Coin, and Time; (until I fee what reception this innovation in figures will meet with.) And for the working thereof, take the following GENERAL RULE. ← MULTIPLY the given Coin, Weight, &c. &c. by the given FACTOR as in Whole Numbers, and the Product is the Decimal, placing your Point of Separation, and prefixing Cyphers where neceffary. Such is the method delivered by the Author; and furely a difcovery that will render the doctrine of vulgar and decimal fractions rather curious than useful, must be of amazing importance to the world! No wonder therefore the Author has thought proper to keep the fecret to himself. But as every man has a right to enjoy his own opinion, and as we do not think so highly of this difcovery (if indeed it be any difcovery at all) we will endeavour to fhew how thefe boafted factors may be found de novo. Nor will there be the leaft neceffity for our having recourfe to any new or abftrufe procefs; the old method of changing vulgar fractions into decimals being abundantly fufficient for the urpofe: for they are in fact nothing more than the decimals of units expreffed in the denominations of the given integers. Thus the factor to find any number of pounds, averdupois weight, the integer being an hundred weight, is,.008928+, The factor for ounces, 1792000558+ The factor for drams, 28672.0000348+. Troy weight, the integer a pound. For ounces,=.0833+. For penny weights, .0417-. For grains, 37=.000173+. Coin, the integer a pound Sterling. T For fhillings, o 05. For pence,=.00416+. For farthings, 80 =.001041+. And in the very fame manner may factors be found for any other denomination. Behold! gentle Reader; the tenebrious veil is withdrawn ; the whole fecret is difcovered; the boafted factors and their origin are seen in open day; and, what is ftill more, feveral of them appear to be inaccurate and defective! Inaccurate, because the laft figure is too great; and defective, because the prefixed cyphers are omitted. Mr. Wefton indeed obferves that cyphers must be prefixed. where neceffary;' but has not told us how we are to know when they are, and when they are not neceffary; whereas, had thofe cyphers been fuffered to have kept their original places, the difficulty would never have exifted. O 4 The The difcovery of one fecret more will we believe be abundantly fufficient to fhew the real merit of this new species of arithmetic. The whole doctrine, with a table of factors, and the application to practice, may be feen in Mr.Ward's well known treatife entitled The Young Mathematician's Guide, page 70. firft Edit.A book which ever fince its first publication in. the year 1707, has been in the hands of almoft every student in arithmetic. In a word, the doctrine of folving questions by factors has been known for ages, and particularly practifed in the art of gauging. Nor is there hardly a school boy fo ignorant as not to know, that, in folving a queftion in the golden rule, he may either multiply the fecond and third numbers together, and divide that product by the firft number; or divide the fecond number by the firft, and multiply the third number by that quotient. Now the above quotient is really a factor, and will indeed often tend to fhorten the operation. But furely this is no new difcovery, unless what has been known ever fince the time of Euclid, at leaft, and probably long before, can be called by that name. An Effay on a Course of liberal Education for civil and active Life. With Plans of Ledures on I. The Study of History and General Policy. II. The Hiftory of England. III. The Conftitution and Laws of England. To which are added, Remarks on a Code of Education, propofed by Dr. Brown, in a late Treatife, intitled, Thoughts on Civil Liberty, &c. By Jofeph Priestley, L. L. D. Tutor in the Languages and Belles Letters in the Academy at Warrington. 8vo. 3s. 6d. Boards. Henderfon, IT is a great defect, as Dr. Priestley very juftly obferves, that in our present fyftem of public education, no peculiar course of ftudy is provided for young gentlemen defigned to fill the principal ftations in active life; thefe being indifcriminately brought up in the fame manner as others intended for the learned profeffions. We have hardly, fays he, any medium between an education for the counting-houfe, confifting of writing, arithmetic, and merchants-accounts, and a method of inftitution in the abstract sciences; fo that we have nothing liberal, that is worth the attention of gentlemen, whofe views neither of thefe two oppofite plans may fuit. Formerly, none but the clergy were thought to have any occafion for learning. It was natural, therefore, that the whole plan of education, from the grammar-school, to the finishing at the the univerfity fhould be calculated for their ufe. If a few other perfons, who were not defigned for holy orders, offered themfelves for education, it could not be expected that a course of ftudies fhould be provided for them only. And, indeed, as all thofe perfons who fuperintended the bufinefs of education were of the clerical order, and had themselves been taught nothing but the rhetoric, logic, and fchool-divinity which comprized the whole compass of human learning for feveral centuries; it could not be expected that they fhould entertain larger or more liberal views of education; and ftill lefs, that they should strike out a courfe of ftudy for the use of men who were univerfally thought to have no need of study; and, of whom, few were fo fenfible of their own wants as to defire any such advantage. Befides, in thofe days, the great ends of human fociety feem to have been but little understood, Men of the greatest rank, fortune, and influence; and who took the lead in all affairs of ftate, had no idea of the great objects of wife and extensive policy; and therefore never apprehended that any fund of knowlege was requifite for the most eminent ftations in the community. Few perfons imagined what were the true fources of wealth, power, and happiness in a nation. Commerce was little underfood, or even attended to; and fo flight was the connec tion of the different nations of Europe, that general politics were very contracted. And thus, men's views being narrow, little previous furniture of mind was requifite to conduct them. A man who was capable of managing a private estate, in the poor manner in which eftates were then managed, had understanding enough to conduct the affairs of a nation. The confequence of all this