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Mode of Applyếng it. upon a more general use of the process of cancelling, than is found in other treatises of a similar kind. Neither the principle itself, nor its application is new; but no previous writer, so far as we know, has made the subject equally prominent.
This method is founded upon the principle, that a dividend and a divisor may both be divided by the same number, and their quotients used instead of the original numbers. It is of course applicable to all those classes of operations in which multiplication and division are combined; and especially to all questions which are resolvable into a proportion. In these the result is often truly surprising.
The general mode of application is briefly this: Whatever quantity is to be so used as to increase the final result, is placed upon the right of a perpendicular line, and those quantities which tend to diminish that result, are placed upon the left.When thus arranged, equal numbers appearing upon each side of the line are cancelled, and the quotients of quantities upon each side admitting of division by the same number, are substituted for the numbers divided. When no further reduction can be made, the answer will be found by making the product of the numbers on the right a dividend, and of those in the left a divisor. The following question may serve as an illustration of the mode of operation in the Rule of Three.
If 7 chaldrons cost 85 1-3 guineas, what will 1 pint cost in pence?
By the common rules, 85 1-3 is made the third term of a proportion, 1 the second, and 7 the first. The first and second are then reduced to the same denomination, and the third to the denomination required in the answer; after which the second and third are multiplied together, and their product divided by the first.
By dividing commensurable quantities, the process is greatly simplified. The second and third terms are placed upon the right of the line, and the first term upon the left. As the third term is a mixed number, 85 1-3, it is reduced to an improper fraction, 256; and since the numerator serves to increase the final result, and the denominator to diminish it; the former only is placed upon the right, and the latter upon the left. Instead of actually reducing the first and third terms, the proper multipliers are merely written under them. When thus arranged, they are reduced as follows: As the product of 3 and 4 upon the left, are equal to 12 upon the right, these numbers are cancelled; and so also, for the same reason are 7 and 4 upon
the left, and 28 upon the right. The remaining numbers 8, 8, and 2, upon the left are successively removed by repeated divisions
Few enter our Colleges.
of 256 upon the right, until 2 alone remains upon the right, which is the answer in pence.
This is undoubtedly a favorable specimen of the method, as in many cases little or no advantage can be derived from it, on account of the numbers being principally or wholly prime to each other. Still it is manifest, that the principle is capable of being very extensively applied, especially in mercantile business.
Mr Burnham is evidently master of his subject, but his work bears evidence of haste, and its principles frequently demand a fuller explanation. Even the doctrine of cancelling is not fully developed, and will require additional explanations from the teacher. The examples throughout the work appear to be well selected, and we were glad to see the answers subjoined to the questions. There seems to us no valid objection to this, but if a key is to be published, it seems to us better to print it in small type, and bind it up with the arithmetic.
In perusing this volume, we noticed a few things which appeared to us susceptible of improvement; but have room to mention only one or two.
After explaining the general nature of Fractions, our author first treats of Decimals. This method is liable to the objection, that certain operations in decimals, as for instance, the rule for placing the decimal point in multiplication and division, cannot be demonstrated without a knowledge of vulgar fractions.
In treating of the Rule of Three, the author has revived the old distinction of Direct and Inverse proportion--a distinction both true and important, but tending, we believe, when introduced into elementary works to produce no little confusion in the mind of the student, with no adequate advantage.
The value of a dollar in the currency of North Carolina should have been stated at 105, and not, as in New York, at 85.
WHAT IS A USEFUL EDUCATION ?
(From the Albany Cultivator.")
We have, to be sure, colleges and academies in abundance, more than can be well supported, or than can be made economical and useful. But these are in a measure consecrated to the learned professions—to the privileged few—for they are privileged, inasmuch as they are the exclusive recipients of public bounty in the higher branches of learning. Few of the youth mho enter their halls, ever seek for a livelihood in the laboring
Knowledge seldom Practical.
arts. They learn to look upon labor, as servile and demeaning, and to seek their level in what they consider the higher classes of society.
They do not go to these schools to learn to work, or to learn to live by work, in the common meaning of these terms ; but to learn to live without work-above work. They are virtually withdrawn from the producing classes. These young aspirants flock to the learned professions, and the genteel employments, as the avenues to honors and to office; and notwithstanding that labor is taxed heavily, in one way or another, to supply their real or imaginary wants, yet the genteel professions have become so overstocked, and the threshold of power so thronged with supplicants, that hundreds and thousands are thrown back, as parasites, upon society, exhibiting the melancholy spectacle of men, born to be useful, but unable, or unwilling, from the bias of wrong education, to become so.
