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known, and is now proved geometrically, that the area of the cycloid is. three times the generating circle. GALILEO practically showed this long before his pupil TORRICELLI demonstrated it, but in a mechanical way. Having selected a piece of metal of equable thickness and uniform texture, he cut from it a piece in the shape of a cycloid and also a piece equal to the generating circle. Upon weighing these separately he found the portion representing the cycloid to be exactly three times as heavy as the portion representing the circle.
Cases showing that theories are really subsequent to facts even in pure mathematics might be indefinitely multiplied, but the above are sufficient for illustration. Then:
How mathematics should be taught in an industrial school is no longer debatable-its sphere is fixed, and the results will be certain.
The right line should be drawn—the ruler and compasses should be the constant companions of the student of mathematics "for the carpenter stretcheth out his rule; he marketh it out with a line; he fitteth it with planes ; and he marketh it with the compass.”
It is a beautiful idea, that the drawings or diagrams of all mathematical and scientific works are the same, regardless of the language of the text, and hence the French artisan can understand and execute the design of an American or German artist with as much facility as if it had been devised by the cunning hand of one speaking his own vernacular.
Drawing is the perfection of illustration, even of our thoughts. Parables are word-drawing, and hence their frequent and successful use by the Greatest of all teachers.
Drawing, therefore, should be taught in conjunction, and at the same time with mathematics; is really an integral part of mathematics.
The order should be as indicated. First-Right LINE; Second-FREE HAND; and third-DESIGN DRAWING, whether for architectural or mechanical purposes.
Physics and Chemistry: It is difficult to determine an order for these, they are so intimately related to each other, and so directly allied to every industrial branch that their importance cannot be overestimated in a course of instruction for practical education.
“The study of physics is twofold. It consists of two distinct yet complementary processes—the tracing of facts to their causes, and the legitimate advance from the cause to the facts. In the former process, called induction, certain moral qualities come into play; requires patient industry—a conscientious acceptance of what nature reveals. The second process in physical investigation is deduction, or the advance of the mind from fixed principles to conclusions which flow from them, so that, in the study of physics, induction and deduction are perpetually married to each other.”
Some one has not inaptly said “that physics is a science lying midway between astronomy and chemistry,” and this may be said to be true ; that physics, as applied to the weights of enormous masses, is astronomy; and as applied to atoms and molecules, is chemistry.
The subjects of physics proper are those which lie nearest to human perception; the heat and light of the sun, sound, motion, color, electrical
attractions and repulsions, thunder, lightning, rain, snow, dew, and so forth. Through our senses we are enabled to examine these phenomena, that is, to unite the external world and the world of thought.
Chemistry: Somewhat in detail may be said to be that science which investigates the composition and properties of bodies, and by which we are enabled to explain the causes of the natural changes which take place in material substances. As a science chemistry is of the highest importance to mankind, since, by its investigations the practical arts are constantly improving. Chemistry is intimately connected with a great variety of natural phenomena. All satisfactory explanations of the causes of rain, hail, dew, wind, earthquakes, and volcanoes, have been given by the aid of chemical knowledge. The phenomena of respiration, the decay and growth of plants, and the functions of the several par of animals are also explained in a satisfactory manner only by its aid. As an art, chemistry is connected more or less intimately with nearly every branch of human industry, and particularly with agriculture and manufactures.
In its application to agriculture, chemistry furnishes the most direct and certain means of ascertaining what a barren soil wants to make it a fruitful one, and also what ingredient any soil requires to adapt it best to any given kind of produce.
Our most common and useful articles are manufactured entirely by chemical processes. The making of soap, glass, bleaching salts, the several kinds of acids, and almost every kind of medicine, depends wholly on the manipulations of chemistry. The arts of the potter, ironsmith, tanner, sugar-maker, distiller, brewer, vintner, paper-maker, and painter, are also connected in various degrees with chemistry.
In a word, the arts draw from it with every succeeding year increased advantage, and the condition of mankind is elevated, and the world advanced by its progressive triumph. It opens to us mines of agricultural wealth in what would otherwise have passed for worthless refuse. It clothes exhausted fields with new fertility, by the addition of some failing constituent whose absence its subtle processes have detected. It carefully investigates the laws and conditions of vegetable growth, by which earth and air are converted into food for man and beast, and thus places us on the highway of sure and rapid improvement.
