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the figure. The length of the diameters may be varied at pleasure by the monitor.

There are various geometrical rules for drawing ellipses, but it is not within the scope of our work to notice more than one of the simplest forms of ovals. Draw a circle and mark its centre and diameter. Then on one end of the diameter, draw another circle of the same size intersecting the former. Then opening the dividers the length of the diameter, place one foot on the lower point of intersection, and connect the two circles at top, and then do the same by the other point of intersection and the bottom part of the oval.

A simple and amusing method is, to stick two pins into a piece of paper firmly, at any distance from each other; tie the ends of a piece of string together, and put the string round both pins. Hold a pencil then at any part of the string, and move it round; an ellipse will be formed, of which the two pins will be the two foci or centres. By lengthening or shortening the string, the figure may be made more or less elliptical.

15. Draw an oblique cone, (fig. 9.)

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Take a circle for the base, and from some point over this plane or level, draw right lines to the circumference

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of the circle, and you have a cone. A cone is, in fact, a pyramid whose base is a circle, and not a polygon. Sugar loaves are cones.

The height of a cone is a perpendicular let fall from the top or apex to the base. If this perpendicular fall exactly upon the centre of the base, the cone is upright.

The perspective by changing the apparent dimensions of bodies, gives to the base of a cone the form of an ellipse. The cone presents no other difficulty than the ellipse.

16. Draw an upright cone. (fig. 10.)

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17. Draw an oblique cone, and cut it by two planes parallel to the base. (fig. 9.)

18. Draw an oblique cylinder. (fig. 11.)

ters.

Draw two horizontal lines parallel to each other. Draw two equal circles, of which these shall be diameLet a right line go from centre to centre, and it will be the axis. Then draw lines from circumference to circumference, and you have a cylinder. A piece of the funnel of a stove is a cylinder. A cylinder is, in fact, a prism whose bases are circles instead of polygons.

The height of a cylinder is the length of the axis, or the distance from one base to the other. If the axis be perpendicular, the cylinder is upright.

Here, as in the cone, the laws of perspective change the circles into ellipses. The axes of the ellipses, and that of the cylinder, may be given in inches by the monitor.

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19. Draw an upright cylinder. (fig. 12.)

20. Cut a cylinder by a section parallel to its base. (figs. 11 and 12.)

21. Make a cylinder whose axis shall be horizontal. (fig. 13.)

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FIFTH CLASS.

THE figures of the Fifth Class are formed by the union of such lines as have already been given, viz. horizontals, perpendiculars, and arcs of circles or ellipses.

1. Draw a fillet. (fig. 1.)

2. Draw a bead. (fig. 2.)

3. Draw a congee. (fig. 3.)

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These mouldings, as they are called in architecture, are so simple as to need no explanation. Horizontals and verticals will be found in them, with circles, of which the dotted lines mark the centre.

4. Draw a torus with its plinth. (fig. 4.)

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The torus, of which the profile is here given, is a large moulding, usually placed at the base of columns. The torus has its diameter, vertical, and parallel, to the axis of the column. The plinth, is the short cylinder which supports the torus.

5. Make a quarter-round with its fillets. (fig. 5.)

6. Make a quarter-round reversed, with its fillets. (fig. 6.)

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7. Make an ogee or talon with its fillets. (fig. 7.)

8. Make an ogee or talon with its fillets reversed. (fig. 8.)