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there is attraction, opposed to the magnetic repulsion : and the total repulsion is diminished. The same holds if the blue pole of the first is presented to the blue pole of the second.

The most accurate information which we possess on the subject is given by Mr W. Ellis, Assistant of the Royal Observatory, Greenwich, in a paper published in The Philosophical Magazine, May 1863, page 325. A magnet 5 inches long was attached to a clock-pendulum, and a similar magnet was so fixed in the clock-case that one pole of the swinging magnet passed over one pole of the fixed magnet: when there was attraction, the clock was accelerated; when there was repulsion, the clock was retarded; and both effects could be measured with extreme accuracy. The following results (extracted from a series) will shew the

effects:

difference of the

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It will be remarked that the part due to induced magnetism diminishes much more rapidly than that due to permanent magnetism.

73. Method of measuring the amount of magnetism produced in a magnet by terrestrial induction.

It is assumed in the following process that the law of distribution of induced magnetism, as regards the length of the magnet, is sensibly the same as that of permanent magnetism: and in fact the law at which we have arrived theoretically of induced magnetism, that the magnetism is exhibited as a coating at the end, is sensibly the same as that found experimentally for permanent magnetism, Article 12. The method adopted at the Kew Observatory for measure of the induced magnetism makes use of that part induced by the terrestrial vertical force, which in this magnetic latitude is large. As in Article 26, a deflexionapparatus is to be used, in which it is made certain, in all stages of the operation, that the deflected needle (carrying a reversed telescope) occupies the same position with

regard to the viewing telescope; the whole apparatus being turned horizontally round a vertical axis till that condition is obtained, and the graduated horizontal circle which registers its rotation being then read. But there is this difference in adjustment from that of Article 26, that the magnet is placed in a vertical position, with a definite point near one pole exactly in the horizontal plane of the disturbed needle.

Suppose now that the red pole of the magnet is downwards, a mark near the red pole being at the same level as the needle, and the blue pole projecting far above the level of the needle. The effect of induction by the earth's vertical force is to add to the red power of the lower end and to the blue power of the upper end, and in fact to make the magnet more powerful. Now invert the magnet, so that the mark near the red pole is still at the same level as the needle, but the blue pole projects far below the level of the needle. As regards the action of the magnet upon the needle, the force exercised is the same as before. But to the red magnetism at the upper end of the magnet there is now added blue magnetism produced by the earth's vertical induction, and to the blue magnetism at the lower end there is added red magnetism produced by induction, and the power of the magnet is diminished. And these vertical magnetisms are not affected by the horizontal rotation of the apparatus round the needle. It is evident here that we have the means of determining the proportion of the induced part to the permanent part of magnetism.

In order to eliminate any conceivable excentricity in the location of the permanent magnetism, the operation may be repeated, using a mark near the blue pole of the magnet and the mean of the two results may be taken. For simplicity of reduction, suppose that all observations are made with the separation between the centers of the magnet and the needle equal to the unit of measure, or (in England) 1 foot. As in Article 29, let A be the magnet-power of the magnet, and E the local horizontal magnet-power of the earth. Also let I be the magnet-power induced by the action of the terrestrial vertical force. In one position of the magnet, its power is A+ I, and in the other position it is A-I. On account of the peculiarity of the magnet's position (which is different from those in Articles 26, &c.) these are not the powers which act in the present experiment: the real acting powers (see Article 53) will be found by multiplying those by an unknown constant e: so that the real acting powers in the experiment are e (A+) and e (A - I). Let 0, and 0, be the deviations in the two experiments. Then as in the last sentence of Article 26, making c=1 and neglecting K (which which will have the same proportion in the two experiments),

whence

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The value of I thus obtained is the amount of induced magnetic force produced by the local terrestrial vertical force. The local terrestrial horizontal force is found by multiplying the local vertical force by cotan. local dip: hence the induced magnet power produced by local terrestrial horizontal force E will be

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It is most carefully to be observed that the terrestrial force E and the dip here spoken of are those peculiar to the place of this experiment; that 0, and 0, are angles peculiar to this experiment; and that A is constant so long as the power of the magnet is not changed.

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74. Correction of the formulæ, used in the determination of the Earth's horizontal magnet-power, for effects of induction.

In examining the process in Articles 26 to 28, it will be seen that we have to consider the effect of a magnet A in disturbing a needle when A is inclined to the meridian and in Article 32, we have to treat of the earth's horizontal force upon A when A is in the meridian. These must be considered separately. Let E' be the earth's horizontal power at a second station.

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First, for the disturbance of a needle by A. If & be

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