magnetic particles to act upon the poles of the horizontal needle. CL, parallel to NS, is the line in which the needle points when uninfluenced by the ball. OZ is a vertical line, from the centre of the table, in which the centre of the ball is moved upwards or downwards; and CB is a line drawn perpendicular to s Cn, and meeting OZ in B. According to the view of the subject which I have advanced, when the centre of the ball is in the point B there should be no deviation of the horizontal needle; when the centre of the ball is above the point B, the north end of the needle should deviate from the ball; and when it is below B, the deviation of the north end should be towards the ball.

To ascertain how near the results of the experiments coincided with these ideas, I computed, for every position of the compass, the height of the point B above the plane of the table, in the following manner. Take the centre of the needle for the origin of three rectangular co-ordinates, x, y, z; the plane of xy being that of the horizontal table; the plane of az a vertical plane parallel to the magnetic meridian. Calling the co-ordinates to the centre of the ball x, y, z, then is the tangent of the angle which the projection of the line joining the centres of the needle and ball, on the plane of xz, makes with the axis of x; and when the line is perpendicular to the direction of the dipping needle, this angle is equal to the complement of the dip. If then we call the dip of the needle, which is at present nearly 70° 30′, d, we shall have, when the line joining the centres of the needle and ball is perpendicular to the direction of the dip,

x

Or, if we call the line drawn from the centre of the needle to the

centre of the table r; and the angle which this line makes with the meridiano, then

and consequently

x = r cos &

z = r cos & cot d.

In this, making successively 10°, 20°, 30°, &c. and putting for r the distance at which the centre of the needle was placed from the centre of the table, the several heights of the centre of the ball above the plane of the table, or depths below it, at which the deviation ought to be nothing are obtained. The following table exhibits these heights in inches, and likewise the heights and depths actually observed at which the deviation was nothing, for every 10° from north to west, and from south to east, the distance of the centre of the compass from the centre of the table being 12 inches.

I made similar observations, placing the needle at the several distances of 14, 16 and 18 inches from the centre of the table, for the values of 40° and 50°, as at these angles the changes in the deviation become very sensible. The following are the results obtained.

That a just estimate may be formed of the degree of coincidence between the calculated heights at which, according to the hypothesis I have advanced, the deviation should be nothing, and those actually observed, it is necessary to mention the manner in which the observations were made, and the degree of accuracy with which, from the nature of the apparatus, these heights could be observed. In order to estimate the height of the centre of the ball above the compass, a horizontal line was drawn on the surface, as much below the great circle of the ball parallel to the horizon, as the centre of the needle was above the plane of the table; and a scale, having the inches divided into tenths, was erected perpendicular to the plane of the table; so that the height of the above line, measured on this scale, gave the height of the centre of the ball above the centre of the compass. The deviations of the

needle, as I have before-mentioned, were observed at every inch in the descent of the ball; and when they became small, the ball was lowered very gradually, the needle being at the same time carefully watched, until it pointed to zero, when the height was observed on the scale. As the scale was only divided into tenths of an inch, when the line on the ball did not exactly coincide with one of these divisions, the difference could only be estimated by the eye, and an error amounting to .025 inch might sometimes easily be made. When the values of were small, the deviations being so likewise, the changes in them were also small, and there was some difficulty in ascertaining the precise point at which the deviation was zero.

When these circumstances are taken into consideration, I think it must be allowed, that the very near coincidence of the calculated and observed heights, will authorise me in concluding, that when the line joining the centres of the needle and ball was perpendicular to the line passing through the centre of the needle in the direction of the dip, the horizontal needle was then not affected by the action of the ball; and that, as far as this condition goes, my views of the manner in which the ball acted are just. I should here likewise mention, that, in the observations made from the south towards the east, the deviations of the north end of the needle were first easterly, that is, from the ball, in which direction they gradually increased, as the ball descended, and attained a maximum: they then decreased to zero; became westerly; attained a maximum in this direction; and then decreased, until the needle resumed its original position, by the ball descending so far below the table that it ceased to affect the compass. This was precisely what I had anticipated, since here the ball being at first nearest to the upper or southern branch of the line s Cn, according to what I have before said, the south end of the needle ought to deviate towards the ball and the north

end from it and this would happen until the ball was equally distant from the two branches of the line s Cn, when neither end should deviate towards the ball; but when the ball was below this point, being then nearest to the northern branch of s Cn, the north end of the needle should deviate towards the ball. In the observations made from the north towards the west, the deviations were, as I had expected, exactly in a contrary order; that is, the north end deviated first westerly; then returned to zero, when the centre of the ball was below the compass, in the line of the perpendicular to s Cn, from C; after which it deviated easterly.

As a further confirmation, if such be deemed necessary, of the accuracy with which the hypothesis agrees with the phænomena, I may notice, that, in a series of observations which Mr. Barlow undertook for the purpose of determining practically the inclination, to the plane of the horizon, of the plane in which there was no deviation, the mean of the observations, the compass being at the distance of 20 inches from the centre of the table, gave an inclination of 19° 24'. According to the theory this angle should be the complement of the dip, and it only differs by 6' from that which I had assumed. It is still nearer to that determined by Captains Kater and Sabine, the difference being, in this case, only 2. Such errors might happen in taking the angle of the dip, even with the most accurate instrument; or, if we suppose that the dip is correctly 70° 30', from a small error in placing the compass on the table, or in estimating the height of the ball. What, I think, adds considerable weight to the confirmation thus afforded to the correctness of the hypothesis in this particular, is, that, in these experiments, Mr. Barlow's views were entirely practical, and that, although, before he made them, I had explained to him the manner in which I viewed the subject, yet they were not by any means undertaken with an idea of confirming the hypothesis, but merely as necessary to his ulterior objects.