your character. Real worth alone commands lasting respect. The charlatan's triumph is short-lived."

Then, teacher, make the inner life pure. Suffer no unhallowed passions to lash its waters into fury with storm and tempest, nor lust and appetite to make it a receptacle of all that is base and groveling. The school-room will then become the most attractive place on earth. Its earnest, exacting duties will become mere pastime its frets and worries mere pleasurable excitements. The consciousness of hourly doing some great good to one who ere long must use the strength and tact you impart to him in the battle of life, will compensate for many weary hours of exhausting labor; many sleepless nights of anxious thought.

SHALL GREEK PREPARATION BE DROPPED?

FRIEND WHITE: Your suggestion in the November Monthly in regard to a change in the studies required to enter college, seems entirely practical; and many other things, I think, can be said in favor of it.

First, it would greatly increase the number of students in all our colleges. Second, as many more of these than now do, would go directly from our free schools, the standard of effort and education in them would be materially raised. For, if these schools may become the gate-ways to our highest institutions of learning, there will soon be an imperative demand for teachers who can keep them open and make them available. Besides, the teachers, knowing that their pupils will be brought under the eye of their superiors, and into competition with many more from similar schools, will naturally be prompted to greater interest and pains-taking in their work. Nor will this competition stop with the teachers: the pupils will feel its influences direct and indirect, and will do more and better work for them. Moreover, there can be no doubt that, other things being equal, one who has had the classic training necessary to an instructor in Latin, is more competent to teach other branches of learning, and thus we have another source of improvement in all the studies of the high school, an influence which would soon be felt as a strong attractive power, drawing, to higher attainments, the teachers. and pupils of every other department of the school.

A third argument in favor of your proposition is, that it will be a benefit to our colleges. Certainly, in the increased attendance which may be safely assumed, and quite as certainly, in the immediate interest and connection which it will create between the school and the college. It will make the step into college the next, and, consequently, natural and expected. This is a great gain. One great hindrance to the usefulness of our colleges, arises from the want of this immediate interest and connection. This hindrance is the gratuitous and false assumption, that a college is an aristocratic institution to which only the more favored may aspire. Now, let the school-room door open into the college, and this assumption will be seen to be, as it is, groundless. The talented and aspiring youth of our schools will see the beautiful form and gentle mien of science and the Muses beckoning them upward to higher seats in the fair temple of knowledge; and they will press forward to fill them. The nearer we can bring the school up to the college-for this must not be lowered the more the college will be benefited.

But will not this movement lower the standard of college education? I think not, but quite the contrary. We raise things by putting more under them. Hence my fourth argument, in favor of your suggestion, is, that under its operation college instruction will be made more efficient, and can be carried further. This appears from the following considerations: 1st. The standard of attainment in Latin required to enter college may and should be raised, and that in Mathematics or the Natural Sciences (or both -better both), must be, in carrying out the proposed measure. Thus there will be, at once, more general information and higher discipline in the entering class, and although there will be fewer new studies, there will be one in the department of language entirely new, which now, ordinarily, has no new study. The advantage of this will be seen, I think, by every one experienced in college life. There is now very little elementary instruction and drill in the department of language in our colleges-it being assumed that this work has already been done, and so that minute study, which is necessary to correct information and thorough discipline, is greatly neglected. Now, if this minute drill were continued in college (as it necessarily would be by the newness of Greek), the student, from previous discipline, would be more competent to receive its benefit, and besides there would be a more competent, thorough and experienced teacher to direct it. The stimulating power of such instruction would be felt by both

professors and students, not only in Greek, but in all the other studies as well, and so, I doubt not, greater progress would be made in all. The value of the habit of minute study, with the fact that it is slow and difficult growth, and is easily dropped, must, I think, give weight to this argument. A very learned and thoughtful professor in one of our best colleges, said to me recently: "After a course of preparation at the Phillip's Academy, I found the study of language in college a mere farce, and was disgusted with the whole thing." His explanation was, that "no thorough work was required or done in that department." The college referred to, stands second to none in all the land in any respect; yet here, certainly, is something in it to be improved. Would your suggestion help it? I hope we shall hear from others on this important subject. W. C. T.

P. S. Since writing the above, I have received a catalogue of Western Reserve College, which says: "Additional Mathematics will be accepted as a substitute for a portion of the Greek." This is a movement, from a high source, in the right direction. w.c.T.

SKETCH OF AN ELEMENTARY COURSE OF MATHEMATICS FOR OUR HIGH SCHOOLS.

