IN Volume IV., No. 5 of the Physical Review I described an experiment for illustrating orbital motion by projectinga steel bicycle ball over a glass plate, perforated by the pole-piece of a large electro-magnet.Several criticisms appeared in Nature and elsewhere, claiming that, under the conditions, the attractive force would vary not as the inverse square, but as the inverse fifth power of the distance. The authors of these notes appear to have overlooked the fact that the ball does not move in along a line of force, being urged towards thecenter by the horizontal component only, the vertical producing pressure on the plate. If the plate is over the magnetic pole this component becomes zero at the center instead of 00, which would of course be the value in an hypothetical case
The first experiments were made with the magnet in a horizontal position, and the ball suspended against a vertical glass plate, from a pan of a balance placed high above the magnet. This method proved unsatisfactory owing to the friction caused by the pressure of the ball against the plate.V ery good results were obtained, however, by fastening the ball to astrip of tempered brass, and measuring the deflections by means of a mirror. The pole of the magnet was at somelittle distance within the end of the bar. The first series shows the variation in the attractive force when the ballmoved in on a plane 3 cms. above the pole, x is the distance from the axis of the magnet, y the deflection which is proportional to the attractive force.Distance of Plane from Pole, 3 cms. Plane passing through Pole.Calculating the attractive force for each of these two conditionsfrom the formula y= - when c and a are unknown constants we findthat for the first series a has a value of about 2.1 indicating an attractive force earing very nearly as the inverse square. For the second series, where the plane in which the ball moves passes through the pole, the value of a is about 3, the force being as the inverse cube. In both cases the law of attraction changes from point to point, which is what one would expect, but within the region in which the orbits are uusally contained, it is approximately that of the inverse square or cube depending on the position of the plane.These results indicate that planetary motion would be better represented on a plate a little above the pole piece, and this I found to be the case. With the plate at a distance of 3 cms. above the pole I have succeeded in makingthe ball make two revolutions in an elliptic orbit. I have abandoned the smoked plate as the friction is greater, and the numerous failures are very exasperating when each records itself, and practically spoils the appearanceof the plate. The motion of the ball can be seen from a considerable distance and the experiment is on the whole more striking. I find that a grooved inclined plane is the best device for starting the ball, as its direction can be easily adjusted and the velocity varied at will. It is a good plan to draw the temper of the steel by heating the ball red hot over a Bunsen burner and cooling it slowly. On projecting the ball with moderate velocity along aline passing some 20 cms. from the pole I find that it will often complete five or six complete revolutions in avery large orbit, moving slower and slower and eventually coming to rest without "falling into the sun." This is avery striking experiment, as it is of six or eight seconds' duration, but it is best to stop the ball before it comes to rest, if one wishes to palm it off as planetary motion! It is, of course, not a case of true orbital motion, though none the less interesting. It is due to the permanent magnetization of the ball, the directive force of the field preventing it from rolling either towards or away from the pole. The ball sets itself with its magnetic axis alongthe lines of force, which make an angle with the plate, as shown in the figure, and if it rolls a little either to theleft or right the directive force will roll it back.
The first experiments were made with the magnet in a horizontal position, and the ball suspended against a vertical glass plate, from a pan of a balance placed high above the magnet. This method proved unsatisfactory owing to the friction caused by the pressure of the ball against the plate.V ery good results were obtained, however, by fastening the ball to astrip of tempered brass, and measuring the deflections by means of a mirror. The pole of the magnet was at somelittle distance within the end of the bar. The first series shows the variation in the attractive force when the ballmoved in on a plane 3 cms. above the pole, x is the distance from the axis of the magnet, y the deflection which is proportional to the attractive force.Distance of Plane from Pole, 3 cms. Plane passing through Pole.Calculating the attractive force for each of these two conditionsfrom the formula y= - when c and a are unknown constants we findthat for the first series a has a value of about 2.1 indicating an attractive force earing very nearly as the inverse square. For the second series, where the plane in which the ball moves passes through the pole, the value of a is about 3, the force being as the inverse cube. In both cases the law of attraction changes from point to point, which is what one would expect, but within the region in which the orbits are uusally contained, it is approximately that of the inverse square or cube depending on the position of the plane.These results indicate that planetary motion would be better represented on a plate a little above the pole piece, and this I found to be the case. With the plate at a distance of 3 cms. above the pole I have succeeded in makingthe ball make two revolutions in an elliptic orbit. I have abandoned the smoked plate as the friction is greater, and the numerous failures are very exasperating when each records itself, and practically spoils the appearanceof the plate. The motion of the ball can be seen from a considerable distance and the experiment is on the whole more striking. I find that a grooved inclined plane is the best device for starting the ball, as its direction can be easily adjusted and the velocity varied at will. It is a good plan to draw the temper of the steel by heating the ball red hot over a Bunsen burner and cooling it slowly. On projecting the ball with moderate velocity along aline passing some 20 cms. from the pole I find that it will often complete five or six complete revolutions in avery large orbit, moving slower and slower and eventually coming to rest without "falling into the sun." This is avery striking experiment, as it is of six or eight seconds' duration, but it is best to stop the ball before it comes to rest, if one wishes to palm it off as planetary motion! It is, of course, not a case of true orbital motion, though none the less interesting. It is due to the permanent magnetization of the ball, the directive force of the field preventing it from rolling either towards or away from the pole. The ball sets itself with its magnetic axis alongthe lines of force, which make an angle with the plate, as shown in the figure, and if it rolls a little either to theleft or right the directive force will roll it back.
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