meridians of America, and the variation will have become, first zero, and then easterly.

As a moved south-westward in the Pacific, it must have been followed by the lines of easterly variation in the Southern Atlantic; and the westerly variation shown in the Indian Ocean in the map of 1600, must have progressed to the westward as a receded, and A advanced.

The motion of the small system of westerly variation from North-east Asia in 1770 and 1787, towards Corea and Japan where it was found in 1805, is explained by the eastern progress of b.

Our knowledge of the lines of variation in the Pacific is confined to recent dates: the phænomena, however, as represented in the map of 1787 and in subsequent maps, are in all particulars accordant with the explanation of them afforded by the hypothesis of two magnetic axes.

Viewing next the phænomena of the dip, we may infer that the south dip in South America decreases, because a is moving further into the Pacific; and the north dip in Europe decreases, because b is moving further eastward in Siberia. The great dips (from 8410 to 891°) observed by Hudson at and near the North Cape and Nova Zembla in 1608 were occasioned by the vicinity of b, which was, at that epoch, to the north-east of Spitzbergen. In Europe the dip will shortly again increase as B approaches our part of the world. The north dip in China increases, and the south dip in the same longitudes decreases, because b approaches the meridians of that quarter; and for the same reason the line of no dip, which was observed by Cunningham in the Chinese Sea in 20° north latitude in 1700, is now found considerably to the south of that parallel.

Proceeding next to consider the intensity of the magnetic force at different parts of the earth's surface corresponding to the two magnetic axes, we must first remember that the axes are supposed to be chords, and that in their present position they are both nearer to the surface of the Pacific than to that of the opposite hemisphere, i. e. than to the continents of Europe and Africa. A line drawn from the centre of the earth perpendicularly on the axis A B, and prolonged, would meet the earth's surface at a point in about 197° E., and near the equator. This would be the nearest point on the earth's surface to the middle of the stronger axis; and a point 180° from it, i. e. about 17° E., (on the continent of Africa, not far from the Bight of Benin,) would be the point on the earth's surface most distant from the middle of that axis; and here necessarily would be the minimum of intensity if this axis were the only one.

But a line drawn from the earth's centre perpen

dicularly on the weaker axis a b, and prolonged, would meet the surface in about 217° E.; this point would be the nearest to, and a point 180° from it, or about 37° E., near the east coast of Africa, would be the most distant from, the middle of the axis a b, and consequently about 37° E. would be the minimum of intensity if ab were the only axis. Hence it follows that the point of minimum intensity in the line of no dip resulting from both axes, must be somewhere in Africa between the two points of 17° E. and 37° E. From this point, then, we may imagine a curve to commence, passing northward through Europe, and southward through Africa, and cutting every line of dip at its point of minimum intensity. This curve, prolonged through all the lines of dip, would at length pass into the points where the dip is 90°, where the character of the curve would change from the curve of minimum to the curve of maximum intensity in the several lines of dip, which it would successively intersect till it again reached the geographical equator at some intermediate point between the meridians of 197° E. and 217° E., which are the points of greatest intensity of the two axes respectively, on the line of no dip.

At the date of publication of M. Hansteen's work there existed very few observations of the intensity with which to compare the system of intensities here presented. Those which did exist were, however, conformable to it. The intensities under equal dips diminished from the west side of America (beyond which, on the side of the Pacific, no observations had been made,) to the coasts of Europe and Africa; where the existence of a minimum must be supposed, since, in proceeding still further to the eastward, the force was again found to increase, under dips of the same amount.

In the fourth chapter, M. Hansteen passes under examination Euler's investigation of the mathematical theory of the lines of variation due to a single magnetic axis under various assumed conditions. Of these, the fifth case discussed by Euler is, when the poles of the axis are in different meridians, and at different distances from the poles of the earth. This case meets precisely the present conditions of both the axes in M. Hansteen's hypothesis. Having premised Euler's formulæ in this case, he employs them in calculating successively the lines of variation corresponding to each of the axes A B and a b, in the positions they are supposed to have occupied in the year 1769. These lines are delineated on maps of both hemispheres, exhibiting separately the variation corresponding to each axis. These maps are then compared with the map showing the actual phænomena in the year 1770; and the result of the comparison may be summed up as follows: 1st, The variation computed from the axis A B agrees

