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mancy in the whole business. John Maw (his Indian name I have forgotten), a full-blood, with several others, were selected for this purpose.-The tribe watched the youths for several months with anxiety, and when they offered themselves for examination, the feelings of all were wrought up to the highest pitch. The youths were separated from their master and from each other, and watched with great care. The uninitiated directed what master and pupil should write to each other, and the tests were viewed in such a manner as not only to destroy their infidelity, but most firmly to fix their faith."

36. Conventional written signs as expressive of numbers and

quantities.

The invention of written signs, as well as oral, gave increased power to the action of the mind; and the assistances thus rendered were so obvious and decisive, that the principle of expressing thoughts by conventional written signs was extended to other cases. Hence the origin of numerical and algebraic expressions. In the science of Algebra, the subjects of mathematical analysis, such as extension, quantities, forces, and their relations, instead of being expressed by words and sentences in the ordinary way, are represented by the letters of the alphabet. At first the large or capital, and afterward the small letters, being in some respects more convenient, were used for this purpose. And the system has been by degrees fully extended, not only to the quantities and forces thus represented, but to the operations performed in respect to them. It was regarded by scientific persons as an improvement worthy of some notice, when the processes of adding and subtracting in algebra came to be expressed by the Latin terms plus and minus; it was considered a further improvement when these terms were in writing abridged into the initial letters p and m, and when they were subsequently altered into the signs + and -, &c.

The late Mr. Playfair, in his Historical Sketch of the Discoveries and Improvements in Science from the Revival of Letters to the present Century, has the following instructive remarks on the subject before us.-Speaking of some improvements by Des Cartes, he adds, "the leadVOL. II. QQ

ing principles of algebra were now unfolded, and the notation was brought, from a mere contrivance for abridging the common language, to a system of symbolical writing, admirably fitted to assist the mind in the exercise of thought.

"The happy idea, indeed, of expressing quantity and the operations on quantity by conventional symbols, instead of representing the first by real magnitudes, and enunciating the second in words, could not but make a great change in the nature of mathematical investigation. The language of mathematics, whatever may be its form, must always consist of two parts; the one denoting quantities simply, and the other denoting the manner in which the quantities are combined, or the operations understood to be performed on them. Geometry expresses the first of these by real magnitudes, or what may be called natural signs; a line by a line, an angle by an angle, an area by an area, &c.; and it describes the latter by words. Algebra, on the other hand, denotes both quantity and the operations on quantity by the same system of conventional symbols. Thus, in the expression 3—ax2 +b2=0, the letters a b x denote quantities, but the terms r3 ax2, &c., denote certain operations performed on those quantities, as well as the quantities themselves; x3 is the quantity raised to the cube; and ax the same quantity a raised to the square, and then multiplied into a, &c.; the combination, by addition or subtraction, being also expressed by the signs + and -.

"Now it is when applied to this latter purpose that the algebraic language possesses such exclusive excellence. The mere magnitudes themselves might be represented by figures, as in geometry, as well as in any way whatever; but the operations they are to be subjected to, if described in words, must be set before the mind slowly and in succession, so that the impression is weakened and the clear apprehension rendered difficult. In the algebraic expression, on the other hand, so much meaning is concentrated into a narrow space, and the impression made by all the parts is so simultaneous, that nothing can be more favourable to the exertion of the reasoning powers, to the continuance of their action, and their security against error."

CHAPTER IV.

CHARACTERISTICS OF LANGUAGES.

37. All languages have their characteristic traits.

FROM the consideration of the origin and use of particular words and phrases, we naturally proceed to the characteristic peculiarities of languages. It is with nations, in some degree, as with individuals; every nation has a character, as each man has; and, in like manner, every language possesses its distinctive traits, not less than the mode of expression which is employed by individuals.

