[Illustration:  Fig. 169.—­Goold’s Twin Elliptic Pendulum Hamonograph.]

But a fresh field is opened if for the one-direction suspension of pendulum B we substitute a gimbal, or universal joint, permitting movement in all directions, so that the pendulum is able to describe a more or less circular path.  The figures obtained by this simple modification are the results of compounded rectilinear and circular movements.

[Illustration:  Fig. 170.—­Benham’s miniature Twin Elliptic Pendulum Harmonograph.]

The reader will probably now see even fresh possibilities if both pendulums are given universal movement.  This can be effected with the independent pendulums; but a more convenient method of obtaining equivalent results is presented in the Twin Elliptic Pendulum invented by Mr. Joseph Goold, and shown in Fig. 169.  It consists of—­(1) a long pendulum, free to swing in all directions, suspended from the ceiling or some other suitable point.  The card on which the figure is to be traced, and the weights, are placed on a platform at the bottom of this pendulum. (2) A second and shorter free pendulum, known as the “deflector,” hung from the bottom of the first.

This form of harmonograph gives figures of infinite variety and of extreme beauty and complexity.  Its chief drawback is its length and weight, which render it more or less of a fixture.

Fortunately, Mr. C. E. Benham of Colchester has devised a Miniature Twin Elliptic Pendulum which possesses the advantages of the Goold, but can be transported easily and set up anywhere.  This apparatus is sketched in Fig. 170.  The main or platform pendulum resembles in this case that of the Rectilinear Harmonograph, the card platform being above the point of suspension.

Value of the Harmonograph.—­A small portable harmonograph will be found to be a good means of entertaining friends at home or elsewhere.  The gradual growth of the figure, as the card moves to and fro under the pen, will arouse the interest of the least scientifically inclined person; in fact, the trouble is rather to persuade spectators that they have had enough than to attract their attention.  The cards on which designs have been drawn are in great request, so that the pleasure of the entertainment does not end with the mere exhibition.  An album filled with picked designs, showing different harmonies and executed in inks of various colours, is a formidable rival to the choicest results of the amateur photographer’s skill.

Practical Instructions for making Harmonographs.

Pendulums.—­For the Rectilinear type of harmonograph wooden rods 5/8 to 3/4 inch in diameter will be found very suitable.  They cost about 2d. each.  Be careful to select straight specimens.  The upper pendulum of the Miniature Twin Elliptic type should be of stouter stuff, say a broomstick; that of the Goold apparatus stouter still.

All pendulums on which weights are slid up and down should be graduated in inches and fractions, reckoning from the point of suspension as zero.  The graduation makes it easy to re-establish any harmony after the weights have been shifted.