the laws of the secular changes may be better studied from the variations of these constants than from immediate observations. Four of these formulæ are here given, with the names of the months to which they belong, and the number of days employed in calculating them; t = the time from Oh Gott. M. T.

June, 10 days. Declination*

90°17′,3-3′,853 sin. (t-162124)-1,537 sin. 2 (t-93124') -0',948 sin. 3 (t+0 279)-0'644 sin. 4 (t-422m9").

August, 4 days. Declination

9°13′,9-3,907 sin. (t-15"12"47')-2'009 sin. 2 (t-946 58')— 0'878 sin. 3 (t+0"51"15").

September, 5 days. Declination

9°21′,9-2′,932 sin. (t-9h34"18")-1′,530 sin. 2 (t-8"128")— 0',494 sin. 3 (t+132 29')-1',090 sin. 4 (t-02958). October, 5 days. Declination

-9°18′,7-1,575 sin.(t-13042)-2',379 sin.2 (t-10"40"58′)— 0',508 sin. 3 (t-04" 58")-0′,034 sin. 4 (t+01232").

Here we close our investigation of the diurnal magnetic curve. The existence of such a curve, regularly formed every day, cannot be doubted; its general uniformity is also very observable. The limits of the times of maximum and minimum declination in different longitudes, show conclusively that it is in some way connected with local solar time. Developing the declination according to the most general form of periodic functions, we have obtained the preceding formulæ, from which the empirical curves drawn on Plate V were calculated. These calculated curves stand there side by side with the mean observed curves, by which the constants of the formulæ were determined. The calculated curve, as we might expect, is less broken than the mean curve; still, the two agree in a striking manner, and the greatest deviations are in those months which suffered most from magnetic perturbations. In June and August the empirical curve and the mean curve keep close together, and these were periods of unusual magnetic repose; for in the mean of the latter month the disturbed term day was omitted. June was most quiet of the two, and shows it by a superior agreement between its mean and empirical curve. If there were no permanent change of declination, but only the daily oscillation uninterrupted by disorderly fluctuations, the meridian would swing, day after day, through the same arc; and a few observations would be sufficient to establish a rigorous formula, which would evolve an

* The first term in the value of the declination is obtained directly in parts of the scale, and is afterwards reduced to absolute numbers in the usual way of deriving the real declination from the reading of the scale. This process will be soon explained.

The

empirical curve strictly coincident with the observed curve. want of this uniformity is felt in the variation of the constants of the formulæ already given. This simplicity does not exist in the motions of the heavenly bodies any more than in the magnetic movements. But the analysis is different. In astronomy we know the cause of the disturbance, and allow for it at once, without deranging the general analytical expression. In the other case we have no theory, no hypothesis; and the mathematical form must vary with the observations. Hence the difference between the constants in the formulæ for the four months. They are no greater than might be expected from the known change of absolute declination from day to day, the limits of the times of maxima and minima, and the longer and more irregular derangements which beset the diurnal movement. The mean curves of many months, drawn from the most abundant materials, are requisite for investigating the law by which these constants vary, and rendering them available for calculating the secular periods of the earth's magnetism. We think it is apparent from all that has been adduced, that the diurnal magnetic curve is as clearly a function of solar time as the daily thermometric curve. We are not to expect any greater uniformity in the effect than in the cause. If the thermometric curve is sometimes imperfectly formed, the same thing may happen to the magnetic curve without destroying our belief in its connexion with the sun. The change of constants in one class of formulæ appears likewise in the other, as the three following thermometric formulæ make manifest:

August, 5 days. Temperature

67°,6+8°,8 sin. (t-15 57 28') + 0°,9 sin. 2 (t-4' 34" 56")+ 1°,1 sin. 3 (t+0" 44" 56").

September, 5 days. Temperature

= 50°,2—10°,0 sin. (t-13" 38" 543)—3°,2 sin. 2 (t—91 31" 4')— 0°,3 sin. 3 (t-2)-0°,8 sin. 4 (t-4" 39" 48").

