a solid a surface is produced. The rough boards, passed under the straight edge of the planer's knife, are rendered smooth. The brickmaker strikes the surplus clay from his moulds with a wire, and gives plane surfaces to the bricks. The mason lays them to a horizontal line, which he moves along a vertical, and gives a plane surface to the wall. By placing layer upon layer he builds a wall; in other words, by moving a plane perpendicularly to itself, he produces a solid. He renders the plastering true and smooth by means of his straight edge and trowel. per is made by being passed between straight rollers. glass is cast upon a table which has passed under the line made by the point of the iron-planer's tool. Then there are the imaginary planes and lines which the surveyor and astronomer make. Every piece of surveyed land is surrounded by planes that extend from zenith to nadir. The astronomer's lines fill the sky like. cob-webs, and his planes divide the universe.

Pa

Plate

The movement of a point generates a line; a line, a plane; a plane, a solid. Lines and planes of various shapes produce planes and solids of various forms. The revolution of a rectangle upon one of its edges generates, by the opposite edge, the convex surface of a cylinder; by the ends, circles; and by its area the cylinder's volume. Moving a line perpendicularly to itself generates a rectangle; diagonally, a parallelogram; and around one of its ends a circle, or the convex surface of a cone. Revolving a circle upon its diameter generates by its circumference the surface of a sphere; by its area, the sphere's volume.

Lines, surfaces, and solids are thus generated, each in a manner peculiar to itself. To gain a clear conception of their structure is, 1st, to see how they are produced: 2d, to separate them into their elementary parts; 3d, to re-arrange these simple elements in equivalent surfaces and solids of more simple forms. All areas and surfaces, whatever their shape, are expressed by equivalent rectangles, and all solids by equivalent rectangular solids. The area of a circle, for example, is equivalent to the area of a rectangle whose dimensions are equal to the circle's radius and semi-diameter. The surface of a sphere is equivalent to a rectangle whose dimensions are the circumference and diam

eter. The sphere's volume is equivalent to a rectangular prism whose dimensions are two-thirds of the diameter, the radius and the semi-circumference.

Fig. 1 is a parallelogram. Dividing it by a perpendicular to its base and re-arranging its parts as in Fig. 2, produces a rect

angle, whose base and altitude are equal to the base and altitude of the parallelogram. It is now plainly seen that the area is found by multiplying the base by the altitude-the number of square units in one tier by the number of tiers. The mathematical operation changes, in fact, the parallelogram into an equivalent rectangle. The ocular demonstration by figures and blocks harmonizes with this process.

Fig. 3 is a triangle. Dividing it at half its altitude by a parallel to its base, and separating the lower part by a perpendicular to its base, produces parts that may be re-arranged to produce a parallelogram and a rectangle. Fig. 4 is the parallelogram. Fig. 5 is the rectangle. Each part carries the same letter with it through all the figures. A is first placed on the

FIG. 3.

B

FIG. 4.

A

FIG. 5.

B

The figure now

appears, which is really produced when the area of any triangle is found by multiplying the base by one-half of the altitude. The demonstration by figures and blocks harmonizes with this process.

form a parallelogram and a rectangle, as in Figs. 7 and 8. The dimensions of the rectangle thus formed are the sum of the upper

B

FIG. 7.

and lower bases and one-half of the altitude of the trapezoid. The area of the three figures is manifestly the same. It is found

that taking the product of the rectangle's dimensions, what is in fact done in the arithmetical operation of finding the area of the trapezoid, is done also by means of the dissected figures and blocks. The trapezoid is reduced to an equivalent rectangle, whose dimensions are as given above.

(To be continued.)

M

THOUGHT-READING.

R. BELL: I should like to be considered on the same

side with you and Prof. Carhart in the plan of thoughtreading. It is nothing new. My first position as teacher was in a school where that plan has been employed for at least a quarter of a century. I think you could not do education a

more signal service than to suggest the following plan for applying and carrying out the suggestions of Prof. Carhart's paper.

In the opening exercises of the morning have all the scholars turn to a new lesson in their readers and study it for five minutes, and then write for ten or fifteen minutes; or, better still, have all the school listen while the teacher reads slowly and distinctly some production-for instance, Æsop's Fables, or a page from Gow's Morals and Manners, or some grand classic gem from the standard authors, Addison, Macaulay, Holland, or others, and then have the pupils write the thoughts they have collected, and the teacher at night examine, correct, and mark the relative standing of each pupil's exercise, and next morning announce the grade and make such suggestions about the writing as may be needed.

This will practically teach: (1) Penmanship; (2) punctua tion; (3) use of capital letters; (4) the forming of paragraphs; (5) attention to what is read or told; (6) to express the thoughts of another in one's own language; (7) as an aid to composition this exercise is invaluable; (8) it will impress on the mind good precepts and valuable gems of literature.

I know of no other school exercise which produces so many and so valuable results. This is intended as a daily exercise. If it be thought too frequent, then the last hour of each Friday afternoon might be devoted to a lecture by superintendent or principal of high school on some scientific or literary topic, and then have the pupils hand in their exercises on Monday morning, and teacher correct, suggest, and return as before.

A trial will demonstrate to any one that you are right.
R. A. TOWNsend.

VINCENNES, IND., Jan. 10, 1881.

A LIBRARY is not like a dead city of stones, nearly crumbling and needing repair, but like a spiritual tree. There it stands, and yields its precious fruit from year to year and from age to age.

THE RELATION OF EDUCATION TO INDUSTRY.

The Annual Address* before the Ohio Teachers' Association at Chautauqua, July 8, 1880, by E. E. White, President of Purdue University.

A

RISTOCRACY has always opposed the education of the people. The aristocracy of Caste asserts that the great majority of mankind are born to serve the few, and, since the less intelligent the servant, the more docile the service, it declares that education unfits the children of toil for their lot in life.

The aristocracy of Capital asserts that popular education is a tax on capital. The more intelligent a man is, the greater are his wants, and the higher must be his wages in order to meet his increased necessities. Ignorant labor has few wants to supply, and hence is content with low wages.

The aristocracy of Culture asserts that the "masses are born dullards, and that all attempts to educate them are futile. The few on whom God has bestowed the gift of brains, are commissioned to do the world's thinking, and they thus monopolize the right to education. This is the doctrine of the hero-worshipper, Carlyle, and it is asserted more or less clearly by many devotees of culture, who have lost all sympathy for the people. It has been faintly echoed

by the learned president of Harvard.

These three great aristocracies (the three C's), unite in opposing all efforts to uplift the laborer by the power of education. Schooling they assert, spoils children for labor; it makes them discontented with their lot; fills them with vain ambitions; makes them idle, etc. These assertions are now more frequently aimed at higher education, and especially at the high school; but they were once urged, with as great earnestness, against the elementary schools of the people. Reading and writing have received many a blow as the dreaded enemy of capital and caste.

The late financial check to the prosperity of the country afforded these aristocracies a coveted opportunity to renew their assault on popular education. The land was filled with idle men, seeking employment, and numerous positio. s which had been open to intelligent young people, were closed against them. This condition of affairs made the idleness of the young painfully evident, and gave increased plausibility to the oft-asserted opinion that popular intelligence is resulting in a growing disinclination among our youth to earn a living by hard work. The schools were assailed as the enemy of industry and labor, and even the ridiculous complaint of Bacon against the schools of the seventeenth century, that they "filled the realm full of indigent, idle, and wanton people," has been made against the public schools of the United States.

* Based upon a paper on "The Education of Labor," read before the American Institute of Instruction in 1878.