Had these men been taught to look upon labor, as it truly is, a necessary, healthful, independent and honorable employment, and been instructed in its principles and its practice, while young, they would have cherished its interests, respected its virtues, and cheerfully shared its toils and its pleasures. We seek not, by these remarks, to pull down that which is, but to build up that which is not. It is not that we love a part less, but the whole more. We would raise the standard of labor, without depressing that of literature.
We have common schools too, munificently endowed, where all may acquire the rudiments of knowledge, but the rudiments only. They teach nothing of the sciences which are necessary to the successful prosecution of the arts—and give no instructions in the best models of practice. They neither teach the boy how to provide for himself, nor fit him for extensive usefulness. They lay the foundation, but they do little to build up and beautify the temple.
Why is it, that six or seven thousand youths, which is about the number in our colleges and academies, should receive gratuities from the public treasury, till the aggregate exceeds three millions of dollars, to enable them to live without work, while half a million of other youth, with like capacities and like claims, destined to labor, and to augment the resources, the wealth and the happiness of their country, are denied a miserable pittance, in the higher branches of knowledge, to qualify them for their more important duties in society? Is not knowledge as beneficial to the arts of labor, as it is to the learned professions ?
We should take care to have good farmers and good mechanics, as well as good lawyers and good doctors. We want, not
Selection of Books for Libraries.
179 only good subjects, bat intelligent freemen—high-minded, independent freemen, who know their rights, and knowing, dare maintain them. We wish to keep the fountains pure, that the stream of power may not become defiled. We wish to base our political and social fabric upon a rock, steadfast and sure-upon the intelligence, industry and moral rectitude of the great working community. When this class shall cease to exert a healthful and a controlling influence in political affairs, our boasted freedom will be at an end.
DISTRICT SCHOOL LIBRARIES.
We have never been quite satisfied with the selections of books for district school libraries, which were published some time ago in the Common School Assistant; and which we suppose have been, to a considerable extent, adopted in the State of N. York. We have wished for something better. The American Society for the Diffusion of Useful Knowledge has made promises, at least indirectly, as we stated in a former number ; but the pressure of the times, or something else, has not permitted the Society is yet to fulfil them.
In the meantime, another selection has been made, which, though it does not by any means meet our wishes, comes nearer our views of the real wants of the community, than anything which has yet been presented. We allude to a selection of one hundred and twentyone, from the four or five hundred volumes published by the American Sunday School Union.They are generally entertaining and instructive biographies; histories of the manners and customs, rites and ceremonies, of various countries and nations; and stories illustrating the great principles of social and personal duty, such as truth, forgiveness, temperance, humanity, honesty, obedience to parents, &c. They are simple in style, adapted in manner and matter to the circumstances of school children, and most salutary in their influence on the order, prosperity, and morals of society.
The libraries are done up in uniform binding-each volume numbered to correspond with its number on the catalogue ; and the lettering to be according to order,–C. S. L., for common school library, or P. S. L., for public school library, or C. L., for children's library, &c. They are put up in a plain case, with a lock and key, and all necessary hangings and fastenings. Upon the door the words School LIBRARY are painted, which
may be altered to suit circumstances. On the inside of the door is pasted a catalogue sheet of the library, and fifty catalogues are furnished besides, in which the design and contents of each volume are concisely described. These are for the use of teachers and pupils. The case is put in a box, and so packed as to be safely transportable to any part of the country, and the whole together is sold for THIRTYTHREE DOLLARS. When it reaches its destination, the case is removed from the outer box, and is all ready to suspend in the school-room arranged for immediate
Now here is a cheap library carefully selected, by judicious men, and instead of existing only in imagination, is ready for delivery. It cannot be called sectarian; since every volume meets the approbation of men of various sects. Among the officers of the American Sunday School Union, are Methodists, Baptists, Congregationalists, Presbyterians, Episcopalians, Lutherans, and we believe of several other denominations.Nor can it well be objected that these books are already scattered through the community by means of our Sunday Schools, since not more than one third of our children and youth attend these schools, and not more than one third of that third have access to the books of the ‘Union ;' and these, even only once or twice a month ; so that unless 5000 books scattered over the whole country among at least 2,500,000 children afford a supply, such an objection can have but little weight. And as to any competition with the American Society for the Diffusion of Useful Knowledge, we think, on the contrary, that it will be the best possible means of preparing the way for the volumes which that Society proposes to issue.
We had almost forgotten to say that the plan meets the entire approbation of good and intelligent men of various parties and sects, in various parts of the country,among whom are Bishop Mc llvaine of Ohio, Gov. Vroom of New Jersey, Chancellor Walworth of New York, Judge Daggett of Connecticut, Hon. Henry Potter of North Carolina, Hon. Francis S. Key, D. C., and Pres. Olin of Randolph-Macon College.