Details of Harmonographs.

The reader may be interested in details of the apparatus shown in Figs. 168 and 170, made by the writer.

The Rectilinear Harmonograph, shown in Fig. 168, has pendulums of 5/8-inch wood, 40 inches long, suspended 30 inches from the lower ends, and set 10 inches apart, centre to centre.  The suspensions are of the point type.  The weights scale 5 lbs. each.  The platform pendulum is provided with a second weight, which can be affixed above the suspension to slow that pendulum for 2:3, 4:5, 7:8, and higher harmonies.

The baseboard is plain, and when the apparatus is in action its ends are supported on boxes or books laid on two tables, or on other convenient supports.  The whole apparatus can be taken to pieces very quickly for transport.  The total cost of materials used did not exceed 3s. 6d.

The Twin Elliptic Pendulum of Fig. 170 is supported on a tripod base made of three pieces of 1-1/2 x 1-1/2 inch wood, 40 inches long, with ends cut off to an angle of 72 degrees to give a convenient straddle, screwed at the top to an oak head 3/4 inch thick, and braced a foot below the top by horizontal crossbars 2 inches wide and 1/2 inch thick.  For transport this stand can be replaced by a flat baseboard similar to that of the Rectilinear Harmonograph described in the last paragraph.

The main pendulum is a straight ash rod, 33 inches long and 1-1/4 inches in diameter, suspended 13-1/2 inches from its upper end.  Two weights of 4-1/2 lbs. each, made of rolled sheet lead, are provided for this pendulum.  According to the nature of the harmony, one only, or both together below the suspension, or one above and one below, are used.

The weight of the lower pendulum, or deflector, is supported on a disc, resting on a pin passing through the bottom of a piece of brass tubing, which is provided with an eye at its upper end.  This eye is connected by a hook with several strands of silk thread, which are attached to the upper pendulum by part of a cycle tyre valve.  The stem part of the valve was cut off from the nut, and driven into a suitably sized hole in the end of the main pendulum.  The screw collar for holding the valve in place had a little brass disc soldered to the outside, and this disc was bored centrally for the threads to pass through.  The edges of the hole had been rounded off carefully to prevent fraying of the threads. (Fig. 177.) The over-all length of the pendulum, reckoning from the point of suspension, is 20 inches.  The weights of the lower pendulum are several in number, ranging from l lb. to 3 lbs.

[Illustration:  Fig. 177.—­Suspension for lower weight of Twin Elliptic Harmonograph.]

Working the Harmonograph.—­A preliminary remark is needed here.  Harmonies are, as we have seen, a question of ratio of swing periods.  The larger the number of swings made by the more quickly moving pendulum relatively to that of the slower pendulum in a given time, the higher or sharper is the harmony said to be.  Thus, 1:3 is a higher harmony than 1:2, and 2:3 is lower or flatter than 3:8.