tired and the daughter wrote; the Indians were wonderstruck, but not entirely satisfied. See-quah-yah then proposed that the tribe should select several youths from among their best young men, that he might communicate the mystery to them. This was at length agreed to, although there was some lurking suspicion of necromancy 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. The Indians, on this, ordered a great feast, and made See-quah-yah conspicuous at it. How nearly alike is man in every age! Pythagoras did the same on the discovery of an important principle in geometry. See-quah-yah became at once school-master, professor, philosopher, and a chief. His countrymen were proud of his talents, and hold him in reverence as one favored by the Great Spirit." §. 136. On 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 afterwards 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 leading 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 x3-ax2+b2 = o, the letters a,b,x, denote quantities, but the terins x,ax2, &c. denote certain operations performed on those quantities, as well as the quantities themselves; is the quantity a 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 FOURTH. RIGHT USE OF WORDS. §. 137. Imperfections of artificial language or words. WE now find men furnished, in addition to the language of natural signs, with the artificial forms of oral, and alphabetical or written language, and possessed of the great advantages, which may be supposed to flow from these powerful instruments of mental action and communication. Artificial or conventional language may be said without exaggeration not only to express ideas, but to multiply them. At least, the facility of expressing and communicating thought by means of it sets men upon renewed thinking, and the result is wider views, more correct principles, moral, civil, and scientific improvement. And notwithstanding, it cannot be denied, that language, (we have reference in this chapter particularly to artificial language or WORDS, which is a term standing both for oral and written signs,) is not without its imperfections. It may be said in general, to be imperfect, or to fail of its object, whenever the same ideas are not excited in the mind of the hearer or reader, as in that of the speaker or writer. Nor can we reasonably expect, when we look at the cause or foundation of this imperfection, that it will ever be otherwise; since that cause will be found to exist ultimately in the condition of the mind and in our ideas, rather than in the words, which stand for them. This requires a brief illustration. It often happens, that men view the same object and actions in different lights; whether it be owing to some difference in early education, or to local prejudices, or to some other cause, the fact itself is well known, and may well be considered, as frequently unavoidable. Hence different persons very often attach the same name to certain objects and actions, when their views of those actions and objects are not the same. One has a greater number, than another, of simple ideas entering into his complex notions, and perhaps, in the formation of the compound, they respectively give to those simple ideas a different relation to each other. The consequence, therefore, is, that, in such cases, as have now been mentioned, the names or words, which are used, necessarily fail of exciting in the hearer the same ideas, that exist in the mind of the speaker. Many of the disputes, which have existed in the world, (and the history of philosophical opinions shows, how numerous they have been,) have been caused by a misunderstanding of this sort; different persons using the same terms, when their ideas are not the same. In support of this remark, it will be enough merely to refer to the often repeated discussions upon virtue, conscience, faith, free will, obligation, nature, religion, infinity, miracles, &c. -But language, in so far as it is imperfect, fails of the great object, for which it was invented and agreed upon, and it, therefore, becomes important to diminish the amount of this failure and to guard against it, as far as possible. To this end, the following rules on the right use of words may be laid down. §. 138. Words are not to be used without meaning. RULE FIRST.-In the employment of language, the first rule to be laid down, is this, that we should never use a word without some meaning. It may be thought extraordinary, that any should use words in this way, but a little examination cannot fail to convince one of the fact. Let any one inquire of those persons, who are in the habit |