October, 5 days. Temperature

= 47°,7-3°,8 sin. (t-14" 21" 44")-0°,8 sin. 2 (t-9h 17 36')—— 0°,4 sin. 3 (t-6" 35" 25")-0°,4 sin. 4 (t-0" 38" 12").

It still remains to discuss briefly those disturbances of the magnetic meridian which have no apparent law. We have occasionally alluded to them as irregular purturbations which produce perplexity in ascertaining the true diurnal curve. We are to inquire whether even they must be regarded as wholly inexplicable, or whether they cannot be connected in coincidence of time at least with other wellknown phenomena of nature. There are few days in the year when strange fluctuations of greater or less amount are not exhibited; but there are some periods distinguished above all others by

their remarkable frequency and magnitude. We annex a brief history of each month in this respect.

1840.

March 27-8. No perturbations of importance; only two unusual excursions, one at 2h 45', A. M. Gott. M. T. (March 28), and the other at 4h 15', A. M.

April. The observations of this month are very defective.

May 29-30. Term-day. Irregular disturbances of large amount, from 11 o'clock, P. M. Gott. M. T. (May 29) to 12h of May 30. The whole sweep of the instrument through the day is 57',2; and once, between 3 50′ A. M. and 4" 10, the declination changes 47', 2 in 11", or four times the average daily swing from maximum to minimum. The other days observed in May were not distinguished above the average by perturbations.

June. The ten days observed in this month were all unusually quiet.

July 24-5. Between 6 and 8 o'clock, P. M. Gott. M. T. (July 25) the arc of vibration of the magnetometer amounted to 20', so as to require the substitution of its extreme limits instead of the 12 readings at intervals of 10 seconds. But this large movement was not accompanied by any considerable change of absolute declination, and the whole magnetic day was undisturbed.

August. The Term-day of Aug. 28-9 was greatly deranged from 10 40′ P. M. Gott. M. T. to 8 A. M., and small perturbations were experienced for four or five hours after this time. The whole range of the magnetic declination amounted to 61'. Once between 6 40' and 7h 20′ A. M. the change of declination exceeded 43′ in 27 minutes. The other days observed in August were still.

The

September 21-2. The sweep during this day was 45'.5. disturbances on the days observed in this month have been already discussed at length. They were distinguished more by number than extent of arc.

October. The October curves were not entirely free from disturbances, though they are all comprehended, in their widest excursions, in a zone of 22' in breadth.

November. The three days of this month have some perturbations, but none deserving especial notice.

December. Two of the curves observed in this month were disturbed considerably; yet the whole range does not surpass 28'.5.

1841.

January. The curves observed in this month were generally regular. On the 26th of January, between 4 and 5 A. M. Gott. M. T., a small disturbance was felt amounting to 17'.

February. General perturbations spread over the three days of this month, particularly observed at night. Those of greatest extent occurred on the term day, February 26-7, amounting in one case to 16' of arc in 15 minutes of time. In addition to these

extracts from the records of the different months, Table II, contains a column showing the extremes of the magnetometer every day when complete observations were made.

The theory of the aurora borealis, which has of late years found most favour with men of science, supposes it to have some connexion with electricity and magnetism. It is important to investigate this subject further, and see whether there be any and what relation between this brilliant appearance of the heavens and the derangements of the magnetic declination. For this purpose a careful record has been kept of all the auroral appearances that have been noticed at the Cambridge Observatory; some of the most remarkable presented themselves at times when the regular observations on the declination magnetometer were in progress, and pains have been taken, whenever it was practicable, to watch the instrument on all other occasions when the heavens gave signs of preparation for such an exhibition. Annexed is a list of those which were displayed on a

grand scale.

April 24-5. Slight aurora.

