At Rio de Janeiro, which was the first station observed at in South America, the cylinder was vibrated in August 1826, September 1827, and December 1828; in the intervals between these dates are comprised the greater part of the observations on the east side of South America. There is no direct observation at Rio subsequently to December 1828; but we are enabled to supply the time of vibration, which would have been observed had the cylinder been employed at Rio on June 1, 1830, in the following manner. We have seen that on the 15th September 1827 the time of vibration was observed at Rio; on the 18th December following it was observed at Monte Video. These observations give the intensity at Monte Video relatively to that at Rio, subject to whatever change of magnetism the cylinder may have undergone in the interval of three months. This comparison was repeated in the following year, on Captain King's return from Monte Video to Rio, the interval being nearly of the same duration, and the order of the experiment reversed, the passage being in this instance from Monte Video to Rio, it having been before from Rio to Monte Video. On the supposition of an uniform, or nearly uniform rate of change in the cylinder, the errors arising therefrom during the two passages would be of opposite kinds, and should compensate each other in a mean of the two comparisons. Calling the force at Rio unity, these comparisons give its value at Monte Video respectively as follows, namely,

On the 1st of June 1830, being then on his return from the west coast of South America, and on the eve of sailing for England, Captain King again observed the time of vibration of the cylinder at Monte Video; whence, through the preceding comparison, we obtain the time of vibration at Rio, which should belong to the same date. We have thus a fourth date at Rio, which, added to those enumerated above, will include the whole of the South American stations; and we have only to distribute in each interval the loss of magnetism which the observations shew to have taken place from one date to the next, in the manner which may appear most suitable. There is no very obvious indication that the loss was other than gradual; and by considering it uniform in each separate interval, the results are found extremely accordant at several other stations at which observations were repeated at distant intervals.

In the first of the subjoined tables are given the times of vibration at Rio at the four periods referred to; and the corresponding times as a dipping needle. In its three last columns are shewn,—the number of days comprised in each interval,—the increase in the time of vibration owing to the loss of magnetism,—and the resulting daily correction, on the supposition in each case of the loss having been uniform in the interval during which it occurred.

The second table contains the corrected times of horizontal vibration at each of the South American stations, at the dates respectively inserted,—the corresponding times as a dipping needle,—the times of vibration as a dipping needle at Rio de Janeiro at the same dates, derived from the observations in the first table,—and the resulting intensity at each station relatively to unity at Rio. Thus far the results are derived from Captain King's observations, unmixed with those of any other observer: but in order to bring Captain King's series into connexion with the general body of results of other observers, the values of his intensities are expressed in the final column in terms of the scale in common use, in which the force at Paris = 1,348, and at Rio de Janeiro 0,884; the latter being the mean of four independent determinations by the following observers, namely,

Port St. Elena is not included in this table, as no dip was observed there, and the total intensity consequently cannot be computed. The three stations, Madeira, Teneriffe, and Port Praya, at which the cylinder was vibrated in the outward voyage, are also without dips observed by Captain King. The deficiency at Port Praya has been supplied from Captain Fitz-Roy's observations and my own, both having been made at the same place at which Captain King's intensity was observed,—Captain Fitz-Roy's at a later, and mine at an earlier date. At Madeira also the dip has been supplied from my observations, which were made in the British consul's garden at Funchal, where Captain King's cylinder was vibrated. I have deducted, from my determination of the dip, 12′ for the probable change between 1822 and 1826. At Teneriffe the dip has been frequently observed; but the values assigned by different observers vary so much as to indicate a more than usual frequency of local disturbance, which might also be expected from the geological character of that island. It would be unsafe therefore to employ any dip for that station but one which was certainly obtained at the same spot at which the horizontal intensity was observed.

The dates of the observations at these three stations fall between the observations at Greenwich in March 1826, and those at Rio de Janeiro in August of the same year. Having the intensity at Greenwich = 1,372 and at Rio = 0,884, and the dip at Greenwich 69° 52′, and at Rio 14° 00, we have the time of vibration of Captain King's cylinder as a dipping needle at Rio at the respective dates as follows, namely,

It appears therefore that but a very slight change took place in the magnetism of the cylinder during the outward voyage, and we may take 536,6 as the time of vibration at Rio, corresponding to the dates of the intermediate observations; and this is done in the table for Madeira and Port Praya.

Table I.

Table II.

4.—The following Table exhibits the Magnetic Observations of Captains King and Fitz-Roy collected in one view.

General Remarks.

1. Variation.

Captain Fitz-Roy's observations are so well distributed over the southern hemisphere, that a good view of the changes which the variation is undergoing throughout its meridians may be obtained by comparing his determinations with those of earlier observers at the same stations. The following table has been formed for the purpose of exhibiting such a comparison at all those stations where materials for it exist; and I may here remark how much such comparisons are facilitated by the valuable collection of early observations contained in the Appendix to the Magnetismus der Erde.

We may derive from the facts in the above table the following general and easily remembered conclusion in regard to the changes of the variation in the southern hemisphere; namely, that taking for our point of departure the meridian of 65° west in South America, we find that at all the stations east of that meridian to the Cape of Good Hope inclusive, the north pole of the needle has moved towards the west; and that all the stations west of the same meridian to Mauritius inclusive, the north pole of the needle has moved towards the east.

