* better off because his coachman reads the paper, but that the coachman himself who reads the paper is better off than the coachman who does not and cannot. I think that we are too apt, in considering the ways and habits of any people, to judge of them by the effect of those ways and habits on us, rather than by their effects on the owners of them. When we express a dislike to the shoeboy reading his newspaper, I fear we do so because we fear that the shoeboy is coming near our own heels. I know there is among us a strong feeling that the lower classes are better without politics, as there is also that they are better without crinoline and artificial flowers; but, if politics and crinoline and artificial flowers are good at all, they are good for all who can honestly come by them and honestly use them. The political coachman is perhaps less valuable to his master as a coachman than he would be without his politics, but he with his politics is more valuable to himself. For myself, I do not like the Americans of the lower orders. I am not comfortable among them. They tread on my corns and offend me. They make my daily life unpleasant. But I do respect them. I acknowledge their intelligence and personal dignity. I know that they are men and women worthy to be so called. I see that they are living as human beings in possession of reasoning faculties; and I perceive that they owe this to the progress that education has made among them." What a conquest over personal feeling and national prejudice! A testimony like this is precious to us when we are in danger of depreciating our work; or when we are sad from the feeling, how feeble are our efforts and imperfect our success, in comparison with our aspirations. It is specially interesting at the present time to see how closely the reasoning of many Englishmen against the enlightenment of the "lower orders" tallies with the reasoning of most Southerners and even some Northerners against the freedom, education, and elevation of the colored race in this country. The reasoning, let it assume what guise it may, is all selfish. One inference more from our author's picture. Will the ruin of such a nation be permitted? Will they be left, as their enemies predict, to "go to the wall?" May we not adopt our author's assurance? "I venture to express an opinion that they will by no means go to the wall, and that they will be saved from such a destiny, if in no other way, then by their EDUCATION.” INTEREST. IN teaching any branch it is always best to "forelay" for what is to come, and, in so doing, have "an eye single " to what will be thoroughly practical. This should be always done in teaching mathematics in all its branches. There is no claim to originality in the method here offered of teaching this important subject, but an earnest desire to save the pupils of our common schools from the task of learning much that will be almost entirely useless in the "counting-room" and in the business operations of life. In teaching Percentage, forecast for Interest. I would find the per cent. of any sum, by getting aliquot parts of that sum, considered as one hundred per cent. E. g., in finding .87 of $9200, take, or .50, of the sum; of the last number, which is .25 of the sum; of the given sum, which is .10 of that sum; of this last number, it being .02 of the whole sum; and the results will be $4600, $2300, $920, and $184, which added give $8004. A little practice will soon enable the pupil to perform the work rapidly and accurately. Having, by practice, laid a good foundation, we are ready to build the "next story," Interest, in the same manner. Take the following example: Required, the interest of $9200 for 14 years, 7 months, and 29 days. The interest of $1.00 for 14 years and 6 months is .87: we find the aliquot parts as before, and have 1 month and 29 days, or 59 days beside, to find the interest for. .01, (one one-hundredth), of the principal is the interest of $1.00 for 2 months, or 60 days, which can always be found by moving the point two places to the left; and moving it three places gives the interest for 6 days. With this explanatory remark on the days, we are ready to go to work. We take the following aliquot parts of 60 days' interest for 30 days, of the same for 20 days, of 30 days' interest for 6 days, of 6 days' interest for 3 days, which give $46.00, $30.666+, $9.20, and $4.60; and these added to $4600, $2300, $920, and $184, give $8094.466+, Ans. Remove the points and find the parts mentally, putting down the results only. This is the method used by "business men," and is readily grasped by the mind of the pupil. The writer has used this method with success, in teaching a class of forty, whose average age was thirteen, it being the first time they had ever studied interest. This method will recommend itself to any teacher who will give it a careful examination, and it seems superior to the "way" of getting aliquot parts of one year's or one month's interest; this "way" combines both, in a measure. Not that the old methods should be discarded, but preference given to the above as the most practical. Boys entering the counting-room are obliged to give up the "old way" and learn a shorter one, so let us give them "that shorter way" at the outset. A few words on "Problems in Interest." Often has it been said by teachers: "If the rule for any problem in interest should be asked of me, I could not give it, nor could I solve such a problem unless I could see the rule." Furthermore, any teacher of experience knows the impossibility of pupils' giving "the way" of performing the problems, if he "skip around" in asking his questions. The fault with the pupils and some teachers is to be found in THEIR teachers. A little explanation of the formula, trp=i, will enable the pupil to grasp the whole subject, and so thoroughly that it will never leave him. In teaching multiplication and division of Simple Numbers, "forecast" for this also, and have this principle well grounded, viz.: "If the product of three numbers, and two of those numbers are given, the third may be found by dividing the product of the three by the product of the two." Use the "old" or new method" in interest here, and if both are well understood, or ,one only, we are ready to go on. t time, r = = rate, p: = principal, and i = interest; and if the principal is multiplied by the rate and time, it gives the interest; therefore, the interest is the product of three numbers, time, rate, and principal, or trp = i; and if two are given, the third can be found as above: thus, trpi, (cross the r, as that is the required quantity), and the class answer: "Divide the interest (i) by the principal (p) multiplied by the time (1) considered as a decimal, and the quotient is the rate (r)." Again, trpi, (crossing the p,) answer: "Divide the interest (i) by time (t) multiplied by rate (r), the quotient is the principal (p)." Again, trpi, (crossing the t,) as before, "Divide interest by rate multiplied by principal, and the quotient is the time." This is practical, and girls and boys always remember trpi. The smothered wrath at every stroke And all disturbances awoke,- And impish trick and vengeful spite Ne'er left occasion, day or night, I see it now: -the whittled doors, The benches levelled! The streaming ink from murky pores, Small reverence for Learning's fane, Was thought of only by the train WOMEN AS TEACHERS. EVERY well educated girl feels perfectly conscious, that, under favorable circumstances, she can conduct, upon an average, nineteen of her twenty little innocent pupils into an honorable existence. Give her a strong arm for discipline, and a wise head for advice, and her labors fix a divinity upon the face of society. I believe in the infinite susceptibility of children, and also in the moral omnipotence of women, their natural teachers; and there are no evils in society, however deep seated, that may not be removed by a wise application of their powers. A highly cultivated woman is God's antidote for sin and suffering.-T. B. Wait. |