tire circle of necessities. It could cut its own timber, erect its saw mills and build its houses. It could take the iron ore from the mountains, build its own furnaces and convert the rough material into any shape in which it might be needed. Having erected a thousand cottages, it could then commence a navy. The hull of its vessels should be made by men who have worked all their lives at the trade; the sails should be woven from the rough material just plucked from the stalk. And when completed, the vessels should be manned and officered by those who have weathered Cape Horn a dozen times, and who have guided their craft through the monsoons of the Indian Seas. This done, and our little village containing a thousand souls, should be studded with sign boards telling of the doctor, the lawyer, the joiner, the dealer in native and foreign products, the editor with his printing press, and the artist to illustrate and immortalize." And these are the men who have been trained in our common schools. III. The relation of common schools to the general prosperity of a community is seen in their direct influence upon labor. Industry is an element of national prosperity; so is wealth. Intelligence diffused among the people, creates habits of industry, and industry guided by intelligence, promotes wealth. Hence, our public schools have an important relation to the prosperity of the State, by producing marked improvements in the leading industries of the people. Our laborers occupy a higher position than in any other country, and in the same proportion, their labors are the more effective and economical. When we buy labor, what do we expect to get? Merely the physical force contained in muscle and bone? Should we employ an animal be. Cause he is strong? Physical strength is necessary, but to be available, it must be guided by intelligence. The descending stream has power to drive machinery and the arm of an idiot has force for mechanical labor, but either is useless without a directing mind. In all employments and professions we pay more for the skill that directs the power than for the power itself; and sometimes it is merely professional skill that we buy. And what is the influence of improved facilities for la bor upon the general prosperity of a community? It is casy to illustrate. The stream that now moves the machinery in which hundreds of men and women earn their daily bread, was, a hundred years ago, employed in driving a single set of millstones. One individual was leisurely employed and sparingly fed in conducting its operations, The Physical power has not changed, but intelligence has controlled that power to produce these wonderful rexults. And is it not a public benefit that these hundreds have found employment and are thus able to obtain an honest livelihood by their own industry? In proportion to the population of our country, we are daily dispensing with manual labor; yet, we are daily increasing the national production. Mind now directs the forces of nature and of the human body. As a result, a given product is furnished by a less outlay of physical power. The old spinningwheel and hand-loom of former days could produce a web of cloth but it was at a wasteful expense of time and strength. Now, intelligence guides the waterwheel, the spindle and the shuttle, which mind has invented. And who does not see the utility and economy of such a change! And who will not acknowledge the importance of men. tal culture in its bearing upon the industry of a community? Is an ignorant farm laborer as serviceable as one who is intelligent ? Would he produce as much in the shop or mill? If not, then the education of the labor. ing classes is of the first importance, both to themselves and to society. Learning makes labor more valuable to him who toils, and, at the same time, reduces the price of his products. Hence, all classes are benefitted. As each laborer, with the same amount of physical strength, produces more, the aggregate products of the state are greatly increased; and as the cost is proportionably diminished, each laborer may have a larger share and acquire a greater amount of independence, comfort and wealth. Hence, just so far as our public schools promote sound learning and diffuse intelligence among the masses, so far they elevate and bless the laboring people. No evidence can be gathered from observation or history, that an ignorant population has ever escaped from some condition of poverty. On the other hand, an inteligent, industrious community will, other things being equal, soon become wealthy. Learning that sustains vir. tue is sure to produce wealth ; and this is the only means by which the poor can escape from poverty. And can any doubt that our system of public instruction, founded as it is upon the Bible, and sustained by the religious Press and the Pulpit, tends to promote virtue ? 0. WHAT IS THE MINUS QUANTITY? In the discussion of this question, "What is the Minus Quantity ? " we must first understand what is meant by a quantity. We believe a quantity to be anything which can be measured. The term quantity is, also, sometimes applied to the expression for it. We will use the term as applicable to either the expression or the thing, but mainly to the expression for it; as, 2, 4, a, or b. Calling a the expression for a quantity, we wish to learn the difference between u and There evidently is a difference of some kind, or there would be no utility whatever in having a minus quantity. The only perce ptible difference seems to be, that, in the latter quantity, a is preceded by the sign minus. And so we infer, from this outward expression, that a minus quantity is a quantity with a minus sign preceding it; and so it is ; but a. this definition does not develop at all the nature or value of the quantity. To know this, we must have recourse to the method by which it was obtained. Before this, let us notice some of the current explanations of minus quantity. It is understood by some to be less than no quantity. I have known pupils, who have made commendable progress in algebra, to state it as their belief, that the minus quantity denoted an absence of quantity, or was less than no quantity, or, to use common language, was less than nothing. The fallacy of this opinion is evident, for what is not a quantity certainly cannot be a minus quantity. Again, it is said that a minus quantity is just like a plus quantity, with the exception that the minus quantity shows a different relation. Now what is meant by show. ing a different relation? It is usually explained by drawing a horizontal line, then taking sonie point near the center, as a starting point, and saying that quantity is reckoned in two directions, and that it increases in both directions equally, the only difference being this, that one is to be added and the other subtracted. Do we not have quantities to be added and subtracted in arithmetic? Then the difference would be, the sign shows what is to be done in algebra ; but in arithmetic we are told by word of mouth, or by the printed words of the book. So we should find no real difference between algebra and arithmetic. It seems that the ideas gained from an explanation like this are exceedingly vague and indefinite, and tend more to confuse than to make clear the real difference between a plus and minus quantity. Let us now look at the process by which it is obtained. Take the quantity a, which is an indefinite, known quantity, (by an indefinite, known quantity I mean a quantity for which any definite, known quantity, as 2, 4, or 6, can be substituted); from this, subtract the indefinite known quantity b, and it gives the formula a,b, which is an ex. pression for the difference of any two numbers. Now, substistute for a the number 3, and for b, 1, the -1. +1 and expression will then be 3-1, which reduced=2; substituting for b the number 2, the expression will read 3-2=1. Again, substituting for b the number 3, it giver 3 -3=0. It will be noticed that the larger the number that is subtracted the less the result will be. If we again substitute for b the number 4, for we have as much right to substitute 4 as any number, since b is indefinite, the expression will read 3 — 4 reduced Substituting 5 for b the reduced expression will be -- 2. Applying the rule which we have found true, that is, that the minuend remaining the same, the greater the subtrahend the less the result; then the result --1 must be considered less than 0, and the result -- 2 less than either 0 or -- 1. Hence it follows that, as - 1 is less than 0, that 1 are unequal, that is, that +1 is greater than -1; and as +1 is the result of adding 1 to 0, and - 1 is the result of subtracting 1 from 0, it follows that +1 is greater than — 1, by 2. Again, of two minus quantities, it follows that that is the greater which is the result of the subtraction of the less number; for instance, 3–4=-1, and 3-55-2. In the first case, 4 is subtracted, in the second case, 5; therefore - 12-2 because it is the result of the subtraction of the less number, likewise --- 4>-- 6. From this illustration it will be seen 1. That a minus quantity arises from subtraction, and that it is an expression for the difference which arises from subtracting a greater quantity from a less. 2. That there is an inequality existing between a plus and a minus quantity represented by the same symbol. 3. That of two minus quantities that is an expression for the greater which is numerically the less. It may, perhaps, be seen more clearly by a few illustrations which show the practical working of it when considered in this light. It is evident that + 1 is not equal to --1, for if that is true, then the unreduced expression for +1, which is 3 —2, must be equal to the unreduced ex |