extremely well with the actual variation in the neighbourhood of Hudson's Bay and Straits, and in the Southern Indian Ocean between New Holland and the Cape of Good Hope; that is to say, in places which are in the immediate vicinity of one or other of the poles of that axis. 2nd, The variations computed from the weaker axis a b represent, but not so perfectly as in the preceding case, the variations observed in the neighbourhood of its poles in South America and in Siberia. Hence we perceive, that in those localities where the force of each pole might be expected respectively to predominate, Euler's lines of variation calculated for the axis of that pole accord with the phænomena. 3rd, The greater the distance that any point on the earth's surface is from the poles of either axis, the less the observations are represented by either system of lines taken separately. Thus, in the eastern hemisphere, we ought to have for the axis A B a line of 25° west variation, passing through Northern Spain, Southern France, Germany, Prussia, Finland, and Russian Lapland; whilst from the weaker axis a b we should expect an easterly variation of from 6° to 7° in Spain, 10° in Finland, and 12° in Lapland. The combined influence of both axes should then produce a variation, in Spain, between the limits of 25° W. and 16° E.; in Finland, between 25° W. and 10° E.; and in Lapland, between 25° W. and 12° E. Now the variation map of 1770 shows in Spain 20° W., in Finland 5° to 6° W., and in Lapland 0. The nearer either pole of the axis a b is approached, the more the observed variation differs from that which would be given by the axis A B, and approximates to that which is due to the axis a b. In the western hemisphere the line of no variation computed from a b passes south-west of the Californian Sea to the intersection of the meridian of 243° E. with the latitude 15° S., from whence its course is more southerly towards the pole a. In the map of the variation in 1770, there is an obvious relation in the configuration of the lines of variation in the Pacific to this line of no variation due to the axis a b. Nowhere on the line is the actual variation in strict accordance with it, the nearest approach being 2° E.; the difference is occasioned by the influence of the stronger pole A. To the westward of this line, if the axis a b acted alone, the variation would have been westerly, but the effect of the stronger pole predominates as it is approached. Near New Zealand AB would give between 20° and 25° E., and a b 15° W.: the map shows 15° E. At Behring's Strait A B would give a somewhat greater easterly variation than is shown by the map of 1770; and here the neighbourhood of the weaker pole b draws the north pole of the needle to the westward. On a close and careful examination, it will be found a general rule, that the

variations shown by observation fall between the limits assigned by the consideration of each axis taken separately. There are two exceptions to this rule, which are in Java, and from Mexico to the Isthmus of Panama. But these apparent anomalies are also capable of being explained, and disappear when a correction is introduced, which M. Hansteen points out in Euler's investigation, which in certain cases slightly affects the calculations here made in strict accordance with Euler's formulæ ; and when the true magnetic poles are substituted in the calculation for the points of convergence, which have hitherto been considered as coincident with them.

In concluding this chapter, M. Hansteen remarks, that as the curves of variation computed on the hypothesis of two magnetic axes either represent well the actual phænomena, or assign the limits within which the observations are found to fall,-and as four magnetic poles sufficiently explain the double flexure of the lines of dip,-and as the alterations of variation and dip are fully explained by the motions above described of the four poles,—and as, lastly, the phænomena of the intensity indicate a double mag. netic axis,—we may consider this hypothesis to be as well established, as a means of representing the phænomena, as any hypothesis whatsoever introduced in physical illustration.

Chapter fifth is entitled "On the Theory of Magnets." Having shown that when two magnetic points act on each other, their mutual action, whether of attraction or repulsion, is the product of the absolute magnetic force of the two points into some function of their distance apart, M. Hansteen proceeds to investigate the elementary laws which regulate the action of a linear magnet upon a magnetic point situated, first, in the prolongation of its axis; second, in the perpendicular passing through its centre, or its equator. The action depends in both cases, first, on the distance of the point from the centre of the magnet; second, (and particularly if the distance be inconsiderable in proportion to the length of the magnet,) on the distribution of the magnetic intensity in the magnet itself. These, therefore, form the subject of two elementary laws, deduced from experiments, which consist in drawing a small compass-needle from its line of repose in the magnetic meridian by a linear magnet, placed horizontally, at different distances in succession, from four to twelve times the half axis of the magnet, in a line through the centre of the needle perpendicular to the magnetic meridian, and in noting the displacements occasioned thereby in the direction of the compassneedle. The displacements so occasioned are then compared with computed expressions, in which the influence of the magnet is considered to vary inversely, first, as the distance itself;

second, as the square; and third, as the cube, of the distance of the magnetic point from the centre of the magnet: and in which the distribution of the intensity along the magnetic axis is considered to vary, first, as the simple distance of the particles from the middle point; second, as the square; and third, as the cube of that distance. It is shown by the comparison, first, as regards the distance of the magnetic point and the centre of the magnet, that when the displacements are computed in the inverse proportion of the simple distance or of the cube, they differ widely from those observed; but that when computed as the squares, the accordance of calculation and experiment is satisfactory throughout the series. Second in regard to the distribution of the intensity along the magnetic axis, that the agreement is best in these experiments when the magnetic intensity of the particles is taken as the square of the distance from the middle point of the magnet.

The experiments, therefore, indicate the following elementary laws, viz.

1. That the attractive force with which two magnetic points influence each other is inversely as the square of their distance apart.

2. That the force in the axis of a linear magnet increases as the square of the distance from the middle point; or, that the absolute intensity of each point in the axis is proportional to the square of its distance from the magnetic

centre.

The first law is the same which was originally derived by Mayer from experiments communicated to the Royal Society of Sciences at Göttingen; it has been since confirmed by other philosophers, and is in full accordance with the experiments of M. Hansteen.

A corroboration of the second law is considered to be obtained from other experiments, subsequently related, in which two linear magnets were employed for the purpose of examining the laws of their mutual action. M. Hansteen also notices the experiments of Professor Steinhausen, which lead to the same inference. He concludes, therefore, that there is at least strong probability in favour of the second law; and as, moreover, that law is only of importance in small distances from the magnet, approaching contact,-and as in its application to the phænomena of terrestrial magnetism the distances are always so considerable as to render almost imperceptible the effect of differences in the distribution of intensity in its magnet itself, its adoption on this occasion cannot give rise to any material error, even if it should not ultimately prove to be the true law.