culation were perfect, would be the correct positions of the points of convergence due, to the stronger axis. The position of that axis being in this manner approximatively gained, its corrected situation was employed, in conjunction with the variations observed near the poles of the weaker axis, in giving fresh points of convergence for that axis; the new position of which axis was in its turn again employed in recorrecting the variations observed near the stronger poles, and in producing a still nearer approximation to the position of the stronger axis. This alternating process was continued until the two last-found results exhibited no material difference.

The approximate places of the extremities of the magnetic chords having been thus found and substituted for the points of convergence, and the values previously calculated of e,, &, &c. deduced afresh, M. Hansteen reverted to the observations of dip in the high magnetic latitudes, from which he had previously derived values for the length and proportionate forces of the magnetic axes, and selecting several of the most trustworthy of these observations, after various trials, he found that the observations were best represented when the length of each of the axes was taken at one third of the earth's axis, and the ratio of the forces as 1·7724 to 1.

With an axis of this length the points of 90° dip and of convergence of the horizontal needle would be nearer the end of the magnetic chord than in the case of an infinitely small axis ; and by trial it was found that a = 0.41 br suited best. Other small corrections, which were pointed out by the comparison of the calculation and observations, were also introduced in several of the elements.

Having reached this stage M. Hansteen considered that the elements were sufficiently corrected to admit of a more extensive comparison. He formed, therefore, a table of the most trustworthy observations of dip, variation, and intensity, made between 1787 and 1800, at eighty-four places, taken indiscriminately on the earth's surface, and divided into three portions, magnetic north polar, south polar, and equatorial. With the observations in this table, the dip, variation, and intensity computed for each of the eighty-four stations were compared, by which still further but very small corrections were introduced in the elements. The principal elements for computing the magnetic phænomena thus corrected are as follow :

the magnetic axes being each one third of the length of the earth's axis, or Q = 3; and the ratio of the forces 1.7724 to 1.

In comparing the phænomena as calculated by the aid of the above quantities and as observed in the eighty-four tabulated stations, it is seen, 1st, with regard to the Variation,-that except at places in the immediate vicinity of the magnetic poles no discordance exists greater than about 5°. 2nd, In regard to the Dip, that the differences are generally inconsiderable, and mostly under 5°, except in a strip of the Atlantic extending from Teneriffe in a south-west direction to about 14° N. latitude and 313 E. longitude, and in a strip of the Indian Ocean extending from the Straits of Babelmandel to the Indian Peninsula. In the Atlantic strip the calculated north dips are from 10° to 11° too small, and in the strip in the Indian Ocean the calculated north dips are about 10° or 12° too great, and the south dips as much too small. 3rd, In regard to the Intensities, the observed and calculated agree well, except in the aforesaid strip of the Atlantic, where the force as well as the dip is made too small by calculation; manifesting that the elements still require some correction, which they will best receive when more observations are obtained near the magnetic poles and along the line of no dip.

The eighty-four stations which have served for the above comparison extend over the most important parts of the earth's surface, both near the magnetic poles and the magnetic equator, and it is not probable that greater differences between the calculated and observed variations and dips will be found anywhere than those which appear in the table.

M. Hansteen remarks in conclusion that most of the differences would diminish, if not wholly disappear, by increasing the angle, which the equatorial planes of the two magnetic axes form with the geographical equator. By increasing the angle for the stronger axis the northerly dip in the northern part of the Atlantic, and the southerly dip in the Indian Ocean would increase, and the northerly dip consequently decrease between the Red Sea and India. Further, the westerly variation in Musketto Cove and in the Indian Ocean, near the Cape of Good Hope, and the easterly variation between Van Diemen's Land and New Zealand would increase. By increasing the angle for the weaker axis, the northerly dip in Petersburgh, Siberia, and Kamschatka, and the southerly dip near Terra del Fuego would increase; and the westerly variation in Petersburgh and at the North Cape, and the easterly variation in Kamschatka would decrease, whilst the easterly variation near Terra del Fuego would increase. It is also probable that this alteration would increase the calculated intensities in the Northern

Atlantic. These are the parts of the globe where the principal differences take place between the calculated and the observed phænomena; but as the approximation has already been pushed sufficiently far to sanction the hypothesis, it is deemed unnecessary, and would probably be eventually time thrown away, to press to a nearer accordance, until the situation of the four points of convergence on the globe has been ascertained, with greater precision, by direct observation.

