Things To Make Part 25

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 pa.s.sing through the bottom of a piece of bra.s.s 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 bra.s.s disc soldered to the outside, and this disc was bored centrally for the threads to pa.s.s 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.

[Ill.u.s.tration: 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.

[Ill.u.s.tration: FIG. 176a.--Hamonograms ill.u.s.trating 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.]

[Ill.u.s.tration: 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.

a.s.suming 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 sum is Uneven, as in 1:2, 2:3, 2:7, the figure is unsymmetrical. (Fig. 177, A.)

3. The ratio 1:3 is the easiest to begin upon, so the experimenter's first efforts may be directed to it. He should watch the growth of the figure closely, and note whether the repeat line is made in front of or behind the previous line of the same loop. In the first case the figure is too flat, and the weight of the upper pendulum must be raised; in the second case the weight must be lowered. Immediately an exact harmonic is found, the position of the weight should be recorded.

Interesting effects are obtained by removing the lower pendulum and allowing the apparatus to describe two elliptical figures successively, one on the top of the other, on the same card. The crossing of the lines gives a "watered silk" appearance to the design, which, if the pen is a very fine one and the lines very close together, is in many cases very beautiful.

Readers who wish for further information on this fascinating subject are recommended to purchase "Harmonic Vibrations," published by Messrs. Newton and Co., 72 Wigmore Street, London, W. This book, to which I am much indebted, contains, besides much practical instruction, a number of charming reproductions of harmonograms.

Before closing this chapter I should like to acknowledge the kind a.s.sistance given me by Mr. C. E. Benham, who has made a long and careful study of the harmonograph.

x.x.xII. A SELF-SUPPLYING MATCHBOX.

This useful little article can be constructed in a couple of hours by a handy person. In general idea it consists of a diamond-shaped box to hold vestas, working up and down diagonally on a vertical member (A in Fig. 179 (1)), which pa.s.ses through slits at the top and bottom, and runs in grooves cut in the sides of the box. The top of A is grooved to allow a match to rest on it. When the box is drawn up to the full extent allowed by a transverse pin in the slot shown in Fig. 179 (2), the groove is at the lowest point of the box, and is covered by the matches. When the box is lowered, A catches a vesta and takes it up through the top, as seen in Fig.

178, for removal by the fingers.

The only materials required are a cigar-box, some pins, and a supply of glue. The box should be carefully taken to pieces, and the parts soaked in hot water till freed of all paper, and then allowed to dry under pressure, small slips of wood being interposed across the grain to keep them separate and permit the pa.s.sage of air.

[Ill.u.s.tration: FIG. 178.--Self-supplying matchbox, with match in position for removal by fingers.]

When the wood is dry, cut out with a fret saw two pieces shaped like Fig.

179 (3), to form the ends of the box. Allow a little surplus, so that the edges may be finished off neatly with chisel and plane. The two ends should match exactly, or there will be trouble at a later stage.

Now cut, down the centre of each a groove for one edge of A to run in. By preference it should be square; but if you do not possess the necessary chisel, a V groove made with a knife will suffice--and, of course, in this case the edges of A will have to be bevelled to fit.

[Ill.u.s.tration: FIG. 179.--Details of self suplying matchbox.]

The four sides of the box, BB and CC, are next cut out. Their sectional shape is shown in Fig. 179 (1). They should be rather longer than the length of the ordinary vesta, and all of exactly the same length, and rectangular. A very small hack saw (costing about 1s.) with fine teeth is the best possible tool for close cutting, and a small 1 shilling iron plane is invaluable for truing and bevelling the edges.

The glue pot, which we will a.s.sume to be ready for use, is now needed to attach the fixed B (the other B is hinged to form a lid for filling the box through) and CC to the ends. This operation must be carried out accurately, so that the slots may not be blocked.

While the glue is setting, cut out A, allowing an extra 1/16 inch of width for fitting. The slot down the centre is best made with a fret saw, and should be smoothed internally by drawing a strip of fine gla.s.s paper to and fro through it. The length of the slot is of great importance. It must reach to just that distance from the top edge which brings that edge flush with the bottom of the box when the box is raised; and in the other direction must permit the box to settle on to its foot, so that the match lifted shall project above the box.

Work the edges of A down carefully (double-bevelling them if the notches are V-shaped) till A will run easily, but not loosely, in the box. Then cut out two slips, DD, and bevel them at the top to an angle of 45 degrees.

Put A in place and glue them on, taking care that the glue does not hold them fast to A.

Pierce a small hole through DD, in line with the slot, and insert a pin.

Draw the box fully up, and see if the top of A sinks to the proper place.

If it projects a little, lengthen the slot a trifle.

Cut out the supports EE, finish them neatly, and glue them to A. Make sure that the pin lets the box touch them.

Fix on the lid B with two pins for pivots, and fit a little catch made of bra.s.s wire. To give extra security, drive ordinary pins, cut off to 5/8 inch, through the sides into fixed B, CC, and DD, and through EE into A.

This is an easy enough business if pilot holes are made with a very fine awl or a tiny drill, and a small, light hammer is used. It now remains only to go over the whole box with gla.s.s paper or emery cloth, and to glue a diamond of coa.r.s.e gla.s.s paper to one end for striking the matches on.

Note that the lid must not be opened when the box is down, as it would be wrenched off its pivots.

x.x.xIII. A WOODEN WORKBOX.

The box ill.u.s.trated by Fig. 181 was copied from an article of Norwegian manufacture. Its construction is an extremely simple matter, provided that one can get a piece of easily bent wood (birch, for instance), not exceeding 3/16 inch in thickness, for the sides.

[Ill.u.s.tration: FIG. 180.--Showing how to draw an ellipse.]

[Ill.u.s.tration: FIG. 181.--Norwegian workbox.]

The bottom of the box is made of 5/16 or 3/8 inch wood, cut to an oval or elliptical shape. To mark out an ellipse about 8 inches long and 5-1/2 inches wide--this will be a. convenient size--stick two pins into the board 5-1/8 inches apart, pa.s.s a loop of thread 14 inches in circ.u.mference round these, and run the point of a pencil round the pins in the path which it has to take when confined by the slack of the loop (Fig. 180). Fret-saw along the line.

The wood strip for the side is 4-1/2 inches deep, and 1-1/2 inches longer than the circ.u.mference of the bottom. The ends are thinned off somewhat, as shown in Fig. 181, to prevent the lap having a clumsy appearance, and the surface is smoothed all over with sandpaper. Bore a number of small nail holes 3/16 inch from one edge, and then steam the wood over a big saucepan or other suitable vessel until it is quite lissom.

When attaching the side piece to the bottom, begin at the middle, and work first towards what will be the inside end of the lap, and then towards the outside end. Nails are driven in through the holes already drilled. When nailing is finished, clip the top of the overlap with a hand-vice or screw spanner, to prevent the tops of the ends sliding over one another, and bore a line of holes l/4 inch apart, and at the same distance from the outer end. Fine copper wire drawn to and fro through alternate holes from one end of the row to the other and back again, will secure the joint.