BY T. E. SULIOT.

II. When the scholar has, for his years and opportunities, become a tolerably expert arithmetician and algebraist, not by having been drilled to work by rote, but trained to discover for himself the law or rationale of each operation, he is ready for geometry.

Geometry should form a part of every boy's and girl's education, provided they have capacity for it. It should not be the exclusive privilege of colleges or of the upper classes in our high schools. But, in order to compass this beautiful study within the narrow limits of time at our disposal, without slurring over or mere memory-work, we must put aside such elaborate treatises as Davies' Legendre, or Loomis's, or even Tappan's elegant work. I have had already occasion to recommend for our common schools Evans' Geometry, which, under a small bulk and in a very inviting form, presents the essentials of the subject, logically

and clearly demonstrated. This excellent text-book can be easily, thoroughly, and comfortably mastered by a previously welltrained class within less than half a year. But I would most earnestly recommend that care be taken to guard the scholars from the temptation of merely committing the demonstrations to memory, and thus perverting into mechanical routine what should be a purely intellectual exercise.

I would again venture to say, as I did once before in this journal, that if I could have my own way, there should be no regular demonstration, but only the enunciation, the diagram, and a few indispensable hints to help the student along. But, seeing that such expurgated text-books are not to be had, the next best way to awaken that precious faculty of geometrical inventiveness to which Mr. Henkle alludes, is to discuss in the class-room each lesson in advance, before the day of recitation; the teacher enunciating the proposition, furnishing, if necessary, the diagram, then challenging the pupils to work out the solution or demonstration, whilst he holds himself ready, all the time, to act as the "Deus ex machina," but let him not forget the precept of HoraceNec Deus intersit, nisi dignus vindice nodus inciderit. Nor let the God in person stand displayed,

Unless the laboring wight deserve his aid.

(See an illustration of this method in the journal for November.) The scholar, now being in possession of those two instruments of mathematical investigation, algebra and the geometry of surfaces, can apply their combined powers to the study of solid geometry, and work out the formulas for the surfaces and volumes of solids, the rules for which are so injudiciously and, I may even say, so mischievously stuck at the end of most of our school arithmetics.

Next should follow Plane Trigonometry, the essential or practical part of which, including so much of the relations of sines and tangents as will enable the learner to understand the construction of the trigonometrical tables, together with practical examples of the measurement of heights and distances, the calculation of the dead reckoning of a ship's course, etc., might be comprised in a volume very little thicker than Evans' Geometry. I do wish that he or some one else would present us with such a book for our common schools. I myself have all the materials ready, which I have used for years, and I would be very glad, if I could be secured from loss, to work them up into a text-book.

Spherical Trigonometry also, with its application to problems of nautical astronomy, and just enough of the principle of stereographic projection to enable the student to draw his spherical triangle geometrically, according to data, could be compressed into a small volume.

I do not see why even the most elementary and practical part of Analytical Geometry and of the Calculus-so much, at least, as refers to the principal properties of conic sections, their areas, the surface and volume of their solids of revolution-might not be so simplified as to be brought within the limits of a half year in the upper mathematical class of a high school. Something of the kind has been done, I know, with remarkable success in the Salem High School under the auspices of MM. Henkle and Mendenhall.

An accomplished mathematician like Prof. Tappan may enrich our colleges with an elaborate and beautifully symmetrical treatise on geometry, soon, I hope, to be followed by a treatise to match, on trigonometry. But, for our common schools, works of smaller compass and of different execution are needed, to give the scholar a mathematical training, complete as far as it goes, instead of our attempting, as now, to teach with voluminous text-books fit only for colleges. The consequence is, that, from want of time, we are obliged to break off in the middle of the course.

Pupils trained on the Pestalozzian principle, of being led to find out for themselves as much as they can, instead of being crammed, as it were, with their intellectual fodder ready cut, can, at any time, follow up, according to their measure of time, opportunity and inclination, the elementary studies of the high school or enter a collegiate course, under far more favorable auspices than those who, according to the too prevalent plan, come stocked with imperfect and ill-digested reminiscences of Davies' Legendre and Bourdon.

I know I have said most of this before; but, in a subject so vital as the importance of a complete, symmetrical and harmonious course of studies for our schools, repetition may be tolerated; the more so, as I can appeal to the convention at Zanesville as a proof that the question, though often discussed in educational meeting and journals, has lost none of its interest, and that the professional public still feels the want of light on the subject, in order to arrive at a conscientious and deliberate conviction.