If we consider Motion, the great instrument of the action of bodies upon each other, its theory is entirely owing to Geometricians, who have demonstrated its laws, both in inflexible and elastic bodies, shewn how to measure its quantity, how to compound and resolve the several forces by which bodies are agitated, and to determine the lines which those compound forces oblige them to describe. Hence, by combining motion with gravity, whose law is invariable, a great variety of useful knowledge is obtained in considering the several motions that happen upon the earth, as the free descent of heavy bodies, the curves of projectiles, the theory of pendulums, &c. The utility of the Mathematics in several other arts and sciences is equally plain ; for example, Chronology and Geography are indis, pensable preparatives to the reading of history ;-without a knowledge of the first, history is only a confused mass of facts ;-the situations, customs, laws, and manners of nations, are the objects of Ilie other, The interest which the Mathematics have in Painting, Music, and Architecture, cannot be questioned. With respect to Painting ; perspective, and the laws of light and shadow, are owing to Geometry and Optics :-Had not the Mathematics reduced Music to a system, it would have been no art, but enthusiastic rapture, subject to the caprice of every practitioner! As for Architecture, there is hardly any department in the Mathematics, but is someway or other connected with it: Geometry and Arithmetic, for the due measure of the building, for models, plans, computation of materials, time, and charges; for a right disposition of its parts, that they may be both firm and beautiful— Mechanics, for its strength, the transporting and raising of materials; and Optics, for the symmetry of the whole ! These are the foundations upon which the edifice must be reared :--to give them effect, taste, genius, and application to other subjects, will be essential; for although, without a knowledge of these rules, it would be impossible to arrive at eminence in either of the above pursuits, yet he who, with no other than mathematical knowledge, should attempt to delineate nature, combine sounds, or erect a palace, would at best only produce a stiff tree, a disinteresting tune, or an uncomfortable mansion! Having shewn the general utility of Mathematics, I shall now proceed to point out their more immediate usefulness in civil affairs. To begin with Arithmetic. An attempt to ascertain its endless advantages in whatever hath reference to number, would be vain; and indeed they are so self-evident, as to render such an attempt useless : I shall therefore only observe, that numbers are applicable even to such things as seem to be governed by no law; I mean such as depend upon chance, in which the degree of probability, and its proportion in any two cases, are as much the subject of calculation as any thing else. The several uses of Geometry are hardly fewer than those of Arithmetic. Men are hereby paid the price of their labour, according to the plain or solid content of their work :--by this science, the plans of estates, and maps of countries, are laid down, and thus land (as well as cloth) is sold by its measure ; hence also, the height of the inaccessible cliff, or the dimensions of the roaring cataract, may be obtained, &c. The numerous machines, or instruments, invented for overcoming resistances, or raising weights, for measuring time or ascertaining the situation of places, for discovering the state of the atınosphere, or exploring the appearance of the heavens, and for an endless variety of other purposes, which contribute greatly toward the benefit of society, sufficiently demonstrate the importance of Mechanics. The value of a pair of spectacles is comfortably felt in the decline of life; the merchant, in the preservation of his ship, hath often reason to be thankful for the improvement of glasses; and the political consequences likely to arise from the application of the telegraphe, will be an additional evidence of the importance of the telescope; these, among others which might be adduced, are advantages which sufficiently prove the value of the science of Optics. The discovery of gunpowder, as it gave rise to new modes of attack and defence, and called forth the art of Gunnery, rendered it necessary to study the theory of projectiles more particularly, and thus increased the practical consequence of Geometry. Arithmetic, Geometry, Mechanics, and Optics, combine their effects in the production of the sublime system of Astronomy, the study of which cotributes much to the happiness of the individual who pursues it, and adds greatly to the general good of society. By this science, the law of attraction is demonstrated, in the revolution of the universe about a common centre of gravity, the return of comets in their flight through infinite space, the periods of the planets in their passage round the sun, the orbits of satellites in circumscribing their principals, and also the diurnal motion of the earth, and the other celestial bodies, upon their own axes :-hereby we discover the necessity of day and night, the duration of twilight, and the change of seasons; hence we perceive the causes of the eclipses and the ebbing and flowing of the sea; by the aid of this science, the situation of places is precisely determined, and hence the mariner is enabled to arrive at countries separated by vast seas from each other, by tracts as well ascertained as the roads which lead to different towns of the same kingdom! These are some of the deductions of Astronomy; and here we naturally enquire, whether all the order thus rendered visible can be the effect of chance ? Accident could not produce such universal harmony! In them I see the emanations of infinite intelligence, and, seeing, do homage to the Author of the universe !--Passion and prejudice may operate in giving effect to systems of religion, but here the finger of Omnipotence is so obviously displayed, that it seems to me impossible that any other motive than pride can prevent our discovering and acknowledging the hand of a divine Architect, in the erection of so immense and boundless a structure! Lastly, Navigation, which is made up of Astronomy and Geometry, is so noble an art, and to it mankind owe so many advantages, that, on this single account, these excellent sciences deserve most of all to be studied, and doubtless merit the greatest encouragement from a nation who owes to it both its riches and security ! By it, the surplus of our own produce is exported, and the wealth of other countries brought into our ports! by a knowledge of this science, Commerce hath been enabled to spread her happy influence over the world, and although she hath been the harbinger of some vice, yet hath she also been a means of diffusing a ray of knowledge, of bursting the iron gates of prejudice asunder; of collecting men together, and hence, by shewing them their mutual wants, taught them the necessity of mutual good offices. Having thus briefly shewn how much Mathematics improve the mind, how subservient they are to other arts, and how immediately useful to the commonwealth, I shall take the liberty of suggesting |