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tations of time; and that he had, like on the Utility of the Mathematics, in finite beings, his present, past, and fu

answer to Queries inserted col. 576, ture. In the preceding part of the same paragraph which Tyro has quoted, he might have found some reasons to supersede his questions; and in col. 25 and 26, of the same number, Sir, he might have perceived the same There is often something in the wordmode of argumentation again resumed: ing of Queries, and the form under to these therefore he is referred. But which they are propounded, which that he may not think his present serves as an index to the opinion of communication slighted, we will sub- the querist, and (if the subject be a conjoin a few remarks on his several ques- troverted one) points to that side of the tions :

controversy, in favour of which he In the First place, he asks—“If an wishes the answer to be given. It is action be past or future to us, how can very probable that some of your coryou make it appear, that it is not so respondents may take the hint, and esto the Almighty, in respect to himself pouse the opinion to which “ G. B. of also ?"-Answer. By proving that He Cardiff,” evidently leans. Allow me, inhabiteth eternity; and that abso- Sir, however, to offer, in behalf of the lutely perfect existence is above all excellence and utility of Mathematical succession. Secondly. Of all the studies, a defence against insinuations transactions which have passed in this to their disadvantage, which to me apworld, are they not past to God, as they pear to be implied in the queries which are to man?”—Answer. If this were the above-mentioned correspondent admitted, God would have successive has submitted for solution. existence, and be continually augment- On this, as on every other occasion ing his experimental knowledge of of dispute, it is essentially necessary things. Thirdly. “ Does not God then to the just discussion of the subject, view the actions as past in regard to that the disputants should attach prehis own perfect or simple knowledge?” cisely the same meaning to whatever - Answer. If this were granted, God terms may be employed in common, would be older to-day than he was in the course of argument. I think it yesterday; and then with him one day proper therefore to premise, that in would not be as a thousand years, nor the term Mathematics, I understand to a thousand years as one day.

be included, not merely what are called The example taken from Abraham pure Mathematics, such as geometry and the Jews, can only be considered and algebra ; but also all the various as illustrative of the preceding ques- branches of mixed Mathematics, as tions. It contains nothing that the astronomy, geography, optics, hydrauformer questions do not include, and lics, hydrostatics, navigation, and metherefore admits of the same replies. chanics; all of which are closely conThe ideas of past and future are merely nected with the former, being chiefly relative, and as such they are suitable indebted to their assistance for the adto the state and condition of beings like vances they have already made towards ourselves. But we cannot reason from perfection, and for whatever there is of the subjects of mortality to the Eternal clearness in the enunciation, or of acGod.

curacy in the demonstration, of their The final question respecting “things principles. To the latter, in fact, the done and to be done” in a disembodied former have served as eyes, by which state, has no connection with the sub- they have found their way up the ject of inquiry. The question should ascent to the commanding eminence have been founded upon the manner they now occupy ; and they still supply in which actions and events are per- the language in which they speak, and ceived by the Almighty, in relation to lend the seal which stamps the authohimself. But instead of this, Tyro has rity of truth and certainty on their delost sight of absolutely perfect, neces- cisions. To the same extent of signisary, and unoriginated existence, and, fication, I hope it is quite fair for me to taking his stand on the nature of finite assume that the term is understood by spirits, has proposed his question on your worthy correspondent. the modes of their perception and First, then, in the way of exordium, knowledge.

I would observe how hard a case it is

On the Utility of the Mathematics.

1754 that the Mathematical Sciences, after | avenues, has a tendency, in proportion the general countenance they have re- to its power of widening, to facilitate ceived, and the credit with which they the acquisition of knowledge of every have maintained their claim on the good description, and, on that account, deopinion and gratitude of the public for serves to be encouraged. On this ages, should now be called to their tri- ground, I conceive, that the Mathebunal, to answer against charges so se- matics have a claim to very particular rious as those implied in the queries attention; since from the peculiar difjust referred to ;-that in spite of the ficulty which attends the full concepgeneral testimony in their favour, a tion of their principles, they may be hint should now be thrown out, that considered as occupying the whole of the whole family ought to be expelled the avenue by which they are received, from the community as useless vaga- and as enlarging the passage for whatbonds, and even branded as traitors to ever may succeed. This illustration the interests of true religion! That in may appear to some a little ludicrous ; every civilized nation they have been but the fact, that the capability of the admired and patronized, in christian mind for receiving knowledge of any countries and by christian people, not kind, is to be estimated, in the progress less than by idolaters and infidels, of its improvement, very greatly from ought to be a safeguard against all the measure of difficulty which has atinsinuations to their disadvantage; tended previous acquisitions of it, is and, till they can be proved to have not to be denied. Hence will appear abused very recently the patronage un- the utility of Mathematical knowder which they have flourished, the ledge; since, for the complete comprelowest claim they can prefer is, to be hension ofits principles, and a thorough allowed to hold on their course clear of knowledge of its pure and abstract molestation. At the same time, how- parts especially, nothing less than the ever, that their advocates feel some- utmost intensity of the most severe atwhat indignant at the frivolous and tention is sufficient. The mental exervexatious charges thrown into the cise by which these are apprehended court of public opinion against them, and received, is an effort which strains they would not confine their apology to the whole mind into a forgetfulness of mere expressions of displeasure, but every thing but its own pure abstracare always ready for a fair and open tions, and renders it for tbe moment trial, either in the court, or on the incapable of the slightest effort of at

