ness. Projecting from the centre of the circumference of each drum, at right angles to the axis, are eight spokes or levers, three inches by four inches in size, and with a projection of ten inches beyond the drum.

A smaller shaft, or axle, Y Y, six inches in diameter, projects, centrally, sixteen inches beyond the ends of the larger shaft, and, immediately beyond the ends of this larger shaft, rests in two bracing supports, each eight inches wide, fitted to receive the axle.

At A the front drum is drawn separately, together with the end of the shaft and the projecting axle, but without the spokes or levers, and without the support in which the axle rests. Here a is the centre of the axle, where it connects with the shaft, and also the centre of the end of the shaft, while b is the centre of the front face of the drum, and c the centre of the farther face or side.

At B is a separate drawing of the support in which the front axle rests. The timber forming the base in which the braces rest is forty inches in length, four inches in vertical thickness, and eight inches in width. The supporting braces are two by eight inches, and about twenty-three inches in length above the base. The tie-brace at the top is cut out in a semicircular form, six inches in diameter, to receive the axle.

At C is a representation of the drum, W, with the spokes in their places. It is here drawn separately for the purpose of showing the method of placing the spokes accurately in the centre of the cylindrical surface of the drum. This drawing may be made in the following order:

1st. Take some point, a, as the centre, from which, with a radius of fourteen inches, describe the circumference of the nearer and visible end of the drum; and from d, twelve inches diagonally from a, on the axis, with the same radius, describe the farther circumference, only half of which is visible.

2d. Now, as the spokes to be inserted are three inches wide on their face or front side, and four inches diagonally, they must be inserted in the central third portion of the cylindrical surface of the drum. We therefore take a d,

representing the line of the axis of the drum, and divide it into three equal parts by the points b and c; and from b and c as centres, with a radius of fourteen inches, we describe the two dotted circles encompassing the drum. These two circles mark out the central third part of the cylindrical surface of the drum, as they would appear to the eye if the drum were transparent. The spokes must therefore start out from the drum between these circles, and touching them.

3d. These spokes we may consider four in number, equidistant from one another, passing at right angles through the axis of the drum, and presenting eight projecting arms to our view. For convenience, we will suppose the circumference of the nearer dotted circle to be divided into eight equal portions by the vertical line 1 2, the horizontal line 56, and the two diagonal lines 3 4 and 7 8, giving us the equidistant points f, h, j, m, o, 9, 9, and 10. From f, as a starting-point, measure off any desired distance, as fg, and take g as the point for the intersection of a corner of the spoke with the dotted line. From h measure off the same space to i, and the same fromj to k, from m to n, from o to p, etc., for points at which the corners of spokes pass through the circumference of the drum.

4th. From each of the several points, g, i, k, n, p, etc., measure off three inches backward on the dotted line, as g 11, i 12, etc., for the width of the face of each spoke. Connect the points that are directly opposite, as 11 p, g 13, etc., by very light lines extended indefinitely, every pair of which will pass equidistant on each side of the central point, b, and will represent the front faces of the spokes as passing through the axis of the drum.

5th. The length of the projecting arms, or spokes, may be determined by circumscribing a circle around the centre, b. Here the circle, which may be called the nearer face circle of the spokes, is drawn with a radius of twenty-four inches, giving ten inches for the length of the spokes, and passing through the points e, 8, x, etc. Now, as the spokes are four inches in diagonal width, we describe another circle with the same radius from c (four inches diagonally from 6), passing

through the points 5, 3, 1, 8, w, y, etc., thus limiting the diagonal width of the spokes. Suppose, now, that the corner face lines of the spokes, as g e, 16 r, etc., extend to the nearer face circle e 8 x. From the intersections of these corner lines with this nearer face circle, giving the points t, r, v, z, x, etc., we draw lines diagonally, as t u, r s, e l, v w, x y, etc., which give us the side boundary-lines of the ends of the spokes.

6th. The lines 16 17, 11 18, 12 19, etc., showing the intersections of the sides of the spokes with the surface of the drum, we also draw diagonally-for all lines that are parallel in the real wheel must be parallel in the drawing..

The outlines of the spokes are thus completed-all accurately drawn in their proper places, as projecting from the central third part of the surface of the drum.

At D the several parts described in the sections A, B, and Care put together, resting on a timber platform. Let the pupil verify the following measures according to the scale.

1st. The distance, xy, between the drums, is fifty-six inches. The distance, c d, on the axis, between the centres of the inner faces of the two drums, must give the same

measure.

2d. As each drum is twelve inches in thickness, the distance, rz, between the outer faces of the drums, must be eighty inches. The distance, bg, between the points on the axis, from which the circumference of these outer faces are described, must give the same measure.

3d. As the large shaft extends four inches beyond the extreme faces of the two drums, the length of the shaft, whether measured diagonally on its surface or on its axis, must be eighty-eight inches. The farther end of the large shaft is concealed from view, but its position can be easily determined by counting twenty-two spaces diagonally from the point 5.

4th. As the tops of the bracing supports of the axle are in immediate contact with the ends of the shaft, the distance between the inner faces of the tops of these supports must also measure eighty-eight inches.

5th. As each of the bracing supports is eight inches in

width, the distance, s t, between the extreme faces of the tops of these supports, must be one hundred and four inches. We thus get the point t, and the outlines of the concealed top of the farther brace.

6th. As we have the point 1 at the bottom of the nearer brace, we now know that the corresponding point 2 of the farther brace must be one hundred and four inches from it diagonally-that is, twenty-six diagonal spaces. The distance from 3 to 4 must measure the same.

We have been thus particular in describing the drawing of this figure for the purpose of showing that every part may be drawn with the most perfect accuracy, and so as to show its exact measurement. With the aid of the ruled drawing-paper all such drawings may be executed with great rapidity; and any required degree of modification, also, from the plain angular forms, may be given to them. Thus the spokes may be round, or even tapering, and lighter than here shown, and all the parts may be modified, while at the same time accuracy of representation may be adhered to, provided the very plain principles of this mode of representation are clearly understood.

DRAWING-BOOK No. IV.

CABINET PERSPECTIVE - MISCELLANEOUS

APPLICATIONS.

I. DIFFERENT DIAGONAL VIEWS OF OBJECTS.

IN the preceding two books on Cabinet Perspective, objects have been represented not only as viewed diagonally, with their principal surfaces in vertical and horizontal positions, but as viewed diagonally from one particular point, which point is supposed to be diagonally at the right of the object, and above it. But although, for the purpose of avoiding confusion, it is best to represent all objects from this one point of view whenever it can be done to advantage, yet objects may be represented diagonally in cabinet perspective equally well from any one of four points of view, as will be seen from the drawing on the first page of Book No. IV.

PAGE ONE.

1st. Upper right-hand view.-In division A the objects. are represented as viewed diagonally from above, and at the right, the same as in all the drawings in the preceding two books. The arrow, m, is represented as coming from the position, at an infinite distance away, from which the objects in A are viewed.

2d. Lower right-hand view.-In division B the objects are represented as viewed from below, and at the right; and here the arrow, n, is represented as coming from the position, at an infinite distance away, from which the objects are viewed. It will be observed that the bracket, ƒ, is best