was, that the advances which were made to a more perfect and improved state of fociety were very flow; and the present happier ftate of things was brought about, rather by an accidental concurrence of circumstances, than by any efforts of human wisdom and forefight. We fee the hand of divine providence in those revolutions which have gradually given a happier turn to affairs, while men have been the paffive and blind inftruments of their own felicity. • But the fituation of things at present is vastly different from what it was two or three centuries ago. The objects of human attention are prodigiously multiplied; the connections of states are extended; a reflection upon our present advantages, and the fteps by which we have arrived to the degree of power and happinefs we now enjoy, has fhewn us the true fources of them; and fo thoroughly awakened are all the states of Europe to a fenfe of their true interefts, that we are convinced, the fame fupine inattention with which affairs were formerly conducted is no longer fafe; and that, without fuperior degrees of wisdom and vigour in politi al measures, every thing we have hitherto gained will infal libly ibly be loft, and be quickly transferred to our more intelligent and vigilant neighbours. In this critical posture of affairs, more lights and fuperior induftry are requifite, both to ministers of ftate, and to all perfons who have any influence in fchemes of public and national advantage; and confequently a different and a better furniture of mind is requifite to be brought into the bufinefs of life.' To effect this defirable purpose, and furnish the minds of youth with the neceffary qualifications for a life of activity and bufinefs, is the laudable end of this effay; the Author's general defign being, as he himfelf fays, beautifully expreffed in the following lines, of Mr. Thomson, defcribing the future happy state of Great Britain; -Inftead of barren heads, Barbarian pedants, wrangling fons of pride, To prevent the Reader, however, from being led into any miftake by the title of this performance, it is not improper to apprize him, that he is not to expect from it, the entire method of conducting the education of a young gentleman defigned to fill any ftation in civil and active life, much lefs the methods which are peculiarly adapted to each feparate department of fuch education. The Author's intention is confeffedly to point out one capital defect in the ufual method of educating young gentlemen who are not defigned for any of the learned profeffions; and at the fame time, in fome measure to fupply that defect, by giving a delineation of a set of lectures equally ufeful for any department of active life; fuch as hath a nearer connection with their conduct in it, and therefore may bid. fairer, both to engage their attention and be of real use to them, than any branch of learning to which they have hitherto been made to apply, after they have left the grammar-school. It would afford little entertainment or inftruction to our readers for us to trace the outlines here laid down; especially as they are indeed bare outlines; being little more than a mere fyllabus or table of contents. It must be confeffed at the fame time, however, that even these outlines form a well-grounded prefumption that the ingenious Author is very capable of executing what he hath fo well planned. With regard to his remarks on Dr. Brown's propofed code of education, the manner of them is too bold and spirited, and the matter of them too interefling, to be paffed flightly over. Dr. Brown had advanced, That the first and beft fecurity of civil liberty confifis, in impreffing the infant mind with fuch habits. of thought and action, as may correspond with, and promote the appoint appointments of public law. Hence he inferred the expedience, and even neceffity, of a prefcribed code of education, or a fyftem of principles, religious, moral and political, whofe tendency may be the prefervation of the bleffings of fociety, as they are enjoyed in a free ftate, to be inftilled effectually into the infant and growing minds of the community, for the great end of publick happiness +.' Thus Dr. Brown pleads for a plan of education established by the legislature, and maintained or kept up by the civil magistrate, And this he affirms to be the only effectual method of preventing faction in the ftate, and fecuring the perpetuity of our excellent conftitution, ecclefiaftical and civil. Dr. Priestley, on the other hand, objects to the interpofition, or, as he calls it, interference, of the legislature, in the bufinefs of education; affirming fuch interpofition to be not only prejudicial to the very end and defign of education, but also to the great ends of civil focieties with refpect to their prefent utility. He maintains farther, that fuch interpofition hath a direct tendency to prevent all future improvement in fociety; and laftly, that it would be abfolutely inconfiftent with the true principles of the English government, and could not be carried into execution, to any purpofe, without the ruin of our prefent conftitution. Our Author confiders these four articles in diftinct and feparate fections. With regard to the first, he doth by no means agree with Dr. Brown, that the proper defign, or only object, of education is the tranquillity of the ftate. The immediate end of education, he obferves, is the forming of wife and virtuous men; which is ultimately an object of the greatest importance in every state. If the conftitution, fays he, be a good one, fuch men will be the greatest bulwarks of it; if it be a bad one, they will be the most able and ready to contribute to its reformation; in either of which cafes they will render it the greatest service.' • Education, continues he, is as much an art (founded, as all arts are, upon fcience) as hufbandry, as architecture, or as fhipbuilding. In all these cafes we have a practical problem propofed to us, which must be performed by the help of data with which experience and obfervation furnifh us. The end of shipbuilding is to make the best ships, of architecture the best houses, and of education, the best men. Now, of all arts, those stand In his Thoughts on Civil Liberty, Licentiousness and Faction :for our thoughts on which work, the Reader may turn to Vol. XXXII. Page 161. In an appendix, relative to a propofed code of education, fubjoined to a fermon on the female character and education. the |