tention to any other subject. And first, these sciences plead against As one consequence of this previous the charge of uselessness, that they mental subjection to discipline of this tend very greatly to enlarge and to im- kind, the mind acquires a readier prove the mental faculties of the indi- power of yielding close and undivided vidual who cultivates them. The hu- attention to whatever subject may afman mind may be considered as a vast terwards present itself. And if success receptacle, not indeed absolutely in- in the investigation or pursuit of knowfinite in its capacity (for nothing is in- ledge depends at all, as it certainly finite that is created) but yet of dimen- does very greatly, on the steadiness of sions which exceed, so far as experi- the attention which is paid to it, the ment can ascertain the fact, all limits mind accustomed to such discipline of which we have any idea ; extending will apply itself to study of any kind to the boundaries of creation, and vi- under circumstances of increased adsiting the margins of the celestial and vantage. The mind is further assisted the infernal regions. But, though the by these studies, as it is trained thereby capacity of the mind thus extends in to a correct method of induction; and every direction to a distance whose the reasoning powers are prepared for limit lies somewhere between the ut- a regular and logical investigation of most stretch of our imagination and in- any questions upon other subjects, finity, yet the avenues into it, by which which may come before them. In this knowledge is admitted, are so very way, the advantage of previous hanarrow, that, considering knowledge bituation to the discipline of the Matheunder the emblem of water, they will matics, will be found in the study of only admit its distillation through them ethics and divinity, and in the consiby single drops at once. Whatever deration of all questions, in which it then has a tendency to enlarge these is possible, by a process of argumentaNo. 8. —Vol. I.

3 С


tion, to distinguish truth from error. | understanding raised and excited to The success of all such investigations more divine contemplations."-See depends very considerably on the Hutton's Philosophical and Mathemastrength of the faculty of abstraction; tical Dictionary, art. Mathematics. and nothing is better calculated to Such are the advantages which acstrengthen and improve that faculty, crue to individuals. But I imagine I than the studies I am now defending hear some persons on the other side I am not surprised, therefore, to find still exclaiming, cui bono? and asking, Quinctilian recommending an ac- where is the public benefit? I answer, quaintance with them, as one of the the public advantage is the aggregate most important qualifications for a of that which individuals acquire ; and public speaker. His language on this therefore, when individuals derive besubject is certainly very strong ; for nefit from Mathematics, in the same he even goes so far as to maintain, that proportion that their number bears to very little can be done without them, the mass of society, society itself may when he says

“nullo modo sine geo- be set down as being benefited by their metria potest esse orator.” (Inst. Orat. acquirements. But much more may 1. 10.)*

be urged in their favour than what I Much more might be said, to shew have advanced ; for, like every thing the benefits accruing individuals else that is really valuable, they diffrom these studies, with regard to men- | fuse their benefits abroad, and their tal improvement; but there are other bounty in a thousand ways descends recommendations in their favour which on every rank and condition of manpress on my attention, and I fear to kind. extend this paper to too great a length. The enumeration of their excelI shall therefore content myself with lencies would in fact be an application giving, as a confirmation of what I of the science itself to the summation have advanced, and as a short sum- of an infinite series, and one which mary of what more might be urged on converges so very slowly, that I could the same point, an extract from an not hope soon to come to a satisfactory inaugural oration delivered by the ce- result. The easier and shorter way lebrated Dr. Isaac Barrow, on occa- perhaps will be, to shew not what the sion of his appointment to the Mathe- public enjoy in consequence of the matical Professorship at Cambridge. cultivation of these sciences, but what