Since the publication of the Magnetismus der Erde M. Hansteen has been engaged in personally determining the lines of dip, variation, and intensity, in the North of Europe, and throughout the Asiatic dominions of Russia. It is understood that he proposes to collect and embody, with the account of his own observations which he is preparing, all that has been accomplished by others since the early part of the present century; and thus to complete, in a second volume, the history of all that has been hitherto made known by observation concerning terrestrial magnetism. I have deemed it the more proper course, as well as that best fitted eventually to advance the inquiry, to await this publication from M. Hansteen, rather than to attempt, in this year's Report and with the materials which I now possess, or which are immediately accessible, the continuation of the condensed view which, by the aid of M. Hansteen's first volume, I have endeavoured to give of the results of observation in the two preceding centuries. The knowledge of the facts, conveyed by a suitably arranged view of what observation has made known, is a proper preliminary to an examination of the hypotheses proposed either to connect or to explain the phenomena.

It is a remarkable coincidence, and one of considerable importance towards a correct systematic knowledge of terrestrial magnetism, that at the same epoch at which the vicinity of the Siberian point of convergence has been visited by an observer of M. Hansteen's experience, furnished with the most perfect instruments, the other influential point in the northern hemisphere, in the North of America, has been also approached in various directions by the British officers employed in North-west discovery and thus the position of the lines of dip, variation, and intensity in those two most interesting localities have been almost simultaneously ascertained, with an exactness heretofore unequalled. Those who have engaged in the endeavour to reduce to a common epoch observations made at intervals of time apart, can best appreciate how much of otherwise inevitable uncertainty is removed, when materials which should be rendered strictly relative to each other for the purpose of combination,

:

correspond in date. It is known that the north dip is at present diminishing in this part of the world about 3 minutes annually, and that it has not differed materially from that rate of diminution for several years past but from a comparison of observations we learn, that in the Gulf of Guinea the annual diminution is little less than ten minutes, if it does not exceed that amount; whilst in the China Seas between the years 1700 and 1780 the north dip, on the contrary, increased, and at an average annual rate which could scarcely have fallen short of fifteen minutes, or a quarter of a degree a year. Our knowledge as yet is very far from being sufficient to enable us to render justly comparative the observations of different years, except in a very few parts of the globe.

In the northern hemisphere we probably now possess the requisite materials for describing the magnetic curves, from observations greatly to be relied on, and so nearly contemporaneous as to occasion but little error in reduction. But it is far otherwise in the southern hemisphere, particularly in what are usually called the high magnetic latitudes, and where an acquaintance with the facts would be of principal value towards a knowledge of the system of Terrestrial Magnetism. The enterprise of our merchant seamen has shown that these latitudes are far more accessible, in certain meridians at least, than had been previously supposed. The magnetic observations of the voyages of Weddell and Biscoe have been confined to those of the variation; these fully confirm M. Hansteen's position of the general westward movement of the lines of equal variation, in the southern hemisphere. But it is in the meridians left untouched by those vessels,-in those which include and are adjacent to those magnetic foci in the southern hemisphere, which M. Hansteen has called points of convergence, that observations would be chiefly useful; and observations confined to the variation, but including also the dip, and intensity of the force. The ice itself, or such lands as might be discovered by a vessel coasting the southern ice between the meridians of 80° E. and 260° E., would furnish the requisite localities for the observations of the three phænomena; and would supply what is wanting to complete a map exhibiting the arrangement, corresponding to a definite epoch, of the curves of equal dip, variation, and intensity, over the whole surface of our globe.

RESEARCHES

UNDERTAKEN AT THE REQUEST OF THE ASSOCIATION.

Report on the Comparative Measurement of the Aberdeen Standard Scale. By FRANCIS BAILY, Treas. Royal Society, &c.

AGREEABLY to the request of the British Association I have compared the Aberdeen standard scale with the standard scale of the Royal Astronomical Society: but, as in a matter of this nicety and importance I did not wish the results to depend on my own comparisons only, I obtained the assistance of Mr. Bryan Donkin, Lieut. M. Johnson, Mr. Thomas Jones, and Mr. William Simms, all conversant with and much versed in micrometrical measurements, and who kindly lent me every assistance in their power.

The centre yard of the Aberdeen scale was chosen as the object of comparison with the centre yard of the Royal Astronomical Society's scale; that being the portion of the latter scale which had been directly compared with the Imperial standard yard prior to its loss by fire, at the destruction of the two houses of Parliament in November last. The following are the results of 56 comparisons made by the several parties above mentioned, and estimated in divisions of the micrometer microscopes (each division denoting of an inch,) and show the number of such divisions by which the centre yard of the Royal Astronomical Society's standard scale exceeds the centre yard of the Aberdeen scale.