May 28-9. Remarkable aurora. An arch was formed, at 2h 39', A. M. Gott. M. T., running, as nearly as could be ascertained, at right angles to the magnetic meridian. A crown began to form at 4" 24'. Its position was referred to a Cor. Borealis, which was then on the meridian. As it was nearly at the same altitude of 74° 52', and to the west of the meridian, it could not have been far from the magnetic pole. Shortly after this the arch was broken up, and the northern sky covered with pulsations of light.

May 29-30. Brilliant aurora. The auroral arch was first seen at 2 32′ A. M. Gott. M. T., extending from a point nearly east, to within a few degrees of the western horizon. The light was intense. The apex of the arch was situated 28° at first, and at 2h 42', 30° south of the zenith. After this time, the light became broken and scattered, flying from east to west. This arch was entirely detached from the main body of the aurora, and resembled a streamer. In the north there was a diffused light, but very bright; and swift flashes towards the zenith. At 3 59' a large meteor was seen in the north, 20° high, descending towards the north-west.

June 26-7. About 2h 36' A. M. Gott. M. T., an aurora was seen at the north, of a white diffused light. At 6 20', the aurora assumed a dull appearance, with dark wane intermixed. At 7 A.M. the aurora became more active, and some streamers were seen. The needle was slightly affected at this time.

July 4-5. Between 5h 28′ and 5h 34′ Gott. M. T., bright diffused northern lights; occasionally long streamers; wane clouds near the northern horizon; magnetometer quiet.

July 29-30. At 2h 45' A. M. Gott. M. T. (July 30), an auroral arch was formed 7° above the horizon, and very still. At 9 40' it began its motion up towards the zenith; rose to the altitude of

30°. At 3h 54' the aurora had ceased. The light was dull during the whole time.

August 19-20. A steady auroral arch was observed. It was double, and the altitude of its apex at 3h 54' A. M. Gott. M. T. (August 20) was 7° or 8°; its colour was dull white. This aurora continued till 4, and at 4" 11' the northern lights had entirely disappeared.

August 28-9. An auroral arch appeared running from east to west, of intense brightness and diffused, but without streamers. Apex nearly on the meridian, and altitude 45° at 2h 30′ A. M. Gott. M. T. At 3h 20' streamers shot up 60° from the horizon; the altitude of its highest part was about 76° 43', as found from its place among the stars.

October 22-3. Between 1 and 2 A. M. Gott. M. T., an aurora of a steady blue light was first perceived; it afterwards became brighter and whiter; the altitude was 3°; wane clouds below. At 5 20',

the aurora was low.

November 30. At 3h 24' A. M. Gott. M. T., an aurora was seen of white diffused light. No regular arch was formed. The magnetometer was quiet.

It appears, from this abstract of the records, that the days most distinguished for auroral appearances, are just those on which the declination of the magnetic meridian experienced the most extraordinary derangement. This was the case on May 29-30, and August 28-9. Unfortunately the magnetometer was not watched on the night of May 28-9. By referring to Plate IV, it will be seen that the declination instrument was subject to more than ordinary influences on the 22nd of October, between 0" M. and 6 A. M., Gott. M. T. The observers on the remarkable days of May and August describe the motions of the magnetometer as peculiar in the highest degree. It was often checked in the midst of its vibration, and suddenly forced back in the opposite direction; and this took place with such frequency at certain seasons, as to give to the motion the appearance of jerks or sharp twitches. No correspondence was noticed between the time of maximum magnetic disturbance and the formation of the auroral crown. But it was sometimes supposed, from successful comparisons in the phases of the different phenomena, that the instrument gave intimation, by some strange motion, of the most signal changes in the aurora. The display of May and August was as fine as any that has been witnessed for several years, and we should not omit to state, that on these occasions the declination magnetometer at Cambridge made the boldest sweep of the scale. As both these days happened to be term days, the opportunity was improved at other magnetic observatories of watching the coincidence between the auroral appearances and the perturbations, and the report is generally uniform from all. Plate II, which represents the May-term diurnal curve of declination, offers a specimen of the extraordinary disturbances to which we refer,