Things To Make by Archibald Williams (which ebook reader TXT) 📕

on the card should be reduced to a minimum by proper balancing, as the friction generated by a "heavy" pen slows the pendulum very quickly; and that the centre of gravity should be below the point of suspension, to put the pen in stable equilibrium. The lever shown in Fig. 169 is suitable for the Twin Elliptic Pendulum.

In this case the lever is not moved about as a whole. Mr. C. E. Benham advocates the use of wood covered with velvet to rest the lever points on.

For keeping the pen, when not in use, off the platform, a small weight attached to the lever by a thread is convenient. When the pen is working, the weight is raised to slacken the thread.

[Illustration: FIG. 175.—End of pen lever.]

Attaching Pen to Lever.—In the case of wooden levers, it is sufficient to slit the end centrally for a few inches after drilling a hole rather smaller than the pen, at a point which lies over the centre of the card platform, and quite squarely to the lever in all directions, so that the pen point may rest squarely on the card. (Fig. 175.)

Another method is to attach to the end of the lever a vertical half-tube of tin, against which the pen is pressed by small rubber bands; but even more convenient is a small spring clip shaped as in Fig. 176.

[Illustration: FIG. 176.—Clip to hold glass pen.]

The card platform should be perfectly flat. This is essential for the production of good diagrams. If wood is used, it is advisable to glue two thin pieces together under pressure, with the grain of one running at right angles to the other, to prevent warping.

Another important point is to have the card platform square to the rod. If a piece of tubing fitting the rod is turned up true in the lathe and soldered to a disc screwed to the underside of the table, perpendicularity will be assured, and incidentally the table is rendered detachable.

To hold the card in place on the table, slit a spring of an old photographic printing frame down the middle, and screw the two halves, convex side upwards, by one end near two opposite corners of the platform. (See Fig. 170.) If cards of the same size are always used, the table should be marked to assist adjustment.

Making Pens.—The most satisfactory form of pen is undoubtedly a piece of glass tubing drawn out to a point, which is ground down quite smooth. The making of such pens is rather a tedious business, but if care be taken of the pen when made it will last an indefinite time.

Tubing 3/16 or 1/8 inch in external diameter is suitable. Break it up (by nicking with a file) into 9-inch lengths. Take a piece and hold its centre in the flame of a small spirit lamp, and revolve it till it softens. Then draw the glass out in as straight a line as possible, so that the points may be central. If the drawing is done too fast, the points will be much too long to be of any use: half an inch of taper is quite enough.

Assuming that a point of satisfactory shape has been attained—and one must expect some failures before this happens—the pen may be placed in the pen lever and ground down on a perfectly clean wet hone laid on the card platform, which should be given a circular movement. Weight the lever so as to put a fair pressure on the point.

The point should be examined from time to time under a strong magnifying-glass, and tested by blowing through it into a glass of water. For very liquid ink the hole should be as small as you can possibly get it; thick inks, such as Indian, require coarser pens.

The sharp edge is taken off and the width of the point reduced by drawing the pen at an angle along the stone, revolving it all the time. The nearer to the hole you can wear the glass away the finer will be the line made by the pen.

Another method is as follows:—Seal the point by holding it a moment in the flame. A tiny bulb forms on the end, and this has to be ground away till the central hole is reached. This is ascertained by the water test, or by holding the pen point upwards, so that light is reflected from the tip, and examining it under the magnifier. Then grind the edge off, as in the first case.

Care of Pens.—The ink should be well strained, to remove the smallest particles of "suspended matter," and be kept corked. Fill the pen by suction. On no account allow the ink to dry in the pen. Squirt any ink out of it when it is done with, and place it point downwards in a vessel of water, which should have a soft rubber pad at the bottom, and be kept covered to exclude dust. Or the pen may be cleaned out with water and slipped into a holder made by rolling up a piece of corrugated packing-paper. If the point gets stopped up, stand the pen in nitric or sulphuric acid, which will probably dissolve the obstruction; and afterwards wash it out.

Inks.—I have found Stephens's coloured inks very satisfactory, and can recommend them.

Paper and Cards.—The paper or cards used to draw the figures on should not have a coated surface, as the coating tends to clog the pen. The cheapest suitable material is hot pressed paper, a few penny-worths of which will suffice for many designs. Plain white cards with a good surface can be bought for from 8s. to 10s. per thousand.

Lantern Slides.—Moisten one side of a clean lantern slide plate with paraffin and hold it over a candle flame till it is a dead black all over. Very fine tracings can be obtained on the smoked surface if a fine steel point is substituted for the glass pen. The design should be protected by a cover-glass attached to it by a binding strip round the edges.

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.

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.

For the upper harmonies, 1:4 down to 3:8, the two pendulums may be almost equally weighted, the top one somewhat more heavily than the other. The upper weight is brought down the rod as the ratio is lowered.

To continue the harmonies beyond, say, 2:5, it is necessary to load the upper pendulum more heavily, and to lighten the lower one so that the proportionate weights are 5 or 6:1. Starting again with the upper weight high on the rod, several more harmonies may be established, perhaps down to 4:7. Then a third alteration of the weights is needed, the lower being reduced to about one-twentieth of the upper, and the upper weight is once more gradually brought down the rod.

Exact figures are not given, as much depends on the proportions of the apparatus, and the experimenter must find out for himself the exact position of the main weight which gives any desired harmonic. A few general remarks on the action and working of the Twin Elliptic will, however, be useful.

1. Every ratio has two forms.

(a) If the pendulums are working against each other— antagonistically—there will be loops or points on the outside of the figure equal in number to the sum of the figures in the ratio.

(b) If the pendulums are working with each other—concurrently—the loops form inside the figure, and are equal in number to the difference between the figures of the ratio. To take the 1:3 ratio as an example. If the tracing has 3+1=4 loops on the outside, it is a specimen of antagonistic rotation. If, on the other hand, there are 3-1=2 loops on the inside, it is a case of concurrent rotation. (Fig. 176, A.)

2. Figures with a ratio of which the sum of the numbers composing it is an even number (examples, 1:3, 3:5, 3:7) are symmetrical, one half of the figure reproducing the other. If the