Let us, therefore, look a moment at this subject in reference to particular writers.-The style of a writer is understood to have relation chiefly to his choice of words and his manner of arranging them. Every writer of genius employs a style in some degree peculiar to himself. It cannot well be otherwise, since the mind of every individual is, in some respects, unlike that of all others. There are differences in situation; differences in intellect and feeling, in knowledge and taste, which necessarily lay the foundation for differences in style. Whenever, therefore, a writer attempts to imbody and set forth to others the series of his intellectual operations and feelings, such exposition will necessarily have a form and impress of its own. So true is this, that it is hardly more difficult to detect an author's style when it is once well-formed, than it is to distinguish one man's handwriting from another's. And what is true of his manner of expression in the case of an individual, is equally so of national dialects. The languages of all nations have a style or peculiarity of manner. They are marked by certain prevailing characteristics, which readily distinguish them from those of other nations.

38. Characteristics of the languages of uncivilized nations. In the first place, there are certain general traits, which

are characteristic of all languages that are spoken by the rude, uncultured tribes of men. As such uncivilized communities are in general ignorant of alphabetical writing, they cannot be expected to furnish us with numerous specimens of mental effort. Their glory is committed to the traditions of their country; and we rarely find among them anything more than some brief historical sketches, war songs, and speeches. But, even from these imperfect sources, we can form a judgment on the present subject.

The words which such tribes employ are generally few in number compared with the vocabulary of civilized nations. Their knowledge is very limited; their ideas are few; and it is a necessary consequence that their words should be few likewise. Incapable of aiding their perceptions by remote deductions of reasoning, they draw instruction from the visible teachings of the woods, the waters, and the sky; but even the external world is very imperfectly learned, while they are almost wholly ignorant of the world within. And the range or compass of their language corresponds to the compass of their knowledge.

It is further worthy of remark, that only a small proportion of the words employed by uncivilized tribes are the signs of abstract ideas. Having but few abstract notions, and, consequently, but few names for them, they are under the necessity of resorting continually to figurative illustrations; so that their language seems to partake of the materiality of the external objects with which they are chiefly conversant. But aided, as they are, by metaphorical expressions, their stock of words still remains small; and the sentences which they utter must therefore, of necessity, be short.

These short and figurative sentences are inspirited by the infusion of the untamed passions of a savage mind. There is a vivacity in their griefs, their joys, and their anger, which is almost peculiar to uncivilized life." The bones of our countrymen," say the Chiefs, " lie uncovered; their bloody bed has not been washed clean; their spirits cry against us; they must be appeased; sit no longer inactive upon your mats; lift the hatchets; console the spirits of the dead."

39. Characteristics of language in civilized and scientific nations. As a nation advances in knowledge, its language becomes more strictly conventional, losing by degrees that metaphorical aspect which it presented in its earlier periods. A variety of new words are introduced, which previously had no existence, because the things for which they stand were not then known. New arts have their technical names and epithets, and new sciences furnish us with their novel nomenclatures.

The distiller speaks of the cohobation of liquors; the worker in mines of collieries; the chymist of sulphates and muriates; the botanist and mineralogist employ a variety of terms peculiar to their respective departments. An increased refinement and abstraction discovers itself in terms appropriated to moral, political, and literary subjects; and the language in all respects is more removed from the senses, and becomes more intellectual. But while it is, by a natural consequence of mental improvement, more exact and scientific, it is less directly and strikingly indicative of external objects and of the passions of men, and is, therefore, less poetical. As terms become more abstract, they are necessarily less picturesque. This is the natural consequence of their not being limited to particular objects, but extended over a vast surface of things. A Savage, if he had the most refined language of Europe at his command, would be at a loss to express in it the strong emotions which agitate him, and the outward and living beauties of his woodland scenery; he would choose for that purpose the dialect of his tribe.

40. Characteristics of languages depend much on the people's habits. Individual writers, as already observed, have a style, that is, characteristics of expression, of their own; for every one has a tendency to connect together thoughts, or words which are the signs of thought, agreeably to his peculiar intellectual habits and passions. But languages also, considered in their whole extent, have a style; because the nations, the whole mass of people that make use of those languages, have their characteristics as well as individuals. It follows, then, from this, that

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