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Coin, and Time; (until I see what reception this innovation in figures will meet with.) And for the working thereof, take the following

GENERAL RULE. s 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 necelary.

Such is the method delivered by the Author ; and surely a discovery 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 secret to himself. But as every man has a right to enjoy his own opinion, and as we do not think so highly of this discovery (if indeed it be any discovery at all) we will endeavour to Thew how these boasted factors may be found de novo. Nor will there be the least necessity for our having recourse to any new or abstruse process; the old method of changing vulgar fractions into decimals being abundantly sufficient for the urpose: for they are in fact nothing more than the decimals of units expressed 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 , ta=.008928+.

The factor for ounces, itha=.000558+.
The factor for drams, 25771 3. 0000348+.

Troy weight, the integer a pound.
For ounces, t'i =.0833+.
For penny weights, z1o =.0417-

47. :
For grains, 37605. 000173+.

Coin, the integer a pound Sterling. . For shillings, zo =.05.

For pence, zlo=, 004167.

For farthings, oto=.001041t: And in the very fame manner may factors be found for any other denomination.

Behold! gentle Reader; the tenebrious veil is withdrawn ; the whole secret is discovered; the boasted factors and their origin are seen in open day; and, what is still more, several of them appear to be inaccurate and defective! Inaccurate, because the last figure is too great ; and defective, because the prefixed cyphers are omitted. Mr. Weston indeed observes that cyphers inust be prefixed, where necessary;' but has not told us how we are to know when they are, and when they are not necessary 5 whereas, had those cyphers been suffered to have kept their original places, the difficulty would never have existed, O 4

The The discovery of one secret more will we believe be abun. danıly fufficient to thew the real merit of this nexu species of arithmetic. The whole doctrine, with a table of factors, and the application to practice, may be seen in Mr.Ward's well known treatise entitled The Young Mathematician's Guide, page 70. first Edit.— A book which ever since its first publication in the year 1707, has been in the hands of almost every student in arithmetic.

In a word, the doctrine of solving questions by factors has been known for ages, and particularly practised in the art of gauging. Nor is there hardly a school boy so ignorant as not to know, that, in folving a question in the golden rule, he may either multiply the second and third numbers together, and divide that product by the first number ; or divide the second number by the first, and multiply the third number by that quotient. Now the above quotient is really a factor, and will indeed often tend to shorten the operation. But surely this is no new discovery, unless what has been known ever fince the time of Euclid, at least, and probably long before, can be called by that name.

in Esay on a Course of liberal Education for civil and aclive Life. With Plans of Lectures on I. The Study of History and General Policy. II. The History of England. III. The Constitution and Laws of England. To which are added, Remarks on a Code of Education, proposed by Dr. Brown, in a late Treatise, intitled, Thaughts on Civil Liberty, &c. By Joseph Priestley, L. L. D. Tutor in the Languages and Belles Letters in the Academy. at Warrington. 8vo. 3$. 6d. Boards. Henderson,

TT is a great defect, as Dr. Priestley, very juftly observes, that I in our present system of public education, no peculiar course of study is provided for young gentlemen designed to fill the principal stations in active life; these being indiscriminately brought up in the same manner as others intended for the learned professions.' We have hardly, says he, any medium between an education for the counting-house, consisting of writing, arithmetic, and merchants-accounts, and a method of institution in the abstract sciences : fo that we have nothing liberal, that is worth the aitention of gentlemen, whose views neither of these two opposite plans may suit. ..Formerly, none but the clergy were thought to have any occasion for learning. It was natural; therefore, that the whole plan of education, from the grammar-school, to the finishing at

the

of educat for the use, and, of Huch advantaman fociety rank,

the university should be calculated for their ufe. If a few other persons, who were not designed for holy orders, offered themTelves for education, it could not be expected that a course of ftudies should be provided for them only. And, indeed, as all those persons who fuperintended the bufiness of education were of the clerical order, and had themselves been taught nothing but the rhetoric, lagic, and school-divinity which comprized the whole compass of human learning for several centuries; it could not be expected that they should entertain larger or more liberal views of education; and still less, that they should strike out a course of study for the use of men who were universally thought to have no need of study; and, of whom, few were so fensible of their own wants as to desire any such advantage.

