The mercury tube should be made first. Take a piece of glass tubing 20
inches long, and bend it at a point 9 inches from one end after heating
in a spirit flame. The legs should be kept as parallel as possible. Lay
the tube, while the heated part is still pliant, on a flat surface, the
bend projecting over the edge, So that the two legs shall be in line.
When the glass has cooled, bend over two inches of the longer leg to an
angle of about 45 degrees.
A standard for the tube is now made out of one-inch wood. Hollow out a
bed in which the tube shall lie and be completely protected. To the
right of the tube the standard is notched to take a small bottle. The
notch should be slightly narrower than the diameter of the bottle, and
have its sides hollowed out to fit.
Halfway up the tube draw a zero mark across the standards, and above
this a scale of inches in fractions on both sides. Each inch represents
1 lb. pressure.
The cork of the bottle must be pierced with a red-hot wire for two
glass tubes, one of which is bent over for the blowing tube. Both tubes
should be pointed at the bottle end so that they may enter the cork
easily. Make the top of the cork air tight with sealing-wax. The
purpose of the bottle is to catch any mercury that might be sucked out
of the tube; one does not wish mercurial poisoning to result from the
experiments. Also it prevents any saliva entering the mercury tube.
When the latter has been secured to the standard by a couple of slips
of tin nailed to the front, connect it up with the bottle, and fill it
up to the zero mark with mercury poured in through a small paper
funnel.
The open end of the tube should be provided with an inch of tubing.
Clips placed on this and on the rubber connection between tube and
bottle will prevent the escape of mercury should the apparatus be upset
when not in use.
The average blowing pressure of which the lungs are capable is about
1-1/2 lbs. per square inch; inspiration pressure without mouth suction
about 1 lb. per square inch; suction pressure 2-1/2 to 3 lbs. per
square inch.
Caution.—Don’t ask people with weak lungs to try experiments with the
apparatus described in this chapter.
XXXI.
HOME-MADE HARMONOGRAPHS.
Have you ever heard of the harmonograph? If not, or if at the most you
have very hazy ideas as to what it is, let me explain. It is an
instrument for recording on paper, or on some other suitable surface,
the figures described by two or more pendulums acting in concert.
The simplest form of harmonograph is shown in Fig. 168. Two pendulums
are so suspended on points that their respective directions of movement
are at right angles to one another—that is, pendulum A can swing only
north and south, as it were, and pendulum B only east and west. On the
top of B is a platform to carry a card, and on the upper end of A a
lever is pivoted so as to be able to swing only vertically upwards and
downwards. At its end this lever carries a pen, which when at rest lies
on the centre of the card platform.
[Illustration: FIG. 168.—Simple Rectilinear Harmonograph.]
The bob, or weight, of a pendulum can be clamped at any point on its
rod, so that the rate or “period” of swing may be adjusted or altered.
The nearer the weight is brought to the point of suspension, the
oftener will the pendulum swing to and fro in a given time—usually
taken as one minute. From this it is obvious that the rates of swing of
the two pendulums can be adjusted relatively to one another. If they
are exactly equal, they are said to be in unison, and under these
conditions the instrument would trace figures varying in outline
between the extremes of a straight line on the one hand and a circle on
the other. A straight line would result if both pendulums were released
at the same time, a circle,[1] if one were released when the other had
half finished a swing, and the intermediate ellipses would be produced
by various alterations of “phase,” or time of the commencement of the
swing of one pendulum relatively to the commencement of the swing of
the other.
[Footnote 1: It should be pointed out here that the presence of
friction reduces the “amplitude,” or distance through which a pendulum
moves, at every swing; so that a true circle cannot be produced by free
swinging pendulums, but only a spiral with coils very close together.]
But the interest of the harmonograph centres round the fact that the
periods of the pendulums can be tuned to one another. Thus, if A be set
to swing twice while B swings three times, an entirely new series of
figures results; and the variety is further increased by altering the
respective amplitudes of swing and phase of the pendulums.
We have now gone far enough to be able to point out why the
harmonograph is so called. In the case just mentioned the period rates
of A and B are as 2: 3. Now, if the note C on the piano be struck the
strings give a certain note, because they vibrate a certain number of
times per second. Strike the G next above the C, and you get a note
resulting from strings vibrating half as many times again per second as
did the C strings—that is, the relative rates of vibration of notes C
and G are the same as those of pendulums A and B—namely, as 2 is to 3.
Hence the “harmony” of the pendulums when so adjusted is known as a
“major fifth,” the musical chord produced by striking C and G
simultaneously.
In like manner if A swings four times to B’s five times, you get a
“major third;” if five times to B’s six times, a “minor third;” and if
once to B’s three times, a “perfect twelfth;” if thrice to B’s five
times, a “major sixth;” if once to B’s twice, an “octave;” and so on.
So far we have considered the figures obtained by two pendulums
swinging in straight lines only. They are beautiful and of infinite
variety, and one advantage attaching to this form of harmonograph is,
that the same figure can be reproduced exactly an indefinite number of
times by releasing the pendulums from the same points.
[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.
Suspensions.—For a harmonograph to give satisfaction it is necessary
that very little friction should be set up at the point of suspension,
so that the pendulums may lose amplitude of swing very slowly.
