ball will be the most powerfully acted upon; or, which is the same, the centre of all the actions on the needle will be in that branch; if, therefore, that branch be found between the ball and the meridian, the attractive powers prevail over the repulsive; but if the meridian be found between the ball and the nearest branch of the needle, then the deflection is due to an excess of the repulsive forces over the attractive.

In the first case, by deteriorating the near branch, we diminish the attractive forces, and in the other case, the repulsive; so that in both instances the needle ought to approach the meridian; as is found to be the case. But by deteriorating the other, that is the most distant branch, we increase the preponderance of attractive power in the one case, and the repulsive in the other, and, consequently, the needle will be more deflected, or recede farther from the meridian.

With respect to the rather uncertain character of the secondary deflections near the points of change, the explanation appears to me to rest on this: that, admitting the attractive and repulsive principle, the centre of attraction and of repulsion may fall both in the same branch of the needle, or in opposite branches. In the one case, the needle is deflected by only the difference of the two forces, and in the other, by their sum. And it is probable that in or near the points of change, the degree of deterioration may produce this uncertain result, by changing these centres from one branch to the other, according to the intensity of the deteriorating power.

After all, however, it will not be expected that the results due to such a complex system of forces can be illustrated in

common language, since in their more uniform state, they require the aid of the most powerful analysis to reduce them to determinate laws. It is sufficient for the present purpose to have shown, that the order of secondary deflections, discovered by Captain WILSON, are, in a general point of view, consistent with that hypothesis, which supposes the magnetism of iron to be due to induction from the earth, and that they are inconsistent with that which attributes the deflection of a magnetised needle to the general central attraction of the iron on its two poles or extremities, or on an imaginary needle passing through the pivot in the line of the dip.

In adopting the hypothesis of induced magnetism in the Second Edition of my Essay, I only attempted the calculation for an indefinitely short needle, or magnetic particle. Since this M. POISSON has, by means of the powerful analysis he knows so well how to apply, obtained a general formula for a needle of any length; and I have little doubt, if we possessed the means of estimating the amount of deterioration, or the actual inequality of magnetism in the two branches of the needle, that all the facts I have stated would become by his formula a subject for calculation.

The following experiments may perhaps in some measure assist towards rendering the results numerical: they were undertaken after the preceding part of the paper had been written on the suggestion of Captain BEAUFORT.

Three needles were procured from Messrs. W. and T. GILBERT, as nearly equal in weight, length, and power as possible, all applicable to the same pivot and compass-box. The radius of each was three inches, and the number of

vibrations made by each in a minute when in their natural magnetic state, was eighteen. No. 1. was left in that state. No. 2. was deteriorated in its northern branch; No. 3. in its southern; after which No. 2. made only 11 vibrations in a minute, and No. 3. 12 vibrations in the same time. With these needles the experiments were conducted as follows.

The ball was raised till its centre was 10 inches above the pivot of the needle, and the latter placed at 13 inches from the centre of the table, making the distance between the pivot and the centre of the ball 16.8 inches, which distance was preserved in all the experiments. The box containing the needle was placed in the situation above mentioned, first north of the ball, then N. 20° E, N. 40° E. and so on all round to the north again. And in each of these positions the deviation of each needle was successively registered, the results being as in the first division in the following table. Precisely a similar set of observations were made with the centre of the ball 10 inches below the pivot of the needle, as in the 3d division of the table; and lastly, a like set were obtained with the centre of the ball level with the pivot of the needle, the latter in this case being placed at the whole distance 16.8 from the centre of the table.

XIX. On the difference of Meridians of the Royal Observatories of Greenwich and Paris. By THOMAS HENDERSON, Esq. Communicated by J. F. W. HERSCHEL, Esq. Sec. R. S.

IN

Read May 17, 1827.

IN the Philosophical Transactions for 1826, Part II. Mr. HERSCHEL has given a detailed account of observations, which were made in the month of July, 1825, for the purpose of ascertaining the difference of the meridians of the Royal Observatories of Greenwich and Paris, with a computation of these observations, from which the most probable value of the difference of longitude appears to be 9" 21"6. But I have perceived that in the copy of the observations delivered to him from the Royal Observatory of Greenwich, an error of one second has been committed; as the true sidereal time of the observation made there on 21st July, ought to be 17h 38 5 7:12 in place of 17h 38m 5610, set down in the Table p. 104, which he informs me was computed at the Observatory, and officially communicated to him from the Astronomer Royal. This error seems to have had its origin in the little Table at the bottom of page 103; for, on subtracting the error of the clock, 47'37, from the time 18h 8m 30*40, the true sidereal time is 18h 7" 43.03, instead of 18h 7TM 42o03, there given. The error in the result of that day's observations, arising from this cause, has been partly compensated by a mistake of three tenths of a second, which