By the study of physics and chemistry we have opened to us treasures of power of which antiquity never dreamed ; we lord it over matter, bnt in so doing we have become better acquainted with the laws of mind, "for to the mental philosopher material nature furnishes a screen against which the human spirit projects its own image, and thus becomes capable of self-inspection.”
Says Dr. HENRY MAUDSLEY: “Of old it was the fashion to try to explain nature from a very incomplete knowledge of man ; but it is the certain tendency of advancing science to explain man on the basis of a perfecting knowledge of nature."
With the researches and results of the labors of this and other distinguished physiologists before me, and believing, as I do, in addition, that we can understand the mind only through a clear and definite understanding of the body; of the man in his entirety, I think the time has come for demanding that the curriculum of modern liberal education be so reconstructed that its courses of study shall have a more direct and positive bearing upon the most desirable of all knowledge-a clear under. standing of the laws of human nature; and for this reason I have added natural history, as embracing physiology.
A term, however, rather limited, and I would prefer to insert as one of the cardinal divisions of the course, the scientific study of human nature, comprehending both physiology and psychology.
Although I have said much, and possibly that, too much in detail, respecting physics and chemistry and the study of human nature, I cannot refrain from adding a word or so in regard to geology and physical geography.
In this scheme geology and physical geography should hold a prominent position. Geology is the history of our earth. It will afford both pleasure and instruction to study these periods—to examine these volumes—to present them in comparative estimate-to note the difference “ between the fancies of ARISTOTLE and the facts of HUMBOLDT—the conjectures of PythaGORAS and the observations of AGASSIZ—the ideal of Plato and the real of LYELL.”
Geology teaches what is useful-what is desirable. It is important to notice that the construction of a building does not consist merely in the nice and beautiful adjustment of its various parts, but in the preparation of suitable material, and the working of that material in such a manner that the building, when complete, shall be handsome, useful, and endurable. Geology tells us that among Azoic rocks, the most valuable for the erection of houses and monuments are granite, gneiss, etc., etc.
Physical geography begins, really, where geology ends. It concerns itself only with the present completed condition of the globe. “To us. our own earth is the most marked feature of nature, viewed on its inorganic side; to us it is the planet best known of all, or rather the only one closely known, the point whence we draw conclusions on the whole universe, the resting ground for the glass that searches the Kosmos, to use HUMBOLDT's word.”
CARL RITTER says: “The earth is the grand floor, so to speak, of nature;
the home, or rather the cradle, of man and of nations—the dwellingplace of our race. It is not merely a region of immense spaces--a vast superficies; it is the theatre where all the forces of nature and the laws of nature are displayed in their variety and independencies. Besides this it is the field of all human effort and the scene of a divine revelation !” Hence the study of our earth, a comprehensive and systematic treatment of the land, the water, the atmosphere, and life upon the earth; the laws that govern the situation, extent, outlines, and relief of the land-masses; the cause, the extent, the connection, and the influence of the great oceanic currents; the distribution of heat upon the surface of the globe; the general atmospheric movements, and what is their cause, course, and influence; what laws control the periods, distribution, and amount of rain upon different portions of the globe; the general laws that govern the distribution of vegetable and animal life, and how all these laws are related to the character and well-being of the human family, should hold no second place in any system of practical education, unless it be to the study of man him. self; for, while science may claim to be "the right interpretation of nature,” man is still THE INTERPRETER.
History and Social Science: These should occupy a place in the finishing of the English-language course; should come as studies in the higher classes, and should be designed to afford a general view of the history of mankind and of the phenomena of the social organization and progress of the race.
Should also embrace the history of the arts and seiences and of civilization, the philosophy of history and the principles of political economy and constitutional law.
Instruction here should be mainly by lectures, together with suitable readings from standard authors prescribed by the professor in charge of the department.
