a cork. Grind down the end of C until it is again flat, and repeat until observations have been obtained with orifices of five or six different sizes. Now place the cork on the dividing engine, Experiment 21, and measure the diameter of each of the ground ends. This may be obtained with great accuracy by placing the axis of the tube vertical so as to look down through it.

x =

Lets be the specific gravity of the liquid and x the height to which it would tend to rise in the tube, if the bore were the same throughout as at the end. The pressure due to this force will then be sx, and in the same way the pressure due to the column h' will be sh'. Both of these pressures will be in equilibrium with the force h of the water in B. In other words, h = sx + sh', or h sh' from which x may be calculated in the various cases. If the liquid in D is water, s = h h'. This method of studying capillarity was first proposed by M. Simon, who, however, found that his results did not agree with those obtained by direct measurement. It has, however, the great advantage that the diameter may be obtained with accuracy, even with very minute tubes, and the latter being heated to redness are rendered Fig. 3.46. See Salleron's Cat, p. 81 chemically clean.

ners.

1, and x =

53. PLATEAU'S EXPERIMENT.

Apparatus. Some of Plateau's soap-bubble mixture, formed by mixing pure oleate of soda with 30 parts of water, and adding two thirds its bulk of glycerine. The oleate is made of olive oil and soda, which is then filtered. Common soap may however be used. Wires are bent into the following forms and soldered at the corA tetrahedron with a single wire as a handle, a cube, a circle, two triangles hinged along one side, and two squares, made in the same way, also a small vertical stand arranged so that two circles may be placed on it at any height. To measure the figures obtained, an upright C, Fig. 43, is attached to the table to support a sheet of paper and at a distance of about two feet is a second support, A, in which is a small hole to look through. A third stand, B, serves to hold the wire figures in any desired position.

Experiment. Dip the tetrahedron into the liquid, and on drawing it out, films will be found extending from each of the six edges, and meeting in the centre. This point is a fourth of the distance from each face to the opposite angle. Attach the tetrahe

A

B

C

dron to B, so that one face shall be nearly horizontal, and one edge perpendicular to the line through ABC. On looking through A it is projected as a triangle on C. Move B, if necessary, so that its lower face shall be projected as a straight line. Attach a piece of paper to C and mark on it the corners of the tetrahedron, also the intersection of the films. Measure on the paper the distance of this point from the top and bottom of the figure. Their ratio should be one to three. Turn the tetrahedron around, and repeat the measurement with one of the other sides. It should be the same for all.

Fig. 43.

A general law of these films is that they are always subjected to tension and continually tend to contract, owing to the molecular attraction of the particles. This may be shown in various ways. Attach a loop of the finest silk thread to the circle of wire. Dip it in the liquid, and a film will be obtained in which the loop will float, irregular in shape and in any position. Break the film inside the loop, and instantly by the contraction of the film around it, it will be drawn out into a perfect circle, leaving of course a hole in the centre. Inclining the circle from side to side the loop moves freely over the film, presenting the curious appearance of a sheet of liquid containing a moveable hole.

Immerse the tetrahedron again in the liquid. The six films pulling equally in opposite directions, hold the centre point in equilibrium. Now break one of the films, and the remainder contracts, forming a curious curved surface drawn towards one side by a single plane film. On breaking this second film, the surfaces again contract and form the warped surface known as the hyperbolic paraboloid.

Immersing the cube in the same way twelve plane surfaces are obtained, meeting in a small square in the centre. This square may be parallel to either face, aud may be made to alter its position by gently blowing, so as in appearance to split it. See how many different figures can be obtained by breaking one or more films, and draw them in your note book. The whole number is twelve, not including a single plane attached to one face only. If

the films attached to two opposite parallel sides are broken, a plane is obtained supported between two curved surfaces, the intersections being curved lines. Draw these lines by attaching the cube to B and see if they are hyperbolas. Another curious effect is obtained by blowing a small bubble and attaching it to the centre square, when it assumes a cubical form with curved sides; in the same way a four-sided bubble may be formed with the tetrahedron. Similar figures may be obtained with an octahedron, or other figures, but they are more complex.

On dipping the two triangles into the liquid a film forms over both, and on increasing the angle between them a single plane film is found attached to their common side, which is split as they separate. Breaking this film the curve springs back as before, forming a very beautiful hyperbolic paraboloid. This is probably the best way of producing this warped surface, and its properties are well shown by it. Varying the angle between the triangles, its form, or, more strictly, its parameter may be altered at will. Make the angle between the triangles about 30°, and draw the curve of intersection of the plane film with the other, also a section through the centre at right angles to it. Try and determine the form of the first of these curves, and see if it is a circle, parabola or hyperbola. Now break the film and draw the enveloping curves on the same sheet as before, to show how the films have contracted. Do the same with the jointed squares. Place the two circles on their stand near together, blow a bubble and lay it on them. Then draw them apart, and a hyperboloid of revolution of one nappe will be obtained.

