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.
The tuning of a harmonograph with independent pendulums is a simple matter. It is merely necessary to move weights up or down until the respective numbers of swings per minute bear to one another the ratio required. This type of harmonograph, if made of convenient size, has its limitations, as it is difficult to get as high a harmonic as 1:2, or the octave with it, owing to the fact that one pendulum must in this case be very much shorter than the other, and therefore is very sensitive to the effects of friction.
[Illustration: FIG. 176a.—Hamonograms illustrating the ratio 1:3. The two on the left are made by the pendulums of a twin elliptical harmonograph when working concurrently; the three on the right by the pendulums when working antagonistically.]
[Illustration: FIG. 177a.—Harmonograms of 3:4 ratio (antagonistically).
(Reproduced with kind permission of Mr. C. E. Benham.)]
The action of the Twin Elliptic Pendulum is more complicated than that of the Rectilinear, as the harmony ratio is not between the swings of deflector and upper pendulum, but rather between the swings of the deflector and that of the system as a whole. Consequently “tuning” is a matter, not of timing, but of experiment.
Assuming that the length of the deflector is kept constant—and in practice this is found to be convenient—the ratios can be altered by altering the weights of one or both pendulums and by adjustment of the upper weight.