Music: Vocal and instrumental, with painting, come under æsthetics, belong rather to the ornamental, the accomplishments, but should occupy a place and receive that attention commensurate with its importance. It is true all cannot be taught to sing or to discourse sweet sounds, neither can all ever be taught the mathematics or the sciences, still they can be taught something. Vocal music should be one of the daily exercises, for this would give proper exercise to the lungs, expanding the chest, and really arming us to ward off pulmonary disease. The celebrated Dr. Rush was of opinion that the fact that the Germans, as a people, are seldom afflicted with consumption, is due to the vocal exercise of singing.
We know that singing constitutes an essential part of their education. Apart, however, from this view, singing is a delightsome pastime and a great preserver of good order.
I go further. The vocal organs ought still more to be trained, for the result it must have upon the power of expression. Too little attention is paid to this in the curriculums for training in the so-called liberal professions. How lavish we are in the purchase of instruments of music, and in keeping them properly tuned and cared for; yet this most wonderful organ, the voice, which God has given to every one of us, is left for the most part in utter neglect, totally uncultivated and undeveloped.
I have omitted from this “course of instruction” the Ancient Languages.
This has been done advisedly; from no disposition to ignore or to underrate the classics, but from the pressing necessity to select from the great number of studies, those not only pertaining to, but, if possible, those directly contributing, to industrial pursuits. Time must be economized. Knowledge is what is demanded.
“To know well is to understand causes,” and in no profession is there a greater demand for varied and extensive knowledge than in the arts.
The study of the ancient classics should be conducted in the same manner as the geologist now studies the fossils—to understand if possible, the character, condition, and peculiarities of the people once speaking theseto determine really their thoughts, their ideas. This is a pleasant and profitable study too, but it does not advance the knowledge of the present day.
The study of the Pyramids may develop some lost characteristic of the Pharaohs and Ptolemies, but is not profitable to American engineers.
The Pyramids, with their hieroglyphics, may do well enough for Egypt-for Africa, but like CLEOPATRA's Needle they will not bear transportation-even their very substance will crumble and decay under the atmosphere of England or America. I have no quarrel with the antiquarian or the archæologist. If you have time, taste, and means to study dead Rome, dead Greece, dead Egypt, and dead Syria,—do so.
“ Is the acorn better than the oak, which is its fulness and completion? Is the parent better than the child into whom he has cast his ripened being ? Whence then this worship of the past ?” Where we were, is night; where we are, is day!
It will also be observed that I have insisted on the study of social science, general history, political economy, and have pointed out when these should be intro ed, viz. :-As the fini ing of the course in the English language; in a word, I have endeavored to be as consistent in the studies pointed out for the education of the whole man, as I have been earnest in my advocacy of the study of man in “his entirety.”
Or, to put it otherwise, in life we have to deal with our fellow-man as well as with earth and air and water. By our experiments upon soils and our superior cultivation we may make "two spires of grass grow where one grew before; we may make two bushels of wheat, or of corn, or of barley; we may double our produce, and thereby double the market, and to no purpose unless we can double the demand. The saine may be said of our mining and our manufacturing; but we have besides to settle with the miner and manufacturer before our science or experiments can do us any good.
Heat and light, electricity and steam are great monarchs; but they are powerless to aid us unless we can come to some understanding with our neighbors. Therefore the study of man in another aspect, in the social relation, must be taken into the account; his past, his present, and from these what his future actions will be. This is provided for in the scheme laid down in the systematic study of history, social science, and political economy.
Again there are numerous allied or kindred subjects of study which grow out of the main branches enumerated. A judicious selection of these must be made. Probably, too, the “
itself, mentioned, may be too extensive for many students; if so a choice again must be made, and the branches selected that will aid most in the preparation for the future pursuit of life.
And here let me illustrate. The older College curriculums may be likened to a splendid banquet, with its numerous cloths and courses. The guests are expected to eat of each, and, in due order, adding at each change, to rich viands rich wines, and the result is, before the banquet is half over, many of the guests are sick, many of them are intoxicated with the round of good things of which, contrary even to their taste, and especially to good taste, they have been forced to partake. Few can drain the cup of HERCULES. ALEXANDER could not do it. When I look at the curriculums of many of our foremost Colleges, I feel sad for the young students who have got, somehow or in some way, to get through them. What I wish set before me is the American Restaurant,“On the European style,” if you please: I wish a choice, however extensive the bill of fare. Our