“ The Mathematics,” he observes, the world would be without them. effectually exercise, not vainly de- Take away the kindred sciences of lude, nor vexatiously torment, studi- astronomy and navigation, which we ous minds with obscure subtleties, but have already noticed as belonging to plainly demonstrate every thing within the Mathematics, and which, but for their reach, draw certain conclusions, what geometry and algebra have done instruct by profitable rules, and unfold for them, instead of deserving the pleasant questions. These disciplines name of sciences, would be only one likewise inure and corroborate the remove, in the scale of utility and exmind to a constant diligence in study; cellence, from being good for nothing, they wholly deliver us from a cre- Suppose them both to be expunged dulous simplicity, most strongly for- from the book of human knowledge

, tify us against the vanity of scepticism, and nothing to be known of either

, effectually restrain us from a rash pre- beyond what observation and practice sumption, most easily incline us to a will supply; I need not say, the Pardue assent, and perfectly subject us to liament of this country might then the government of right reason. While withdraw the offer they have made of a the mind is abstracted and elevated reward for improvements in the mode from sensible matter, distinctly views of determining the longitude ; for the pure forms, conceives the beauty of mariner, instead of spreading his canideas, and investigates the harmony of vas to every wind on every ocean, proportions; the manners themselves would be found only in the waters imare sensibly corrected and improved, mediately adjoining to the shore

, or in the affections composed and rectified, those diminutive seas that are surthe fancy calmed and settled, and the rounded almost every where by land.

Ages would again elapse before dis* Without a knowledge of geometry, no one

tant continents would be explored; or can be a perfect orator.

more probably they would never be


On the Utility of the Mathematics.


discovered. And all the additional | the frequent occurrence of which, knowledge and advantages of every would greatly diminish their real kind which we derive from friendly in- value, and perhaps render many of tercourse with nations separated from them too generally unpopular, ever to us by a vast expanse of waters, would, be employed much to the general adwith a few trifling exceptions, remain vantage. The latter supposition is utterly beyond our reach : and we most probable; as even with the admight truly say with Horace, “ deas vantage of the additional security and abscidit oceano dissociabili."

certainty which they derive from Ma. Instead of the mutual equilibrium thematics, it is not without great diffinow established by commerce, between culty, and after the lapse of a considerthe wants and the superfluities of va- able length of time, that mechanical rious nations, the inequality of pro- inventions find their way to general duce, consequent on difference of soil employment. I am not saying that and climate, would occasion, accord- men would not, without the knowledge ing to circumstances, a waste on one of Mathematics, stumble on the use hand and a deficiency on the other ; of the lever, the wedge, the inclined and every man's ingenuity and indus- plane, the wheel and axle, the pulley try, would be limited to the land of his and the screw. But if the approprianativity. Nay, more than this; vast tion of these powers be of any service, multitudes of human beings must then why not the science, which defines remain without the light of scriptural their use, and points to the most effirevelation, and destitute of the benefit cient mode of application ? In the of Christian instruction: for the Bible, estimation of all reasonable men, imwhich, since it was first given by in- provements in mechanics are chiefly to spiration, has never found its way any be expected from those, who are well where, but by communication from acquainted with the theory ; as a man man to man, could not then be sup- with eye-sight is much more likely to plied to them, but through difficulties find a treasure that is hidden, than a bordering almost upon impossibility; man without it. If this point be disand the Christian missionary would puted, let history decide the question. either remain ignorant of their real I grant that “ habits of abstraction state, or stand without the power of and theorizing, may be carried to exaffording them relief, and be compelled cess," and that mere theory is good for to leave them to all the horrors, all very little. But there is a correspondent the fatality, of the moral darkness and equivalent disadvantage, on the which surrounds them.

