EAST HAMPTON, MASS.

WILLISTON SEMINARY, located in the village of East Hampton, Mass., owes its existence to the munificence of SAMUEL WILLISTON, who has at various times since 1841, given the sum of fifty-five thousand dollars* ($55,000) toward "the establishment and endowment of an Institution for the intellectual, moral, and religious education of youth." The founder has set forth in a written and published instrument, his wishes for the guidance of those who are, or may be entrusted with the management of its concerns. From this remarkable document, entitled "Constitution of Williston Seminary, at East Hampton, Mass.," we make such extracts as set forth clearly the motivest which actuated the founder, the objects he had in view, and the way in which he hopes to have his objects accomplished. It will be borne in mind by the reader, that these extracts do not contain all that the founder has written under the several heads, but only a portion of the provisions and suggestions which we think may prove serviceable to others who may feel a disposition "to go and do likewise."

Believing, that the image and glory of an all-wise and holy God are most brightly reflected in the knowledge and holiness of his rational creatures, and that the best interests of our country, the church and the world are all involved in the intelligence, virtue, and piety of the rising generation; desiring also, if possible, to bring into existence some permanent agency, that shall live, when I am dead, and extend my usefulness to remote ages, I have thought I could in no other way more effectually serve God or my fellow-men, than by devoting a portion of the property which he has given me, to the establishment and ample endowment of an Institution, for the intellectual, moral and religious education of youth.

Adapting the Institution to the existing wants of the community, and the times in which my lot is cast, I have designed it to be neither a common Academy or an ordinary College, but a Seminary of intermediate grade, which shall combine all the advantages of a Classical Academy of the highest order with such other provisions as shall entitle it to the name of an English College, and which shall be sacredly consecrated with all its pecuniary and moral resources to the common cause of sound learning and of pure and undefiled religion.

It is my wish, that the young men, who repair to it for the purpose of fitting themselves for College, may be thoroughly drilled in all the preparatory studies, particularly in the elements of accurate scholarship in the Latin and Greek * Besides the liberal endowment of the Seminary which bears his name, Mr. Williston is the largest pecuniary benefactor of Amherst College, having given to that Institution the sum of fifty thousand dollars.

t It would be interesting and instructive-and we think impulsive to others, to lift the veil from the first inception, and gradual development of such an institution as this, in the mind of the founder, until we find it a glorious reality in beautiful grounds, substantial buildings, and a well selected library and apparatus, faithful trustees, competent teachers, and diligent and improving pupils.

and it is desired that the Trustees and Teachers should hold out suitable encouragement and inducements to the same.

BOARDING HOUSE.

It is my desire that the Boarding House be kept open and furnished, as it now is, for a Commons or Club, where such students as choose, may associate and board themselves at their own expense, and in their own way; provided, always, that due order be preserved and strict economy and temperance be practiced. Students may also board with private families in the neighborhood; provided, however, that the Trustees may require all to board in some other way, and no student shall be allowed to board in any place which the Trustees shall not approve.

FUNDS OF THE SEMINARY.

To prevent the funds of Williston Seminary from being wasted, I direct that they be loaned, if practicable, on unencumbered real estate, within this Commonwealth, worth, without the buildings, at least twice as much as the sum loaned.

MORAL AND RELIGIOUS CHARACTER.

To preclude all misunderstanding of the design of Williston Seminary, I declare again, in conclusion, that the primary and principal object of the Institution, is the glory of God in the extension of the Christian Religion, and in the promotion of true virtue and piety among men; that the discipline of the mind in all its noble faculties is, and should be deemed next in importance; and that in subservience to these paramount ends, the several branches of useful knowledge, above mentioned, should be assiduously cultivated. Accordingly, I hereby ordain and require, that the School Exercises of each day shall be opened and closed with the reading of the Scriptures and prayer; that at some convenient and suitable hour of each week, an Exercise in the Bible, either a Lecture or Recitation, as may be thought best, shall be held for the benefit of the whole school; that by precept and example, the Teachers shall encourage the pupils in holding occasional meetings for social, religious worship; and that at other times and in other ways, they shall take frequent opportunities to impart moral and religious instruction to the members of the Seminary. And that all these efforts may not be thwarted by the influence of bad members, it is proper and indispensable that great pains be taken, both by Trustees and Teachers, for the prompt removal, by private dismission or public expulsion, as the case may require, of any incorrigibly indolent, disorderly, profane, or otherwise vicious youth from all connection with the Seminary.

The Institution thus constituted by its founder, was organized, mainly, by Rev. Luther Wright, its first Principal, who was consulted by Mr. Williston, from the first inception of the plan. Prof. Wright graduated at Yale College, in 1822-was Tutor there for several years. In 1830, he took charge of Leceister Academy, Mass., which he raised from a depressed condition to one of the most flourishing academies of New England. Mr. Wright built up the reputation of Williston Seminary from the start, on the solid foundation of requiring from his pupils hard study and strict discipline; and when he retired from the school, from impaired health, in 1846, he left this new Seminary second to none other in New England, for the thoroughness of its teaching.

According to the Fourteenth Annual Catalogue, (1854-55,) there were 180 pupils in the classical department, of whom 33 were females, and 163 in the English department, of whom 55 were females. The present Principal is JOSIAH CLARK, M. A.

XIV. SUBJECTS AND METHODS OF INSTRUCTION IN MATHEMATICS;

AS PRESCRIBED FOR ADMISSION TO THE POLYTECHNIC SCHOOL OF PARIS.

BY W. M. GILLESPIE,

Professor of Civil Engineering in Union College.

