To inscribe an octagon in a square. Draw the diagonals a c and b d. With a as a center, and a e as a radius, strike an arc cutting the sides of the square at ƒ and h. Repeat the operation at b, c, and d, and draw lines connecting the eight points thus found to form the figure required. a To draw any regular polygon in a circle. Divide 360° by the number of sides; the quotient will be the angle a o b. Lay off this angle at the center with a protractor, and draw its chord, a side of the required polygon. Step this side around on the circumference, and connect the points found. To draw a segment of a circle, having given the chord ab and height c d. Draw ef, through d, parallel to a b; also, a d and db. Draw ae and b ƒ perpendicular to ad and db; also a h and bk perpendicular to ab. Divide ed, df, ac, cb, a h, and bk into the same number of equal parts. Draw lines connecting the points as shown, and trace the curve through the intersections. h a d с To draw a segment of a circle by means of a fixed triangle. Let ab be the required chord, and de the rise. Drive nails at a and b. Make a triangle, as shown, from thin strips, so that the vertex comer at c, and stiffen it with the crossbrace. Now, by moving the triangle, always keeping the sides touching the nails at a and b, the arc may be traced by a pencil held at c. To draw an ellipse, having given the axes. Draw concentric circles whose diameters are equal to the axes ab and cd. From o draw any radius, as o e. From g, where o e cuts the inner circle, draw gf parallel to the major axis a b. From e, draw ef parallel to the minor axis d c. The intersection f gives a point on the ellipse. Other points are similarly found. To draw an ellipse with a string, having given the axes a b and c d. With c as a center, and a radius equal to o b, strike arcs cutting the major axis at e and ƒ, the foci of the ellipse. Stick pins at e and ƒ, and attach a string as shown, the length of the string being equal to the length of the major axis. Keep the string stretched with a pencil point, and sweep around the ellipse. To draw a parabola. Having given the coordinates a band b c, to draw a parabola, complete the rectangle a b c d. Divide be and c d into the same number of equal parts. From 1', 2', 3', etc., draw lines through a. Through 1, 2, 3, etc., draw lines parallel to a b. The intersections of 1' a and 1-1", of 2' points on the required parabola. a and 2-2", etc. are LAYING OUT ANGLES. 216 By Two-Foot Rule.-To lay off any angle given in the table, open the rule at the middle until the distance between the inside corners at the knuckle joints (6-inches mark) is equal to the distance given for that angle under Chord. To lay off an angle greater than 90°, subtract the angle from 180°; lay out the latter angle, extending one side. BLUEPRINTS. Plumbers and fitters' drawings are usually blueprints. They are copies of drawings of the plumbing or heating system made on tracing cloth. Blueprint paper for copying tracings of plans and other drawings may be prepared as follows: Dissolve 1 oz. avoirdupois, of ammonia citrate of iron in 6 oz. of water, and in a separate bottle dissolve the same quantity of potassium ferricyanide in 6 oz. of water. Keep these solutions separate, and in a dark place, or in opaque bottles. To prepare the paper, mix equal quantities of the two solutions, and with a sponge spread it evenly over the surface. Let the paper remain in a horizontal position until the chemical has set on the surface, which will take but a few minutes; then hang the paper up to dry. In preparing the paper darken the room by pulling down the shades, as direct rays of light affect sensitized surfaces. The prepared paper should be kept in a closed drawer, well covered with heavy paper, so that no light can come in contact with the sensitized surface; otherwise it will lose much of its value. To make a blueprint from a tracing, lay the tracing with ink side down against the glass of the printing frame, then take the prepared paper, and place the sensitized surface down on the tracing. On the top of the paper place the felt cushion, on top of which place the hinged back of the printing frame, after which expose to the sunlight. The exposure will vary in sunlight from about 3 to 10 minutes. After the exposure, wash the paper thoroughly in a trough of cold water for about 10 minutes, and hang it up to dry. The print after washing should be of a deep-blue color, with clear white lines. If the color is a pale blue, this indicates that the print has not had sufficient exposure, and if the lines of the drawing are not perfectly clear and white, that the exposure has been too long. Corrections may be made on the print with an ordinary writing or ruling pen and a solution of washing soda, caustic potash, strong ammonia, or any other alkali. When any of these are mixed with carmine ink, the marks on the print will be red, thus making the corrections clear. MECHANICS. FALLING BODIES. Let g = 32 16 = constant acceleration due to the attraction of the earth; number of seconds that the body falls; velocity in feet per second at the end of the time t; distance that the body falls during the time t. h F W = = CENTRIFUGAL FORCE. centrifugal force in pounds; weight of revolving body in pounds; r = distance from the axis of motion to the center of gravity of the body in feet; N = number of revolutions per minute; v = velocity in feet per second. In calculating the centrifugal force of flywheels, it is customary to neglect the arms and take r equal to the mean radius of the rim; in such cases W is taken as one-half the weight of the rim. The result thus obtained, divided by π is approximately the force tending to burst the flywheel rim. EXAMPLE.-What is the force tending to burst a flywheel rim weighing 7 tons, making 150 rev. per min., and having a mean radius of 5 ft.? SOLUTION. F= .00034 X (X7 × 2,000) 5 X 1502 85,227 lb. |