"These comparative observations on the intensity of the dipping and horizontal needles, were made with a particular object in view, which it will be proper to explain before giving the details.

"It was found by observation, that the intensity of the horizontal needle was hourly varying. This appeared by the results already given; but it was doubtful whether this variation of horizontal intensity of a needle, proceeded from an actual variation in the intensity of the terrestrial magnetism, or from a variation in the amount of its direction, as indicated by the dip itself.

"The power of the horizontal needle varying as the cosine of the dip, a change to the amount of a few minutes in the dip, at places where it is very great, would be sufficient to explain all the variations of intensity observed in the horizontal needle, without supposing any change to have taken place in the intensity of the terrestrial magnetic force.

"The variation in dip, however, if it did occur, was too small to be detected by direct observation; and I failed also to render it sensible by the application of magnets, as stated in a former communi

cation.

"My object, therefore, in making the experiments contained in the following table, was to ascertain, by several series of vibrations made with the same needle, mounted alternately as a dipping needle, and as a horizontal one, whether or not a corresponding variation of intensity would manifest itself in these two positions respectively, as ought to be the case, if the diurnal changes of intensity in the horizontal needle proceeded from a general change of intensity in the terrestrial magnetic power. But, on the other hand, if the force indicated by the dipping needle should be found to remain constant, then it would be equally clear, that the variations of intensity in the horizontal needle proceeded from an actual change of dip only.

"As this question is of considerable importance in the theory of terrestrial magnetism, I regret that I had not an opportunity of making a more extended series of experiments of this kind; but, as far as they go, they certainly appear to indicate, that the alterations of intensity in the horizontal needle, are due rather to a daily change in the amount of the dip, than to any variation in the general intensity of the earth's magnetic force, although some change in this also is observable by vibrations of the dipping needle. This explanation of the cause of the change of horizontal intensity, it may be remarked, is consistent with the observations made in Europe, which likewise shew an alteration of intensity in the horizontal needle during the day, but in a much less degree than at Port Bowen. Now, if the variation in question really proceed from a change of dip, to the amount of three, four or five minutes of a degree, the change of intensity in the horizontal needle will be less and less obvious, as the dip decreases; but if it proceed from a change in the actual intensity of the earth's magnetism, it ought to be constant in all parts of the world, which is contrary to observation.

"The following are the results of these experiments. The table is divided into two parts; the first contains the observations on the times of vibration of the needle in its horizontal position; and the second, those on it when used as a dipping needle. In the first column of each part, is inserted the day of the month; in the second,

the hour and minute at which the observations were commenced; the third column of each part contains the mean time in seconds taken by the needle in its different positions, to perform one hundred vibrations; and, in the fourth, is inserted the temperature of the needle at the time of observation.

"The above results show, that the mean of all the observed times which the horizontal needle required to make 100 vibrations, was 2092.33 seconds, but that differences appear in these times amounting to 94.3 seconds, or d part of the interval; whereas, in the dipping needle, in which the mean of the times required to perform 100 vibrations was 408.65 seconds, the greatest difference is only 57 seconds, ord part of the interval, which is a much less proportional change than the former.

"Therefore, as has been stated, the change of intensity in the horizontal needle is due, principally, to a daily variation in the amount of the dip, not to a real change of intensity in the terrestrial magnetic force. This, at least, appears to be a legitimate deduction from the preceding observations; from which circumstance, and that of the daily variation in the direction of the horizontal needle, we are naturally led to the conception of a small variation in position of the magnetic axis, corresponding to a revolution of the polar point round its mean position as a centre, produced by the action of the sun, on the magnetism

* The dip of the needle resulting from these elements is 87° 48' 8 N.

of the parts of the earth successively exposed to its influence. And, moreover, it seems by no means improbable that the annual variation of the position of the magnetic pole, may ultimately be traced to the same universal cause.

"I have not attempted to enter into any minute calculations on this subject, but I believe it will be found, that, if the radius of the circle, described by the pole of the general magnetic axis of the earth during the day, be supposed to subtend at the centre an angle of 2 or 24 minutes, it will reconcile, to a considerable degree of precision, nearly al the observations on the daily variation of the direction, and daily change of intensity of the horizontal needle, made both in Europe and with. in the Arctic Circle."

In order to illustrate the very ingenious hypotheses which Lieutenant Foster has thus deduced from the experiments last reported, it will be best to refer to Fig. 1. In this, P represents the terrestrial pole, M the magnetic pole of any place L, of which the dip and variation are given; join M L, which is the magnetic meridian of the place L, and produce M L to l, m Q L representing the equator; as also, P L be produced to meet the equator in Q, then MLQ will be the meridian of the place L; and from M draw Mm, perpendicular to ML. Then, confining our illustrations to the time when the sun is in the equator, the arc Ql, converted into time, will give the time when the sun is on the magnetic meridian of the place L; Qm, converted into time, will give the time when the sun is perpendicular to that meridian, and, of course, from these may be readily determined the time when the sun is again on the magnetic meridian, and when again he is perpendicular to the same; let us, therefore, go through the necessary calculations, and see how nearly the several phenomena which have been recorded, agree with the hypotheses in question.

First, let L represent London, Lat. 51°31', dip 70°34', Long 0°0'. tan 70°34' Here, since tan dip = 2 tan mag. lat. we have 2 mag. lat. conseq. ML variation.