[Concluded from the May number.]

III. ALGEBRA.

ALGEBRA is not, as are Arithmetic and Geometry, indispensable to every one. It should be very sparingly introduced into the general education of youth, and we would there willingly dispense with it entirely, excepting logarithms, if this would benefit the study of arithmetic and geometry. The programme of it which we are now to give, considers it purely in view of its utility to engineers, and we will carefully eliminate every thing not necessary for them.

Algebraical calculation presents no serious difficulty, when its students become well impressed with this idea, that every letter represents a number; and particularly when the consideration of negative quantities is not brought in at the outset and in an absolute manner. These quantities and their properties should not be introduced except as the solution of questions by means of equations causes their necessity to be felt, either for generalizing the rules of calculation, or for extending the meaning of the formulas to which it leads. CLAIRAUT pursues this course. He says, "I treat of the multiplication of negative quantities, that dangerous shoal for both scholars and teachers, only after having shown its necessity to the learner, by giving him a problem in which he has to consider negative quantities independently of any positive quantities from which they are subtracted. When I have arrived at that point in the problem where I have to multiply or divide negative quantities by one another, I take the course which was undoubtedly taken by the first analysts who have had those operations to perform and who have wished to follow a perfectly sure route: I seek for a solution of the problem which does not involve these operations; I thus arrive at the result by reasonings which admit of no doubt, and I thus see what those products or quotients of negative quantities, which had given me the first solution, must be." BEZOUT proceeds in the same way.

We recommend to teachers to follow these examples; not to speak to their pupils about negative quantities till the necessity of it is felt, and No. 5.-[VOL. II, No. 1.-12.

when they have become familiar with algebraic calculation; and above all not to lose precious time in obscure discussions and demonstrations, which the best theory will never teach students so well as numerous applications.

It has been customary to take up again, in algebra, the calculus of fractions, so as to generalize the explanations given in arithmetic, since the terms of literal fractions may be any quantities whatsoever. Rigorously, this may be well, but to save time we omit this, thinking it better to employ this time in advancing and exercising the mind on new truths, rather than in returning continually to rules already given, in order to imprint a new degree of rigor on their demonstration, or to give them an extension of which no one doubts.

The study of numerical equations of the first degree, with one or several unknown quantities, must be made with great care. We have required the solution of these equations to be made by the method of substitution. We have done this, not only because this method really comprehends the others, particularly that of comparison, but for this farther reason. In treatises on algebra, those equations alone are considered whose numerical coefficients and solutions are very simple numbers. It then makes very little difference what method is used, or in what order the unknown quantities are eliminated. But it is a very different thing in practice, where the coefficients are complicated numbers, given with decimal parts, and where the numerical values of these coefficients may be very different in the same equation, some being very great and some very small. In such cases the method of substitution can alone be employed to advantage, and that with the precaution of taking the value of the unknown quantity to be eliminated from that equation in which it has relatively the greatest coefficient. Now the method of comparison is only the method of substitution put in a form in which these precautions cannot be observed, so that in practice it will give bad results with much labor.

The candidates must present to the examiners the complete calculations of the resolution of four equations with four unknown quantities, made with all the precision permitted by the logarithmic tables of Callet, and the proof that that precision has been obtained. The coefficients must contain decimals and be very different from one another, and the elimination must be effected with the above precautions.

The teaching of the present day disregards too much the applicability of the methods given, provided only that they be elegant in their form; so that they have to be abandoned and changed when the pupils enter on practice. This disdain of practical utility was not felt by our great mathematicians, who incessantly turned their attention towards applica

tions. Thus the illustrious Lagrange made suggestions like those just given; and Laplace recommended the drawing of curves for solving directly all kinds of numerical equations.

As to literal equations of the first degree, we call for formulas sufficient for the resolution of equations of two or three unknown quantities. Bezout's method of elimination must be given as a first application of that fruitful method of indeterminates. The general discussion of formulas will be confined to the case of two unknown quantities. The discussion of three equations with three unknown quantities, x, y, and z, in which the terms independent of the unknown quantities are null, will be made directly, by this simple consideration that the system then really includes only two unknown quantities, to wit, the ratios of x and y, for example,

to z.

The resolution of inequalities of the first degree with one or more unknown quantities, was added to equations of the first degree some years ago. We do not retain that addition.

The equations of the second degree, like the first, must be very carefully given. In dwelling on the case where the coefficient of x2 converges towards zero, it will be remarked that, when the coefficient is very small, the ordinary formula would give one of the roots by the difference of two numbers almost equal; so that sufficient exactness could not be obtained without much labor. It must be shown how that inconvenience may be avoided.

It is common to meet with expressions of which the maximum or the minimum can be determined by the consideration of an equation of the second degree. We retain the study of them, especially for the benefit of those who will not have the opportunity of advancing to the general theory of maxima and minima.

The theory of the algebraic calculation of imaginary quantities, given à priori, may, on the contrary, be set aside without inconvenience. It is enough that the pupils know that the different powers of √-1 continually reproduce in turn one of these four values, ±1, ±√1. We will say as much of the calculation of the algebraic values of radicals, which is of no use. The calculation of their arithmetical values will alone be demanded. In this connection will be taught the notation of fractional exponents and that of negative exponents.

The theory of numbers has taken by degrees a disproportionate development in the examinations for admission; it is of no use in practice, and, besides, constitutes in the pure mathematics a science apart.

The theory of continued fractions at first seems more useful. It is employed in the resolution of algebraic equations, and in that of the ex