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JOURNAL OF SCIENCE AND ARTS.
Art. I.-On Terrestrial Magnetism ; by WILLIAM A. NORTON,
Professor of Mathematics and Natural Philosophy in Delaware College.
I PROPOSE in the present article to show that, adopting certain fundamental conceptions with respect to the terrestrial magnetic forces, the magnetic may be deduced from the thermal elements of the earth. The first investigations tending to establish the existence of a physical connection between the heat and magnetism of the earth, seem to have been made by Sir David Brewster. In 1820 he announced the “discovery of two poles of maximum cold on opposite sides of the north pole of the earth," and in the vicinity of the two magnetic poles; and maintained the probability of some physical connection between the poles of maximum cold, and the magnetic poles. He also proved “that the circle of maximum heat, like the magnetic equator, did not coincide with the equinoctial line; that the isothermal lines and the lines of equal magnetic intensity, had the same general form surrounding and enclosing the magnetic poles and those of maximum cold; and that, by the same formula, mutatis mutandis, we could calculate the temperature and the magnetic intensity of any point of the globe.” This subject has since been studied by several philosophers; and particularly by Captain Duperrey, and M. Kupffer of Kasan. The original memoirs of these authors I have not seen. The following is the substance of the account which Sir David Brewster gives of their investigations. In the years 1822-1825, Captain Duperrey made an extended system of magnetic observations in the vicinity of the equator, by which
Second Series, Vol. IV, No. 10.—July, 1847. 1
he was enabled to trace the magnetic equator, with peculiar accuracy, through an extent of 247° of longitude. In his paper on the magnetic equator, subsequently published, he announced that he had discovered that “the points of this great circle, or those where the magnetic intensity is a minimum, are also the warmest points of each meridian," and thus that "the thermal and magnetic equator are connected, as Sir David Brewster had already proved to be the case with the thermal and magnetic poles ;" also, “that in comparing the isothermal and isodynamic lines, he had found a remarkable analogy in their curvatures and particularly in the direction of their concavities, and convexities." M. Kupffer, in certain memoirs read before the Russian Academy about the year 1829, attempted to establish that terrestrial magnetism resides at the surface of the globe, and thence inferred the existence of a connection between the magnetic and thermal phenomena of the earth : conceiving that the intensity of the earth's magnetism would vary directly or inversely as the temperature, according as it was of the nature of permanent or induced magnetism.
Several conjectures have been formed as to the nature of the connection between the temperature and magnetism of the earth. Dr. Traill has expressed the opinion that "the disturbance of the equilibrium of the temperature of our planet, by the continual action of the sun's rays on its intertropical regions, and by the polar ices, must convert the earth into a vast thermo-magnetic apparatus." Christie has suggested that "difference of temperature may be the primary cause of the polarity of the earth, though its influences may be modified by other circumstances.” Ersted conceives that the sun, by producing evaporation, deoxydation, &c., as well as by increasing the temperature, is the exciting cause of electrical currents, which perpetually traversing the earth's surface in a direction nearly parallel to the equator, give to the earth “a constant magnetic polarity." Perhaps the more generally received theory of the present day concerning the physical nature of the earth's magnetism, is that it consists of thermoelectric currents circulating at or near the earth's surface, duced by the heat of the sun. Prof. Barlow, who adopts this view, conceives that only one link is wanting to complete the explanation of terrestrial magnetism, viz. the discovery of the metallic thermo-magnetic apparatus. Brewster remarks upon this, that “if it could be shown that the action of solar heat is capable of developing magnetism in particles such as those which are known to constitute our globe, the great difficulty would be removed."
In seeking for the explanation of the connection between the magnetic and thermal phenomena of the earth, philosophers seem hitherto to have regarded the heat as only modifying in some in
explicable manner the intensity of the magnetism of the terrestrial particles; or as bearing towards it the relation of cause and effect. But there is another view to be taken of the matter. We may regard the two principles of heat and magnetism as similar in their ultimate physical nature, as every where subsisting together, and that the causes which produce a variation of temperature at the surface of the earth, as we pass from one point to another, occasion at the same time and in like manner a variation of the magnetic intensity of the particles. So that the temperature at each particular place may be taken as the approximate measure of the molecular magnetic intensity there. The conception that I have formed of the probable physical nature of the imponderables, of which I have given an exposition in a paper read before the American Philosophical Society in December last, has led me to take this view of the physical relations subsisting between the heat and magnetism of the earth. This conception is, essentially, that all the phenomena of the imponderables are but different effects of different vibratory motions of the particles of matter, and of the ethereal undulations produced by these vibrations ;—the vibrations answering to the different principles of light, heat and electricity, differing in time and intensity, and
possibly in some instances in direction, of vibration. Agreeably to this general theory I conceive each particle of the earth's mass to be the centre of a system of undulatory movements propagated through the surrounding ether, and of every variety of time and intensity of vibration within certain limits. To the waves or pulses of feeblest intensity and shortest time of vibration I attribute the phenomena of magnetism; or, at all events, I suppose the waves of magnetism to lie at the opposite extreme from the waves of heat. It thus happens that all the particles of the magnetic needle receive the impulsive actions of the waves of magnetism propagated from the particles of matter at the earth's surface, and at certain depths below the surface from how great a depth will depend upon the degree of transparency, to these waves, of the matter of the earth. That the principle of magnetism is incoercible, or that it passes freely through opake bodies of ordinary thickness, has been fully established by the experiments of M. Haldat: and that all the particles of the magnetic needle are subject to the action of the magnetic force of the earth, is evident from the fact that the directive force of the needle is proportional to its mass. Why it is that magnets alone are sensibly influenced by the impulsive actions of the ethereal pulses, I cannot now stop to consider. These theoretical views, I do not here present for the purpose of advocating them, but simply because they furnish a simple and comprehensive conception of the terrestrial magnetic forces and of their relations to the earth's temperature. The mechanical theory of terrestrial magnetism which
it is the main design of the present article to exhibit, and apply, although suggested by these views, is not necessarily dependent upon them. The quantitative results arrived at, simply establish the existence of the forces supposed and of the relations conceived to subsist between them and the temperature of the earth. Different views may be entertained of the physical origin of these forces; or, we may rest upon the forces themselves as so many primary properties of matter.
