the schwearing off and the not counting it this time; that wonderful drunken scene; the final, fearful giving away of all forbearance when the light grows dim in the room and those terrible words are spoken: "Begone, you drunkard! Out you sot! Henceforth you have no part in me or mine!" when his voice, suddenly sobering, answers out of the silence-in that weird, heart-breaking monotone-"Why, Gretchen! will youwill you turn me out of your house like a dog? You are right; it is your house; it is not mine. I will go. Gretchen! after what you have said to me, I can never darken your door again." That eloquent gesture as he points to his child lying on the floor between them; Gretchen's agonized, repentant cries as he rushes out into the rain and lightning; that witty, awful colloquy with Hendrick Hudson's ghost; the fatal draught; the odd, rheumatic awakening, "on top of the Catskill Mountains, as sure as a gun!" the old man's perplexed wandering through the transformed village; the queer, pathetic mystification about his own identity; and the final quick mastery of himself and of the situation when he flings back upon Derrick that magnificent "Give him a cold potato and let him go!"

Is it all paint, and canvas, and clap-trap? Is it all unreal? No, no, no. It is true as truth, real as life, deep as humanity! And the lesson-for there is a lesson-what is it? Only that wine is a mocker and strong drink is raging ?-that it "brings a man to rags, and hunger, and want (is dere any more dere in dat glass ?)"—"for when de tirst is on me I believe I would part wid my leg for a glass of liquor; and when dat is in me I would part wid my whole body, limb by limb, for de rest of de bottle!" It is this, and it is more than this: that Gretchen's way of dealing with Rip is not the true way. The true way, alas! who may tell?

And yet there are "Rips" off as well as on the stage, and you and we may be learning how to save them-through the pitiful God only knows what trial and agony.-"Jefferson's Rip Van Winkle"-Scribner's Monthly.

Knowledge is more than equivalent to force.

MENSURATION.

A. H. KENNEDY, SUPT. ROCKPORT SCHOOLS.

(CONCLUDED.)

LIG. 9 is a circle. The first question that must be answered to give a clear explanation of the process of finding the circle's area is, how is it produced? of what elementary parts is it composed? This question must be asked concerning all the surfaces and solids of revolution. If one extremity of a line is moved around in the same place, while the other remains fixed, a circle is produced. This circle is composed of the parts over which the line has passed. These parts, when considered as infinitesimal, are triangles whose bases are the the circle's circumference and whose altitudes are the circle's radius. Dissecting the circle as in Fig. 9, and unfolding its parts as in Fig. 10, a series of triangles is formed. These triangles are the elementary parts that were produced when the circle was generated. The circle is thus unfolded as it was put together. Interposing onehalf of the series of triangles, in the other a parallelogram is

FIG. 9.

wwwwwwww

FIG. 10.

formed, as in Fig. 11. The dimensions of this parallelogram are the circle's semi-circumference and semi-diameter. The product of these dimensions gives the area of the circle. But why is it

FIG. 11.

that the square of the diameter multiplied by that mystic number .7854 will give the area? By rolling a wheel upon a straight edge and accurately

measuring the distance it passes over in one revolution the circumference is found to be about three and one-seventh times the diameter.

Σ =A. (2)

2

Substituting the value of C from (1) in (2) DX3.1416 D

2

=

Cancelling and reducing, D X .7854 A.

X

2

2

This formula expresses the area in a rectangle whose length is

D and whose altitude is 854 ofD.

Fig. 12 is a cylinder. How is it produced? Revolve a rectangle upon one of its edges. The solid thus produced is a cylinder. The

parts, over which this rectangle has passed, when considered as infinitesimal, are triangular prisms, and are the elementary parts. of the cylinder. Dividing the cylinder as in Fig. 12 and unfolding its parts as in Fig. 13, a series of triangular prisms is formed. The cylinder is thus unfolded as it is put together. When onehalf of this series is interposed in the other half, as in Fig. 14, a parallelopiped is formed, whose dimensions are the cylinder's length, semi-diameter and semi-circumference. These dimensions multiplied together give the volume of the cylinder.

The demonstration by means of the blocks harmonizes with the arithmetic process as well as with the manner of the cylinder's generation.

When the length and diameter alone are given, the process may be explained in the same manner as in the case of the circle.

The cylinder, by this process, is reduced to an equivalent, rectangular prism, whose length is that of the cylinder, whose width is the cylinder's diameter, and whose thickness is .7854 of the same. The two processes give rectangular prisms of different dimensions. The convex surface of the cylinder is shown by unfolding it as in Fig. 13. It is a rectangle, whose dimensions are the circle's length and circumference.

The right pyramid and the right cone are of the same nature. Their convex surfaces and volumes are composed of the same elements. Their volumes and convex surfaces are found in the same manner when their altitudes, circumferences and slant

heights are given. I have no cuts of either-only dissected blocks. A triangular prism may be divided into three triangular pyramids, whose bases and altitudes are the same. The volume, then, of the pyramid is one-third of a prism of the same dimensions. The convex surface is composed of triangles, whose altitude is the slant-height. Covering the convex surface of the pyramid with paper and cutting it along the edges, a series of triangles is formed, whose area is found in the same manner as that of the circle.

How is the cone produced? It is produced by revolving a right-angled triangle about the perpendicular. The parts, over which the triangle passes, when considered as infinitesimal, are triangular pyramids. Dissecting the cone reveals its structure. The united volume of these triangular pyramids is computed in the same manner as that of the pyramid. I prove it also by means of conical and cylindrical cups of the same dimensions. The one can be filled from the other exactly three times. The dullest of pupils will make the rule, when he sees it done. By means of the dissected cone the structure of the convex surface appears. It is composed of triangles. These were produced by the revolution of the hypothenuse around the perpendicular. Their combined area is computed in the same manner as that of the circle.

By means of dissected blocks the convex surface of the frustum of the cone, or pyramid, is shown to be made up of trapezoids, whose combined area is computed as shown in Figs. 6, 7 and 8. (See March Journal.)

The sphere-how is it produced? If a semi-circle is revolved about its diameter, a sphere is produced.

The semi-circle is composed of triangles. By their motion about their vertices they generate pyramids, whose bases lie in the surface of the sphere, and whose altitudes are equal to the radius. Dissecting the sphere and unfolding its parts, as in Fig. 15, a set of pyramids is produced. The elementary structure of the sphere is thus rendered visible. to compute the sphere's volume?

Who can not see now how
The surface multiplied by

one-third of the radius, or by one-eighth of the diameter. For