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a portion of every course of general education. During the first stages of elementary instruction, a knowledge of the names and some of the properties of angles, triangles, squares, parallelograms, trapezoids, trapeziums, circles, ellipses, parallels, perpendiculars, and other geometrical lines and figures, may be imparted, on different occasions, by way of amusement, as is generally done in infant schools, which would prepare the way for entering on the regular study of mathematical science. The usual method of teaching mathematics is to commence with the "Elements of Euclid," proceeding through the first six, and the eleventh and twelfth books, and afterwards directing the attention to the elements of plane and spherical trigonometry, conic sections, fluxions and the higher algebraic equations, in which the attention of the student is chiefly directed to the demonstration of mathematical propositions, without being much exercised in practical calculations. This is the scientific method of instruction generally pursued in colleges and academies, and if youths of the age of fourteen or fifteen were capable of the attention and abstraction of angelic beings, it would likewise be the natural method. But a different method, I presume, ought to be pursued in schools chiefly devoted to popular instruction. After the pupil has acquired a competent knowledge of arithmetic, let him be conducted through the different branches of practical geometry, including the mensuration of surfaces and solids, artificers' work and land-surveying, exhibiting occasionally a demonstration of some of the rules, in so far as he is able to comprehend it. After which, a selection should be made from Euclid, (chiefly from the first book,) of those propositions which have a practical bearing, and which form the foundation of practical geometry and the operations of plane trigonometry. These, which might be comprehended within the limits of thirty or forty propositions, should be arranged into a kind of system, which might be divided into propositions relating to quadrilateral figures, triangles, circles, and conic sections. The demonstrations of these should be clear and explicit, and as simple as the nature of the subject will admit, and the steps of the demonstration of each proposition should be thoroughly understood before proceeding to another. At the same time, the bearing of the truths demonstrated upon the several practical operations of geometry, and their gene. ral utility, should be distinctly pointed out as the teacher proceeds in his demonstrations; and the pupil, having previously been occupied in calculations relating to geometrical figures, will be enabled to appreciate such demonstrations, and will feel a greater interest in such exercises than he would otherwise do, were he to consider them as relating merely to abstract truths which have

no useful tendency. He might next proceed to the statements and calculations connected with the different cases of plane trigonometry, applying them to the mensuration of all the cases of terrestrial heights and distances, and to the determining of the distances and magnitudes of the heavenly bodies and the altitude of the lunar mountains.

This is the whole course of mathematical instruction I would deem it necessary to communicate in the first instance ;—and, with a knowledge of the practical operations of geometry and trigonometry, and of the principles on which they are founded, the pupil would be enabled to understand all the prominent parts of useful science to which mathematical principles are applicable, and to apply them to the practical purposes of life. If he feel a peculiar relish for mathematical investigations, or if his situation or profession in future life require an extensive knowledge of the higher departments of this study, he can easily prosecute, at his leisure, such studies to any extent, on the foundation of what he had previously acquired. When a young person, of the age of twelve or fourteen, commences the study of "Euclid's Elements," or any similar work, he is at a loss to conceive what useful pur. pose can be served by fixing his mind on squares, parallelograms and triangles, and pestering himself in demonstrating their relations and proportions. After encountering some difficulties, he perhaps acquires a pretty clear conception of the demonstrations of the first and most simple propositions; but as he proceeds in his course, the propositions become more complex and difficult to be conceived, and the steps of the demonstration more tedious and complicated; he forgets the conclusions formerly deduced, his mind becomes bewildered, and, in too many instances, he follows his preceptor in the dark, relying more on his authoritative assertions than on a clear perception of the force of his demonstrations; his ideas become confused, and he loses all relish for the study, because he cannot perceive the practical purposes to which such abstract speculations can be applied. This, it may be affirmed, is the case with more than one-half of those who attempt the study of pure mathematics at an early age, without having previously been exercised in the practical operations of the science. It is for this reason I would recommend a short course, or outline of practical geometry and trigonometry before proceeding to the demonstration of theorems, or the more abstract parts of mathematical science. So far as my experience goes, I have uniformly found, that those who had been well exercised in the different branches of mensuration, and the practical parts of trigonometry, previous to their entering on a course of pure

mathematics, have acquired a relish for such studies, and become eminent proficients in them; while their fellow-students, who had no previous experience in practical calculations, lagged far behind them, and seldom entered into the spirit of such subjects. I could point to several individuals of this description, who ultimately attained the highest mathematical prizes bestowed at the colleges and academies at which they attended.

