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ARITHMETICÁL QUESTIONS,

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TO WHICH ARE SUBJOINED,
A COLLECTION OF ARITHMETICAL TABLES,

QUESTIONS FOR PRACTICAL EXAMINATION,

ANDA

COPIOUS INDEX

BY WILLIAM BUTLER,

TEACHER OF WRITING, ACCOUNTS, AND GEOGRAP!! Y,

IN LADIES' SCHOOLS,

The knowledge of numbers is necessary for every one who is acquainted with
the first elements of learning.

QUINTILIAN.
Arithmetic is of so general use, in all parts of life and bufness, that scarcely
any thing is to be done without it.

LOCKE.
He that requires the attention and application of children, fhould endeavour to
make what he proposes as grateful and agreeable as pollible.

Ibride

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T has been well remarked, that "it is every

man's duty who comes into the world, to use his beft endeavours, however insignificant, to leave it as much wiser and as much better as he can. If this observation inculcates a general duty, it applies with peculiar force to persons engaged in instruction by their profession. Viewing the admonition in this obligatory light, I constantly endeavour to render the several parts of my professional occupation as subservient to the great end that it aims to promote, as their nature will admit. Upon this plan most of the following questions have been composed, which, with several others of a similar kind, but on a more confined scale, have been long distributed among my own scholars; and I have often had the satisfaction of finding them signally instrumental in inspiring a defire of more extensive and circumstantial information. A hope of rendering the questions more generally useful, and a desire of removing the toil of frequent transcription, are my motives for the publication of them. I am nevertheless, aware, that the accomplishment of the former far more important view must depend greatly upon the exertions of the teacher. Should he, inheriting the apathy of Mrs. Shandy, esteem it a matter of utter indifference, " whether the world turns round or stands ftill ;" he will, of course, benefit bis pupils just as much by the common fums, as by A 2

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any that could be selected for him. But other instructors, possessing more animation and zeal, will occasionally require minute accounts of the historical, geographical, chronological, and other subjects which had before served as arithmetical themes. They will, perhaps, with the author, deem the time when the scholars are assembled in classes to repeat their tables (which, I shall take for granted, is always once a week) the best suited for promoting general emulation, and disseminating the desired knowledge among such as are less diligent, or less advanced. For this purpose I have found it highly beneficial to my pupils to give them a task out of the Index, enjoining them to acquire a perfect knowledge of the words, the exact situation of the places, &c. &c. that may occur in the respective parts of their lessons.

The Questions for Examination are employed alternately, in the fame manner, and also occasionally asked when the sums are presented for inspection *. It

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It will not, I trust, be thought irrelevant to the present fubje&t to remark in this place, that, besides the method here recommended, of an attempt to diffuse, in a small degree at least, general knowledge, through the medium of a particular branch of education, a WRITING-MASTER has it, moreover, in his power, to introduce much miscellaneous information into the schools that he attends, by means of a judicious choice of copies for the senior pupils t, particularly geographical ones, (both sacred and profane) and such as contain historical facts, biographical anecdotes, &c. relative to places, rivers, and the like. These examples being transcribed by the scholar, committed to memory, the respective places sought in an atlas (a pursuit which will always afford great entertainment) and then recited to the master, at the times above specified, the pupil, withal, being enjoined to relate in what particular part of the map, section of the globe, &c. the places were found, will, in a short time, and with very little additional trouble to either

+ See the Preface to my engraved Introduction to Arithmetic.

party,

is, however, confefled, that the methods now proposed are impracticable in their full extent, except on the supposition that, during the master's absence, the senior pupils have access to books which treat more largely of some of the subjects recommended to their study. The mention of this circumstance naturally leads me to advert to the great utility of a school-library for the use of those scholars.

In

party, be found to furnish even such as do not learn geography scientifically, with a considerable portion of the knowledge in question, and tend to impress, almost indelibly, upon the minds of those who do, the most valuable part of the lessons which they periodically receive in this delightful ftudy. Let me add, that this is not a mere speculative, theoretical plan, but one the practicability and success of which have been fance tioned by more than forty years extensive experience. Inus circumstanced, I may, without an inexcusable presumption, consider myself as having earned the privilege of speaking with some degree of confidence on the subject, I do therefore most earnestly recommend to the younger part of my professional brethren, the adoption of a similar mode of instruction, as a certain way. of augmenting their usefulness in life, of gratifying the intelligent part of their connexions, and of infallibly promoting their own interest and reputation.

* To a library properly furnished, the parents of such chil. dren as are capable of benefiting by it, could not reafonably object to subscribe 1os. 60. a year; a fum which, in a tolerably large school, would, in no great length of time, completely reimburse the governess for the expence incurred by the first purchase of the books, and enable her to make occasional additions. In the former Editions of this Volume, I had suggefed hints for the formation of a library suitable to the female mind and manners; but so many works of merit have recently been added to the stores of polite literature, and the task of recommending some of these for selection in preference to others, might appear so invi us, that I shall presume on the good sense, tafte, and discrimination of the governelses, for making their respective bibliothecal arrangements; only obferving, in general terms, that they should comprise books of General History, Biography, Geography, Voyages and Tra

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