An almost equally simple generalization may be drawn in respect to the changes of situation of the lines of equal variation in the southern hemisphere: but here it must be supposed either that the reader is thoroughly familiar with the general arrangement of these lines, or that he has a map of them before him. He will find such a map of the variation lines in 1787 in the Fifth Report of the British Association; but any other map, corresponding to any epoch within the last hundred years, will equally serve the purpose. Referring to such a map, it will be seen that the lines of variation in the South Pacific, form a system of nearly concentric curves, of an oval, or pear-shaped form, the outside curves having a higher variation, which progressively diminishes to the centre. We may regard this system as comprehending the whole of the geographical space between the coast of South America and the meridian of New Zealand. Throughout this space the variation is easterly, and increases: we may consequently characterize the change in the situation of the lines of equal variation as a progressive closing-in of the curves from all sides towards the centre, by which the areas severally comprehended by them become less; and the lower variations, as they successively reach the centre, disappear, and are replaced by the closing-in of those of next higher amount. The changes which have taken place at all Captain Fitz-Roy's stations comprised within the space referred to, are accordant with the systematic alteration thus described.

In all other parts of the hemisphere the lines of variation have a progressive westerly movement, and to this also Captain Fitz-Roy's observations correspond.

It follows, from what has been stated, that the lines on the western side of the concentric system in the South Pacific have an eastward movement, which presents an apparent anomaly to the general progress of the lines of variation in the southern hemisphere, which is from east to west.

Otaheite, and the Bay of Islands in New Zealand, present examples of changes in the variation corresponding to this apparent anomaly. The consistency, however, both of the movement and of the configuration of the lines of variation in this quarter, with those in other parts of the southern hemisphere, and with the general system of the magnetic phenomena, has been shewn by Mr. Hansteen in the Magnetismus der Erde, and in the Annalen der Physik, vol. xxi.

The annual amount of the change of the variation appears considerably greater at the Cape of Good Hope and Mauritius than at any other of Captain Fitz-Roy's stations, amounting to about eight minutes; shewing that the variation lines in that quarter are changing their position more rapidly than elsewhere. The north pole of the needle is moving to the west at the Cape, and to the east at Mauritius; but it will be seen, by a reference to the map, that these opposite movements are in perfect correspondence with the uniform westerly progression of the variation lines, and result from their configuration.

At the stations in the vicinity of the meridian of 65° west, the change appears to be very small.

[The variation at Ascension (13° 30′ W.) is correctly inserted in the tables: it is the only one of Captain Fitz-Roy's stations at which his observations are not accordant with those of other observers: the discordance may be occasioned by the great prevalence of local disturbances at Ascension.]

II. Dip.

The following table exhibits the comparison of Captain Fitz-Roy's observations of the dip in the southern hemisphere, with those of earlier observers, at stations where the materials for such a comparison exist.

We may classify the changes which are taking place in the dip in the southern hemisphere in four divisions, characterised by an alternate increase and decrease of dip. Commencing with the meridian of Greenwich, and proceeding eastwardly round the hemisphere, we may distinguish the divisions as follows, in the order of their geographical succession.

1st. South dip increasing.

To this division also belongs Ascension; but as the north end of the needle dips at that island, the change is north dip diminishing, instead of south dip increasing.

4th. South dip decreasing.

In the 2d and 3d divisions the annual change is small; in the 1st and 4th considerably greater. It is greatest at the southern station in South America; the observations at Valparaiso, Concepçion, Tierra del Fuego, and the Falkland Islands, concur in shewing it to exceed 8′. The observations at Ascension, St. Helena, and the Cape of Good Hope, concur in shewing an annual change in that quarter of the 1st division exceeding 6′.

As the south dip decreases in South America, and increases in Africa, it is obvious that somewhere intermediately the dip must be stationary. Between Africa and New Zealand, for the same reason, there must be a second locality so characterised. Between New Zealand and Otaheite, a third; and between Otaheite and the west coast of South America, a fourth. Captain Fitz-Roy has stations in the second of these localities only, between Africa and New Zealand. At Hobart Town, Sydney, and King George Sound, there appears to have been little or no change in the dip since the commencement of the present century.

The arrangement of the changes of dip in the southern hemisphere in four divisions, characterised by an alternate increase and decrease of dip, is in correspondence with the double flexure of the lines of dip; and is a consequence of the western motion of the two southern magnetic poles.

Careful observations made at St. Petersburgh, have shewn that the annual change of the dip in the northern hemisphere takes place altogether between the months of May and December; there being in fact a small movement in an opposite direction between December and May. This fact is of great interest in its bearing on the study of the causes of the magnetic phenomena. We have as yet no corresponding knowledge in regard to the southern hemisphere. The magnitude of the annual change which Captain Fitz-Roy's observations show is now taking place at the Cape of Good Hope, is deserving of attention in this respect. A large amount of annual change is obviously highly favourable for a determination of all the circumstances belonging to it; and its existence at the Cape, where there is already a fixed observatory, points to that station as most eligible for this investigation.

The observations at Ascension shew that the epoch is fast approaching when the needle will pass from north to south dip at that island: it is extremely desirable that the period at which this change takes place should be determined with as much precision as possible.

III. Intensity.

I have discussed in the Seventh Report of the British Association, the very important inferences in regard to the general distribution of magnetism in the southern hemisphere, afforded by Captains King and Fitz-Roy's most valuable series of intensity observations; but no inferences in regard to the changes which this phenomenon may be supposed to undergo can be drawn, as has been done in the cases of the variation and dip, because we possess no observations of the intensity made at a sufficiently early period to afford good materials for such a comparison.