other hand, in practice without theory; Take from mankind the noble science and if these two extremes, in the conof mechanics, and remove along with sideration of the question, should be it all the inventions and improve- allowed to serve as a counterbalance ments in the various arts, which it has to each other, the palm of merit will given to the world ; suppose mankind be awarded to practice and theory to have been left from the beginning, combined together. On this point I or to be left henceforth, to the rude shall beg leave to speak in the lanand uncertain efforts of nature, untu- guage of Professor Dugald Stewart. tored by mathematical science, and as- Care should be taken,” he obsisted only by such maxims as might serves, when writing on this subject, be accumulated in the course of ages “ to guard against both these extremes, by practice and experience; the con- and to unite habits of abstraction with sequence would be, that men would habits of business, in such a manner either depend for the accomplishment as to enable men to consider things of works of art and labour, on their either in general or in detail, as the own unassisted strength, (as the poet occasion may require. Whichever of compels the men engaged in the build- these habits may happen to gain an ing of Carthage, “ manibus subvolvere undue ascendant over the mind, it will saxa,” to roll the stones up with their necessarily produce a character limited hands ;) or, if they had recourse to in its powers, and fitted only for parengines and machines of any kind, ticular exertions. When theoretical would be liable, for want of a theore- knowledge and practical skill are haptical knowledge of mechanics, to many pily combined in the same person, the mistakes in their construction, and to intellectual power of man appears in many accidents in their application, lits full perfection, and fits him equally


to conduct with a masterly hand the absorbed in mathematical studies, that details of ordinary business, and to he did not know when the city of Syracontend successfully with the untried cuse, in which he lived, was taken by difficulties of new and hazardous situa- the enemy. He was killed by a soltions. In conducting the former, mere dier as he was drawing bis figures in experience may frequently be a suffi- the dust. This man had previously cient guide ; but experience and spe- for several months, by the use of his culation must be combined together, to powerful and ingenious contrivances, prepare us for the latter."

Expert bid defiance to all the skill and force men,' says Lord Bacon, 'can execute of the besiegers; and he might proand judge of particulars one by one ; bably, in the end, have saved the city but the general counsels, and the plots, for that time from being taken, but that and the marshalling of affairs, come best the guards (it is supposed) were bribed, from those who are learned.'”—Ele- and Marcellus prevailed against it by ments of the Philosophy of the Human the more powerful influence of gold. Mind, p. 231, &c.)

[To be continued.] It will be needless for me to extend these remarks to any of the other sciences. It is quite enough to have

THE CHOICE. taken a glance at what the world would Wuile others bow at partial Fortune's shrine, be, without those of which we have been speaking. And yet I have a few. Regardless of their sordid choice, be mine

Or run with eager steps Fame's airy chase, examples to bring forward, which will

Fair Science, thro' her secret paths to trace. tend to shew that even the mere theorist is not on certain occasions so contempt

With Newton let me oft advent'rous soar ible a creature, as on others he may The blazing Comet's devious course explore,

“ Above this visible diurnal sphere," seem to be. We may deride the poor

Or mark the progress of the circling year. cheek-worn Mathematician, when we see him sitting encircled by diagrams Or, urg'd remote across the spacious sky, and figures, before a lamp which he Beyond where Georgium greets the wearied never thinks of trimming; but there

sight, have been seasons when such a man

Let Contemplation's philosophic eye, was worth the whole world of mere

Gaze o'er unnumber'd systems with delight. practitioners.

And let the midnight caverns of the deep, On one occasion, Pericles the Athe- Whose shades obscure unnumber'd charms nian, and on another Dion of Syra

conceal, cuse, by their knowledge of astronomy, Where richest gems in endless durance sleep, saved a whole army from being terrified

To Fancy's view their boundless stores reveal. by an eclipse, at a time when the hesi- And while Creation's ample fields unfold tation and delay which would have been Their countless wonders to my bold survey, otherwise occasioned, would have been May ev'ry scene my raptur'd eyes behold, likely to prove ruinous. On the other The great Omnipotent himself display. hand, Nicias, on a similar occasion,

WM. COATES. being unable himself to account for the Balmanno-street, Glasgow. phenomenon, and obtaining from the soothsayers, whom he consulted on the subject, nothing but an augmentation of his terrors, suffered himself and his

TO MARIA, whole army to be struck with a foolish consternation, and although everything Nor the blossoms of Spring such attractions was then ready for his departure on a

disclose, most important expedition, and he was

As beam, lovely nymph, in thy countenance actually going to set sail at the moment

fair; when the eclipse began, he suspended Tho'sweet is the blush that impurples the rose, the enterprise so many days, that he With thee, not the rose can for beauty comlost all the advantage which he would

pare. have gained by surprising his enemies But O shall the blasts of misfortune assail? before they were aware of his ap

Shall want or sball sickness those graces colproach; and the issue of the expedi

sume? tion was in consequence, ruinous to his Or, the victim of guilt, shalt thou hopeless bewail

, whole army. And who has not heard of And shrink in disgust and despair to the Archimedes? who was indeed so deeply tomb ?

# Milton.


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