= 54°48' = 35°12′ PL = 38°29′, and PLM = 24°30'

=

From these we readily find MP 14.58' colat. of magnetic pole, and angle LPM 67°41' = long. west of magnetic pole. In the triangle LQ1, right angled at Q, we have LQ = 51°31', and the angles QL/= 24°30', whence we find / Q 19°38', which, converted into time, gives about 10h 40m A. M. for the time when the sun is on the magnetic meridian of London; and, in a similar manner, we find Qm = 55°24' equal to about 3h 40m P. M., the time when the sun is perpendicular to the magnetic meridian of London.

These being determined, let us proceed to a comparison of recorded phenomena with the hypotheses in question. Lieutenant Foster conceives, that the sun, by some influence or other, causes the magnetic pole M to describe, in the course of 24 hours, a little circle about the mean point M, whose diameter is about 5' or 6', the pole being constantly deflected towards the sun. Now, first, according to this supposition, at 10h 40m A. M. M will be deflected towards L, the magnetie colat. will be diminished, and, consequently, the dip increased; and this increase of dip will induce a less magnetic intensity on the hori

zontal needle, and the least that ought to take place in the 24 hours, and this is precisely the time that the minimum intensity is recorded to take place. At 10h 40m P. M. we ought, in like manner, to have the greatest intensity, because then the sun will be again on the meridian, but its tendency will be to increase the magnetic colat., and, consequently, to diminish the dip. We have no distinct account of the intensity at this hour, but at 9h 30m P. M.* it is greater than at any other hour recorded; we may, therefore, I conceive, fairly state this as a confirmation of the agreement of the hypotheses with observations on these cases of intensity.

Again, at about 3h 40m P. M., we have seen that the sun is to the west-of the magnetic meridian, the needle ought, therefore, at this hour to have its greatest westerly bearing. This hour agrees very well with a number of recorded observations, but, in the recent observations by Colonel Beaufoy, the maximum is said to happen at 1h 30m, at least this was the time at which he always recorded his noon observations. Here, therefore, is some discrepance in time; but the motion of the needle is nearly suspended for some considerable time about this part of the day, and the whole amount is so very small, that I can by no means admit this as an objection to the hypotheses. It is only by a very great number of hourly observations that the exact time of the maximum can be deduced; and where these are most numerous, the time is variously stated from 2h to 4h P. M. We have no good recorded experiments during the night in London; it is only generally said, that the motion of the needle is less to the eastward in the night than to the westward in the day, and this ought to be expected from the hypotheses, for the sun will pass during the night 30° farther from the pole than in the day, and its effects, of course, ought to be proportionally less. Upon the whole, therefore, Lieutenant Foster's hypothesis is by no means at variance with our recorded observations in London.

Let us now submit it to a similar test with the Port Bowen observations.

* See Mr Christie's Paper on the Effect of Temperature, &c.—Phil.

Trans. for 1824.

Here, referring to fig. 2. and repeating the calculations already indicated, we find,

PL = 16°46′ angle PLM
PM 4 0 angle LPM

= 124°
- 10 23, Qm

1Q

= 54°51'
=25 49

The two latter, converted into time, give 3h 40m P. M. for the time the sun is on the magnetic meridian of Port Bowen, and 10h 40m A. M. for the time when he is perpendicular to the same.

It is remarkable, that these times are nearly the reverse of those in London, and cannot, therefore, but furnish an excellent test of the hypothesis in question. According to these the needle ought to have its greatest westerly variation, which is, however, due to an actually eastward motion at 10h 40m A. M., and its least westerly at 10h 40m P. M., whereas the times stated from a mean of all the observations is 11h 49m A. M. and 10h 1m P. M., which is as close an approximation as can be expected. Again, according to this calculation, the time of the sun traversing the magnetic meridian, when the needle ought to be found in its natural meridian, is 3h 40 P. M. and 3h 40m A. M. And the time stated of the needle passing what is called the mean daily zero is 6h 15m A. M. and 4h 37m P. M., and as this time was merely an approximate assumption of the mean meridian by taking it at half the extreme range for the day, it is far from being unsatisfactory.

The times of greatest and least intensity of the horizontal needle are not so well defined as some of the other points. By referring to the table we have given, it will, however, be found to be greatest from about three or four o'clock afternoon to about six or seven; and least at about the same hours in the morning; and, according to what we have computed, these effects should have taken place at 3h 40m P. M. and A. M. precisely.

Upon the whole, therefore, I conceive that the experiments, observations, and computations, are very consistent with each other, and afford a strong presumption in favour of the hypothesis, particularly when it is observed, that the illustration has been given wholly with reference to the sun being in the equator; and that all the circum. stances of time, &c., will be different when the sun has either north or south declination, and thereby produce that kind of uncertain and variable results, which are so strongly marked in the general table. There can, moreover, be no doubt, that all the phenomena are modified by other circumstances, besides those of the sun's motion; and that, although the latter is the great primary cause, it is not the only one which is influential in producing the changes we have been endeavouring to explain. It may be proper also to add a few words with regard to the amount of daily variation in different latitudes.

Lieutenant Foster says, that he conceives a mean radius of about 2' or 2 for the orbit of the daily motion of the pole, will agree very well with the quantity of daily variation observed in different latitudes. We would, however, rather say 2 or 3′; and assuming this, let us examine how nearly the observed and computed quantities agree with each other. According to this, the daily variations at the magnetic