Besides, in those days, the great ends of human fociety seem to have been but little understood, Men of the greatest rank, fortune, and influence; and who took the lead in all affairs of state, had no idea of the great objects of wise and extensive policy; and therefore never apprehended that any fund of knowlege was requisite for the most eminent ftations in the community. Few perfons imagined what were the true sources of wealth, power, and happiness in a nation. Commerce was little understood, or even attended to; and so flight was the connection 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 requisite 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 consequence of all this was, that the advances which were made to a more perfect and improved state of society were very flow; and the present happier state 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 instruments of their own felicity. ... But the situation 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 reħection upon our present advantages, and the Iteps by which we have arrived to the degree of power and happiness we now enjoy, has shewn us the true sources of them; and To thoroughly awakened are all the states of Europe to a sense of their true interests, that we are convinced, the same fupine inattention with which affairs were formerly conducted is no longer fafe; and that, without superior degrees of wisdom and vigour in politil al measures, every thing we have hitherto gained will infal

sibly be loft, and be quickly transferred to our more intelligent and vigilant neighbours. In this critical posture of affairs, more lights and superior industry are requisite, both to ministers of itate, and to all persons who have any influence in schemes of public and national advantage; and confequently a different and a better furniture of mind is requisite to be brought into the business of life.'

To effect this defirable purpose, and furnish the minds of youth with the necessary qualifications for a life of activity and business, is the laudable end of this essay; the Author's general design being, as he himself says, beautifully expressed in the following lines, of Mr. Thomson, describing the future happy state of Great Britain ;...

Instead of barren heads,
Barbarian pedants, wrangling sons of pride,
And truth-perplexing metaphysic wits,

Men, patricts, chiefs and citizens are form’d. To prevent the Reader, however, from being led into any mistake 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 designed to fiil any station in civil and active life, much less the methods which are peculiarly adapted to each separate department of fuch education. The Author's intention is confessedly to point out one capital defect in the usual method of educating young gentlemen who are not designed for any of the learned professions; and at the same time, in some measure to supply that defect, by giving a delineation of a set of lectures equally useful for any department of active life; such 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 becn made to apply, after they have left the grammar-school.

It would afford little entertainment or instruction 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 confessed at the same ' time, however, that even these outlines form a well-grounded presumption that the ingenious Author is very capable of executing what he hath so well planned.

With regard to his remarks on Dr. Brown's proposed code of education, the manner of them is too bold and spirited, and the matter of them too interesing, to be passed slightly over. Dr. Brown had advanced, “That the first and best security of civil · liberty consilis, in impressing the infant mind with such habits of thought and action, aş may correspond with, and promote the

appoint,

appointments of public law*.' Hence he inferred the expedience, and even neceffity, of a prescribed code of education, or sa system of principles, religious, moral and political, whose tendency may be the preservation of the blessings of society, as they are enjoyed in a free state, to be instilled effectually into the infant and growing minds of the community, for the great end of publick happiness ti'

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 state, and securing the perpetuity of our excellent constitution, ecclesiastical and civil.

Dr. Priestley, on the other hand, objects to the interposition, or, as he calls it, interference, of the legillature, in the business of education ; affirming such interposition to be not only prejudicial to the very end and design of education, but also to the great ends of civil societies with respect to their present utility. · He maintains farther, that fuch interposition hath a direct tendency to prevent all future improvement in society; and lastly, that it would be absolutely inconsistent with the true prinçiples of the English government, and could not be carried into execution, to any purpose, without the ruin of our present conftitution.

Our Author confiders these four articles in diftinct and separate sections. With regard to the first, he doth by no ineans agree with Dr. Brown, that the proper design, or only object, of education is the tranquillity of the state. The immediate end of education, he observes, is the forming of wise and virtuous men; which is ultimately an object of the greatest importance in every state. If the constitution, says he, be a good one, < such 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 cases they will render it the greatest service.'

Education, continues he, is as much an art (founded, as all arts are, upon science) as husbandry, as architecture, or as shipbuilding. In all these cases we have a practical problem proposed to us, which must be performed by the help of data with which experience and observation furnish 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 proposed code of education, subjoined to a sermon on the female character and education.

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