minutely described, and illustrated by experiments, and their extensive influence in the system of nature particularly detailed. The laws of chemical affinity-the nature and properties of heat, its radiation and expansive power, and the effects it produces on all bodies-the composition and decomposition of water, the nature of crystallization, the properties of earths, metals, acids, and alkalies, the nature of combustion, chemical action and combinations, the component principles of animal and vegetable substances, and various other particulars, may be impressed upon the minds of the young, and rendered familiar by a variety of simple experiments which can be easily performed. Many of the most important and luminous facts of this science may be exhibited by the aid of a few Florence flasks, glass tubes, common phials, tumblers, wine and ale glasses of which I intended exhibiting some specimens, had my limits permitted. In the meantime I refer the reader to Accum's volume entitled "Chemical Amusements," which contains a perspicuous description of nearly 200 interesting experiments on this subject, with an explanation of the rationale of each experiment. Griffin's Recreations in Chemistry; Thomson's, Turner's, Parkes', Graham's and Donovan's treatises, or any other modern system of chemistry, may also be consulted.*

SECTION X.-Mathematics.

A knowledge of certain departments of the mathematical sciences is essentially requisite for understanding many of the discussions and investigations connected with natural philosophy, astronomy, geography, and navigation, and for various practical purposes in the mechanical arts; and, consequently, ought to form

⚫ Notwithstanding the numerous excellent treatises on natural philosophy and chemistry which have been published of late years, we have scarcely any books on these subjects exactly adapted for the use of schools. Blair's "Grammar of Natural Philosophy," and "Conversations" on the same subject, by Mrs. Marcet, contain a comprehensive view of the leading subjects of natural philosophy, which may be recommended to the perusal of young persons; but they are scarcely adapted to the purpose of teaching. Dr. Comstock of America, formerly mentioned, (page 210,) lately published a "System of Natural Philosphy," for the use of students and preceptors, which has already passed through nine editions. This volume contains about 300 closely printed pages, and above 200 wood-cuts, and comprises a popular and scientific illustration of the "Properties of Bodies, Mechanics. Hydrostatics, Hydraulics, Pneumatics, Acoustics, Optics, Astronomy, Elec tricity, and Magnetism," with questions in the margin of every page for exercising the judgment of the student. It is calculated for being an excellent text-book in colleges and academies; but would require to be somewhat reduced and simplified, to adapt it to the use of common schools

possessed of an elec and is acquainted with Over to chint & great variety

Fonts in relation to electricity,

wever Sill to arrest the at and page it te entering on explana

CR of ne. But without th minents of any degree of interest c to these subers. The lustration of motives to expessive apparatus. mang hage bar ragets a large de compess, and a fer needles, Sing my be sufficient for illustrating To this department of philosophy. Soome at a Few This con this subject in Jurine Spent would be needless to w for susting the above hints and anchor, at a very small expense, estate, in a pileusing manner, practical touchs connected with Cunts alluded to above could moxided the experimedter In regard to tion of it himself, which he seg scription, were there a general sisses of the community, it might be of the price now charged for it, as ced of cheaper materials silencis instruments is not always wulf seduce their price to the Sure wall be wasty five great profits tores wat in of a quick and extensive

seat improved state, is a sci

er conected with the of the usefill arts, and ntial science, that an outand thats should be com The distinguishing proshagen igen, carbon, phosphors particularly to ipingen, should be

minutely described, and illustrated by experiments, and their extensive influence in the system of nature particularly detailed. The laws of chemical affinity-the nature and properties of heat, its radiation and expansive power, and the effects it produces on all bodies-the composition and decomposition of water, the nature of crystallization, the properties of earths, metals, acids, and alkalies, the nature of combustion, chemical action and combina tions, the component principles of animal and vegetable substances, and various other particulars, may be impressed upon the minds of the young, and rendered familiar by a variety of simple experiments which can be easily performed. Many of the most important and luminous facts of this science may be exhibited by the aid of a few Florence flasks, glass tubes, common phials, tumblers, wine and ale glasses of which I intended exhibiting some specimens, had my limits permitted. In the meantime I refer the reader to Accum's volume entitled "Chemical Amusements," which contains a perspicuous description of nearly 200 interesting experiments on this subject, with an explanation of the rationale of each experiment. Griffin's Recreations in Chemis try; Thomson's, Turner's, Parkes', Graham's and Donovan's treatises, or any other modern system of chemistry, may also be consulted.*

SECTION X.-Mathematics.

A knowledge of certain departments of the mathematical sciences is essentially requisite for understanding many of the discussions and investigations connected with natural philosophy, astronomy, geography, and navigation, and for various practical purposes in the mechanical arts; and, consequently, ought to form

ptors,

*Notwithstanding the numerous excellent treatises on natural philosophy and chemistry which have been published of late years, we have scarcely any books on these subjects exactly adapted for the use of schools. Blair's "Grammar of Natural Philosophy," and "Conversations" on the same subject, by Mrs. Marcet, contain a comprehensive view of the leading subjects of natural philosophy, which may be recommended to the perusal of young persons; but they are scarcely adapted to the purpose of teaching. Dr. Comstock of America, formerly mentioned, (page 210,) lately published a "System of Natural Philosphy," for the use of students which has already passed through nine editions. T about 300 closely printed pages, and above 200 wood popular and scientific illustration of the "Properties Hydrostatics, Hydraulics, Pneumatics, Acoustics, ( tricity, and Magnetism,” with questions in the m exercising the judgment of the student. It is calc cellent text-book in colleges and academies; but w ed and simplified, to adapt it to the use o

114

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, with out 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 general utility, should be distinctly pointed out as the teacher proceeds in his demonstrations; and the pupil, having previously been oc cupied 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 rela tions 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