One-way suspensions are easily made. Two types, the point and
knife-edge respectively, are shown in Fig. 168 and the top part of Fig.
172. The point suspension is most suitable for small rods and moderate
weights; the knife-edge for large rods and heavy weights which would
tend to crush a fine point.
[Illustration: FIG. 171.—Gimbal giving universal movement: point
suspension.]
Points should rest in cup-shaped depressions in a metal plate;
knife-edges in V-shaped grooves in a metal ring.
[Illustration: FIG. 172.—Knife-edge universal-motion gimbal.]
Screws turned or filed to a sharp end make convenient points, as they
can be quickly adjusted so that a line joining the points lies exactly
at right angles to the pendulum. The cups to take the points should not
be drilled until the points have been thus adjusted. Make a punch mark
on the bedplate, and using this as centre for one of the points,
describe an arc of a circle with the other. This will give the exact
centre for the other cup. It is evident that if points and cup centres
do not coincide exactly there must be a certain amount of jamming and
consequent friction.
In making a knife-edge, such as that shown in Fig. 172, put the
finishing touches on with a flat file drawn lengthwise to ensure the
edge being rectilinear. For the same reason the V slots in the ring
support should be worked out together. If they are formed separately,
the chances are against their being in line with one another.
Gimbals, or universal joints, giving motion in all directions, require
the employment of a ring which supports one pair of edges or points
(Fig. 172), and is itself supported on another pair of edges or points
set at right angles to the first. The cups or nicks in the ring should
come halfway through, so that all four points of suspension shall be in
the same plane. If they are not, the pendulum will not have the same
swing-period in all directions. If a gimbal does not work with equal
freedom in all ways, there will be a tendency for the pendulum to lose
motion in the direction in which most friction occurs.
By wedging up the ring of a gimbal the motion of the pendulum is
changed from universal to rectilinear. If you are making a harmonograph
of the type shown in Fig. 168, use a gimbal for the platform pendulum,
and design it so that the upper suspension gives a motion at right
angles to the pen pendulum. The use of two little wedges will then
convert the apparatus in a moment from semirectilinear to purely
rectilinear.
Weights.—The provision of weights which can be slipped up and down a
rod may present some difficulty. Of iron and lead, lead is the more
convenient material, as occupying less space, weight for weight, and
being more easily cast or shaped. I have found thin sheet roofing lead,
running 2 lbs. to the square foot, very suitable for making weights, by
rolling a carefully squared strip of the material round the rod on
which it will have to move, or round a piece of brass tubing which fits
the rod. When the weight has been rolled, drill four holes in it, on
opposite sides near the ends, to take nails, shortened so that they
just penetrate all the laps but do not enter the central circular
space. These will prevent the laps sliding over one another endways. A
few turns of wire round the weight over the heads makes everything
snug.
Just one caution here. The outside lap of lead should finish at the
point on the circumference where the first lap began, for the weight to
be approximately symmetrical about the centre.
An alternative method is to melt up scrap lead and cast weights in tins
or flowerpots sunk in sand, using an accurately centred stick as the
core. This stick should be very slightly larger than the pendulum rod,
to allow for the charring away of the outside by the molten metal.
(Caution.—The mould must be quite dry.)
Failing lead, tin canisters filled with metal scrap may be made to
serve. It will in this case be necessary to bore the lid and bottom
centrally and solder in a tube fitting the rod, and to make an opening
through which the weighting material can be inserted.
Adjustment of Weights.—As lead is too soft a metal to give a
satisfactory purchase to a screw—a thread cut in it soon wears out—it
is better to support a leaden weight from underneath by means of a
brass collar and screw. A collar is easily made out of a bit of tubing
thickened at the point where the screw will pass by soldering on a
suitably shaped piece of metal. Drill through the reinforcement and
tubing and tap to suit the screw used, which may well be a camera tail
screw, with a large flat head.
I experienced some trouble from the crushing of wooden rods by a screw,
but got over it as follows. The tubing selected for the collar was
large enough to allow a piece of slightly smaller tubing to be
introduced between it and the rod. This inner piece was slit from one
end almost to the other, on opposite sides, and soldered at one end to
the outer tube, a line joining the slots being at right angles to the
axis of the screw. The pressure of the screw point was thus distributed
over a sufficient area of the wood to prevent indentation. (See Fig.
173.)
[Illustration: FIG. 173.]
[Illustration: FIG. 174.—Pivot for pen lever.]
Pen Levers.—The pen lever, of whatever kind it be, must work on its
pivots with very little friction, and be capable of fine adjustment as
regards balance. For the Rectilinear Harmonograph the form of lever
pivot shown in Fig. 174 is very suitable. The spindle is a wire nail or
piece of knitting needle sharpened at both ends; the bearings, two
screws filed flat at the ends and notched with a drill.
The brass standard should be drilled and tapped to fit the screws
fairly tight, so that when once adjusted they may not slacken off. If
the lever is made of wood, the tail may be provided with a number of
metal pegs on which to place the weights; if of wire, the tail should
be threaded so that a brass weight and lock screw may be moved along it
to any desired position. It is very important that the pressure of the
pen 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.