THE PARADOX OP ASCENSION.

The apparatus required is :—

1. An inclined plane, the angle of which can be changed from 0° to about 80°. No special dimensions are required: say a board (smooth) 5 or 6 ft. long, by 9 in. wide, with a slight ledge along the two edges of the plane.

2. A cylinder (A, Fig. 8) of wood, or any other material. The ends, B C, of the cylinder are reduced, so as to receive movable wheels, as above; no special dimensions required.

3. Movable wheels, each pair of different diameter. Thus, for example, let the cylinder be 1 in. in diameter, the first pair 2 in. in diameter, the second pair 3 in., third pair 5 in., and so on up to about 12 in. These wheels (discs of wood) should fit so tight as to roll with the cylinder only.

4. Two narrow strips of ribbon, or tape (Fig. 9, A B), pass under the cylinder, and are glued on the side of the cylinder, facing the reader, as in the Fig., 0 D. The free ends of the tape are kept parallel by a very light bar of wood, E, from which they, the tapes, are drawn together to Gr, where a light cord is joined and passes off to a pulley disposed as may be convenient. The tapes should be something longer than the inclined plane. They are shown as cut, not to take too much of the page; the cord, too, for the same reason.

Experiment 1.—Roll the cylinder in the direction of the arrows (Fig. 9, a), until two or three coils of the tape are laid over; now, taking the bar E in one hand, and the cylinder in the other, if the cylinder be let go, it will of course, in the air, unroll the tape and fall. Not so on the inclined plane, when the wheels are on the cylinder. Put on wheels No. 1, roll the tape as before, raise the plane, say to 10°, place the cylinder upon it, hang on the end of the cord Gr a weight, W,just enough to prevent the sliding down of the cylinder as, a whole; the cylinder will remain at rest; it will not roll down, uncoiling the tape.

Experiment 2.—Let the plane remain at the same angle, place the cylinder at the foot of the plane, the tapes as in Fig. 9, the balancing weight, W, as before; draw the weight gently down; the cylinder will roll up the plane, coiling the tapes, and will remain at rest at any part of the plane, if the additional force on W be withdrawn.

Experiment 4.—Leave the plane at the angle just reached ; put on wheels No. 2; place the cylinder, &c, as in Experiment 2. The cylinder will roll up the new incline. The limiting angle of equilibrium is found as in Experiment 4. In fine, as the difference between the diameters of the cylinder and its wheels is increased, the angle of the plane may be increased, and Examples 1 and 2 still realized. It will be found that even at an angle of more than 70°, Experiments 1 and 2 are possible.

N.B.—1. Kommerel proposes one broad ribbon, centred on the cylinder; the two tapes seem more manageable.

2. There is required some sort of movable roller to keep the tapes, or ribbon, parallel to the plane when the wheels are changed.

3. The motion of the wheels up the plane is well seen by a large audience, by one radius marked on the wheel next them. Thus, e.g., if the wheel be white, one black radius shows the least motion.

4. The tapes might end at the bar E, from the ends of which a light cord might form the angular joining to G. There is thus secured a means of delicate adjustment of the single cord, so that its pull may draw the cylinder straight up the plane.

A simple variation is thus made of this experiment: Lay two billiard or bagatelle cues on a table level, the points together and the butts a little apart. On placing a ball on the small ends, it will roll up the rods.

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