SECTION XL-Physiology.

This is a department of knowledge which has never yet been introduced into any seminary, as a branch of general education. It is somewhat unaccountable, and not a little inconsistent, that, while we direct the young to look abroad over the surface of the earth and survey its mountains, rivers, seas, and continents, and guide their views to the regions of the firmament, where they may contemplate the moons of Jupiter, the rings of Saturn, and thousands of luminaries placed at immeasurable distances,—that, while we direct their attention to the structure and habits of quadrupeds, birds, fishes, and insects, and even to the microscopic animalculæ in a drop of water—we should never teach them to look into themselves, to consider their own corporeal structures, the numerous parts of which they are composed, the admirable functions they perform, the wisdom and goodness displayed in their mechanism, and the lessons of practical instruction which may be derived from such contemplations. An intelligent writer in the " American Annals of Education," has justly remarked— "The person who should occupy a dwelling seventy, eighty, or a hundred years, and yet be unable to tell the number of its apartments, or the nature and properties of any of its materials, perhaps even the number of stories of which it consisted-would be thought inexcusably ignorant. Yet, with the exception of medical men, and here and there an individual belonging to the other professions, is there one person in a thousand who knows any thing about the elementary materials-the structure or even the number of apartments in the present habitation of his mind?" It is not because this study is either uninteresting or unaccompanied with mental gratification, that it is so generally neglected; for to "know ourselves," both physically and intellectually, is one of the first duties of man, and such knowledge has an extensive practical tendency, and is calculated to gratify the principle of curiosity, and to produce emotions of admiration and pleasure. "Does it afford no pleasure," says the writer I have now quoted, "to study the functions of the stomach and liver, and other organs concerned in changing a mass of beaten food, perhaps some of

the coarser vegetables, into blood?-of the heart, and arteries, and veins, which convey this fluid, to the amount of three gallons, through all parts of the body once in four minutes ?—of the lungs, which restore the half-spoiled blood to its wonted purity, as fast as it is sent into them, and enable it once more to pursue a healthful course through its ten thousand channels?—of the brain, and especially the nerves, which by their innumerable branches spread themselves over every soft part of the human system (and some of the harder parts) which they can possibly penetrate, in such numbers that we can nowhere insert the point of the finest needle without piercing them?—of the skin, every square inch of which contains the mouths or extremities of a million of minute vessels? Is all this, I say, uninteresting? Is there no wisdom displayed in the construction of so complicated, and yet so wonderful a machine, and endowing it with the power of retaining an average heat of 96 or 98 degrees, whether the surrounding atmosphere be heated to 100 degrees or cooled to 32, or even to a much lower point? Is there, moreover, no mental discipline involved in the study of physiology?"*

The evils arising from ignorance of the corporeal functions, and of the circumstances by which they are impaired, are numerous and much to be deplored. From ignorance of the structure and functions of the digestive organs, parents, in many instances, allow their children to eat and drink every thing they desire, and to gorge their stomachs, till diseased action of the organs connected with digestion necessarily ensues, accompanied with the other disorders which generally follow in its train. To the same cause is owing the practice of administering to infants, cordials, elixirs, laudanum, and spirituous liquors-a practice in which no person will indulge who is acquainted with the laws which regulate the functions of the corporeal frame, and which has a tendency not only to injure the individual, but to perpetuate a degenerated race through successive generations. From ignorance of the nature of perspiration, and the functions of the skin, children are permitted to wallow in dirtiness and filth, to remain moist, cold, and benumbed, and to pass days and even weeks without being washed or receiving a change of linens; by which they are, sooner or later, subjected to cutaneous and inflammatory disorders. Ignorance of this subject has likewise led to those awkward at

* Mr. Alcott," American Annals of Education," for September, 1833,a journal which is conducted with admirable spirit by Mr. Woodbridge, and which contains a variety of valuable communications, and much important statistical information, respecting the improvements going forward in Europe and America, in connection with the subject of education.

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the muscular part of the body. They are taken from No. 58. of the " Penny Magazine." Fig. 1. is an outline of the celebrated statue of the Venus de Medicis, which is considered as the most beautiful and symmetrical model of a fine female figure. Fig. 2. is the skeleton of a similar figure, with the bones in

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