54. PNEUMATICS.

Apparatus. The object of this experiment is to familiarize the student with the ordinary lecture-room apparatus in pneumatics, and is therefore chiefly of value to those who propose to adopt teaching as a profession. The apparatus needed will depend on the objects of each student, but may be made to include almost all the instruments used in a full course of lectures on this branch of physics. The following description, however, applies only to such experiments as could properly be introduced in any common school. The most important instrument is of course the air pump, which need not be of large size, or (for most of these experiments) capable of producing a very high degree of exhaustion. The

other apparatus needed is best determined from the following list of experiments, which may be varied almost indefinitely.

Experiment. Place a receiver on the pump-plate, taking care that no dust or grit is retained under the edge, which should be freely supplied with sperm oil, or tallow, to ensure contact. Open communication between the pump and receiver, and close that leading to the outer air. Exhaust, by working the handle of the pump, and see if any leakage takes place around the bottom of the receiver, in which case air bubbles will be seen forcing their way through the oil. The greatest trouble in using the air-pump is to make this joint tight, especially if the plate or receiver is not ground perfectly true. When the exhaustion is nearly complete the pump handle will work freely, until the very end of the stroke, when a slight hissing will be heard, due to the expulsion of the remaining air. For this reason the piston must be moved until it strikes the end of the cylinder each time, and the strokes must be taken steadily, and not too fast. When the air is removed the exterior pressure becomes so great that it is impossible to move the receiver without breaking the glass. On opening communication with the outer air, the latter rushes in, and the receiver is easily removed. To determine the degree of exhaustion, a syphon vacuum gauge may be employed. This consists of a bent glass tube like a syphon barometer, with the closed end only about half a foot in length, and containing mercury, which of course rises to the top. Place it under a receiver and exhaust, when it will be found that as soon as the pressure inside is reduced to less than six inches the mercury begins to fall, until in a perfect vacuum it would stand at the same height in both branches of the tube. Read the difference in level, which in a common pump should not exceed two or three millimetres. If a barometer gauge, or long tube dipping in mercury, is attached to the pump, subtract its reading from that of the standard barometer, and the difference should equal that of the syphon gauge. Place a beaker of water on the pump-plate with a bolt head (or tube with a bulb blown at one end) in it, cover with a receiver and exhaust slowly. The air will now bubble up through the water, owing to its tendency to expand when the outer pressure is removed. If the pump is a very nice one, this

experiment, and others requiring water, should be omitted, as the vapor may rust the interior of the pump. On readmitting the air the water will rush up into the bolt-head until but a small bubble of air remains. The ratio of the volume of this bubble to the whole interior of the bolt-head, shows the degree of exhaustion. When nearly all the pressure of the air is removed from the surface, the water bubbles make their appearance in it, due to the dissolved air. Carrying the exhaustion still farther, vapor begins to be formed so rapidly that the water enters into ebullition. This effect is more easily obtained if the water is somewhat warm. Select two tubes about three feet long, and closed at one end, fill one, B, with mercury (Experiment 58), the other, A, with air, and dip both into a small vessel containing mercury. Cover them with a tall receiver and exhaust. The mercury will descend in B until nearly on a level with that in the cistern, the air meanwhile escaping from A in bubbles. Readmit the air and the mercury will rise in both tubes, that in A being the lowest. Any leakage in the pump is well shown in these experiments, as it will cause the liquid to begin to rise slowly as soon as the pumping stops. To see if the leak is in the pump, or under the receiver, close the connection between them when leaks in the latter only will be perceptible. The great pressure of the air may be shown in various ways. Thus the palm-glass is a cylindrical vessel open at both ends, which is placed on the pump-plate and closed above by the hand; after exhaustion the latter is removed only with difficulty. Replacing the hand by a sheet of rubber, a single stroke of the pump will draw it strongly inwards, and in the same way a tightly stretched bladder may be made to burst with a loud report. In the upward pressure apparatus the air, being withdrawn above a piston, the latter, with a heavy weight attached, is raised by the pressure of the air below. The Magdeburg hemispheres consist of two brass hemispheres, accurately ground together, which require a great force to separate them when the air is withdrawn from the interior. Great care is needed in handling this apparatus as a slight blow will bend the brass sufficiently to cause leakage. Bursting squares are sealed rectangular vessels of glass, which explode when placed under an exhausted receiver. To prevent injury they should be covered with wire gauze, and the orifice