The mechanical theory of the magnetism of the earth, of which I propose to give an exposition, is based upon the following fundamental principles. These were obtained inferentially from the physical theory of terrestrial magnetism which has been briefly explained: but for our present purpose, they may be regarded as mere assumptions, to be tested by the conclusions and results to which they lead.
1. Every particle of matter at the earth's surface, and to a certain depth below the surface, is the centre of a magnetic force exerted tangentially to the circumference of every vertical circle that may be conceived to be traced around it. Thus, if A, fig. 1,
Fig. 1. be a particle of the earth's mass at or near the surface, P a particle of a magnetic needle, and BPC a circle traced in a vertical plane around A as a centre and passing through P, P will be urged by a force whose line of direction is the tangent mPn. Whether there are probably tangential forces ly. ing also in oblique planes, I do not here consider. If there are such forces it appears from the results of the investigation that they may be disregarded in the present inquiry. According to the views which have been offered of the probable physical nature of magnetism, the tangential forces here supposed are due to the transversal vibrations of the ethereal waves of magnetism propagated from the point A, and originated by certain vibratory movements of the particle at A.
2. The direction of this force will be different according as it solicits the north or south end of the needle; and it is always such, that to the north of the acting particle the north end of the needle is urged downwards and the south end upwards, and that to the south of the same particle the north end is urged upwards and the south end downward. Thus, in fig. 1, if P be to the north of A and P to the south of it, at P the north end of a magnetic needle will be solicited to move in the direction Pn, and the south end in the direction Pm; and at P' the north end will be solicited in the direction P'm', and the south end in the
direction P'n'. This amounts to saying that the magnetic force of A in its action upon the north end of the needle is directed tangentially in the circle from right to left, as shown by the arrow, and in its action upon the south end of the needle is directed from left to right.
Upon the undulatory theory of magnetism these differences of action are attributable to ethereal waves whose transversal forces of vibration lie in opposite directions, and to certain differences in the magnetic states of the two ends of the needle.
3. The intensity of the magnetic force of a particle of the earth, at a given distance, is assumed to be approximately
proportional to its temperature, or amount of sensible heat. This assumption was made under the idea that the sun was the source, at the same time of waves of heat, light and magnetism, and that the molecular forces of vibration due to the different kinds of waves would probably vary according to the same law in passing from one point to another on the earth's surface.
The magnetic force of a particle at the earth's surface, and for a certain depth below the surface, will have a certain mean intensity about which the actual intensity will vary during the day and year, by an amount decreasing with the depth. Beyond a certain depth, the magnetic intensity, like the temperature, will remain the same throughout the year, and will have a value greater than the surface mean in proportion as we descend lower. Lines conceived to be traced on the earth's surface connecting the points where the annual mean magnetic intensity of the particles near the surface is the same, will, according to the present view, coincide with the isogeothermal lines, and very nearly therefore with the isothermal lines. Let then, AB, CD, EF, fig. 2, represent portions of three isogeothermal lines, regarded as parallel to each other, and GPH an arc of a great circle crossing these lines perpendicularly. ī If we take four points m, n, r, s, similarly situated with respect to GPH, the action of the particle m upon the north end of a magnetic needle will be perpendicular to mP and directed obliquely downward. The action of the particle n will be perpendicular to nP and also directed obliquely downward. The magnetic forces of the particles r, s, will be respectively perpendicular to rP and SP and directed obliquely upward. Now it is evident that while one effect of the action of m will be to urge the north end of the needle toward C, the particle n will have an equal tendency to urge it toward D. In like manner, the components of the forces of r and s, which solicit the north end of the needle in the directions PC