At first, the British stations were established for three years only; but it was thought advisable to extend this period three years longer, to end in 1845. And when the termination of that period arrived, a discussion was held among the magneticians themselves, whether it was better to continue the observations still, or to examine and compare the vast mass of observations already collected, so as to see to what results and improvements of methods they pointed. This question was argued at the meeting of the British Association at Cambridge in that year; and the conference ended in the magneticians requesting to have the observations continued, at some of the observatories for an indefinite period, at others, till the year 1848. In the mean time the Antarctic expedition had brought back a rich store of observations, fitted to disclose the magnetic condition of those regions which it had explored. These were discussed, and their results exhibited, in the Philosophical Transactions for 1843, by Col. Sabine, who had himself at various periods, made magnetic observations in the Arctic regions, and in several remote parts of the globe, and had always been a zealous laborer in this fruitful field. The general mass of the observations was placed under the management of Professor Lloyd, of Dublin, who has enriched the science of magnetism with several valuable instruments and methods, and who, along with Col. Sabine, made a magnetic survey of the British Isles in 1835 and 1836.
I do not dwell upon magnetic surveys of various countries made by many excellent observers; as MM. Quetelet, Forbes, Fox, Bache and others.
The facts observed at each station were, the intensity of the magnetic force; the declination of the needle from the meridian, sometimes called the variation; and its inclination to the horizon, the dip;—or at least, some elements equivalent to these. The values of these elements at any given time, if known, can be expressed by charts of the earth’s surface, on which are drawn the isodynamic, isogonal, and isoclinal curves. The second of these kinds of charts contain the “Halleian lines” spoken of in a previous [page]. Moreover the magnetic elements at each place are to be observed in such a [229] manner as to determine both their periodical variations (the changes which occur in the period of a day, and of a year), the secular changes, as the gradual increase or diminution of the declination at the same place for many years; and the irregular fluctuations which, as we have said, are simultaneous over a large part, or the whole, of the earth’s surface.
When these Facts have been ascertained over the whole extent of the earth’s surface, we shall still have to inquire what is the Cause of the changes in the forces which these phenomena disclose. But as a basis for all speculation on that subject, we must know the law of the phenomena, and of the forces which immediately produce them. I have already [said] that Euler tried to account for the Halleian lines by means of two magnetic “poles,” but that M. Hansteen conceived it necessary to assume four. But an entirely new light has been thrown upon this subject by the beautiful investigations of Gauss, in his Theory of Terrestrial Magnetism, published in 1839. He remarks that the term “poles,” as used by his predecessors, involves an assumption arbitrary, and, as it is now found, false; namely, that certain definite points, two, four, or more, acting according to the laws of ordinary magnetical poles, will explain the phenomena. He starts from a more comprehensive assumption, that magnetism is distributed throughout the mass of the earth in an unknown manner. On this assumption he obtains a function V, by the differentials of which the elements of the magnetic force at any point will be expressed. This function V is well known in physical astronomy, and is obtained by summing all the elements of magnetic force in each particle, each multiplied by the reciprocal of its distance; or as we may express it, by taking the sum of each element and its proximity jointly. Hence it has been proposed[25] to term this function the “integral proximity” of the attracting mass.[26] By using the most refined [230] mathematical artifices for deducing the values of V and its differentials in converging series, he is able to derive the coefficients of these series from the observed magnetic elements at certain places, and hence, to calculate them for all places. The comparison of the calculation with the observed results is, of course, the test of the truth of the theory.
[25] Quart. Rev. No. 131, p. 283.
[26] The function V is of constant occurrence in investigations respecting attractions. It is introduced by Laplace in his investigations respecting the attractions of spheroids, Méc. Cél. Livr. iii. Art. 4. Mr. Green and Professor Mac Cullagh have proposed to term this function the Potential of the system; but this term (though suggested, I suppose, by analogy with the substantive Exponential), does not appear convenient in its form. On the other hand, the term Integral Proximity does not indicate that which gives the function its peculiar claim to distinction; namely, that its differentials express the power or attraction of the system. Perhaps Integral Potentiality, or Integral Attractivity, would be a term combining the recommendations of both the others.
The degree of convergence of the series depends upon the unknown distribution of magnetism within the earth. “If we could venture to assume,” says M. Gauss, “that the members have a sensible influence only as far as the fourth order, complete observations from eight points would be sufficient, theoretically considered, for the determination of the coefficients.” And under certain limitations, making this assumption, as the best we can do at present, M. Gauss obtains from eight places, 24 coefficients (each supplying three elements), and hence calculates the magnetic elements (intensity, variation and dip) at 91 places in all parts of the earth. He finds his calculations approach the observed values with a degree of exactness which appears to be quite convincing as to the general truth of his results; especially taking into account how entirely unlimited is his original hypothesis.
It is one of the most curious results of this investigation that according to the most simple meaning which we can give to the term “pole” the earth has only two magnetic poles; that is, two points where the direction of the magnetic force is vertical. And thus the isogonal curves may be looked upon as deformations of the curves deduced by Euler from the supposition of two poles, the deformation arising from this, that the earth does not contain a single definite magnet, but irregularly diffused magnetical elements, which still have collectively a distinct resemblance to a single magnet. And instead of Hansteen’s Siberian pole, we have a Siberian region in which the needles converge; but if the apparent convergence be pursued it nowhere comes to a point; and the like is the case in the Antarctic region. When the 24 Gaussian elements at any time are known the magnetic condition of the globe is known, just as the mechanical condition of the solar system is known, when we know the elements of the orbits of the satellites and planets and the mass of each. And the comparison of this magnetic condition of the globe at distant periods of time cannot fail to supply materials for future researches and speculations with regard to the agencies by which the condition of the earth is determined. The condition of which we here speak must necessarily be its mechanico-chemical condition, being expressed, as it will be, in terms of the mechanico-chemical sciences. The [231] investigations I have been describing belong to the mechanical side of the subject: but when philosophers have to consider the causes of the secular changes which are found to occur in this mechanical condition, they cannot fail to be driven to electrical, that is, chemical agencies and laws.
I can only allude to Gauss’s investigations respecting the Absolute Measure of the Earth’s Magnetic Force. To determine the ratio of the magnetic force of the earth to that of a known magnet, Poisson proposed to observe the time of vibration of a second magnet. The method of Gauss, now universally adopted, consists in observing the position of equilibrium of the second magnet when deflected by the first.
The manner in which the business of magnetic observation has been taken up by the governments of our time makes this by far the greatest scientific undertaking which the world has ever seen. The result will be that we shall obtain in a few years a knowledge of the magnetic constitution of the earth which otherwise it might have required centuries to accumulate. The secular magnetic changes must still require a long time to reduce to their laws of phenomena, except observation be anticipated or assisted by some happy discovery as to the cause of these changes. But besides the special gain to magnetic science by this great plan of joint action among the nations of the earth, there is thereby a beginning made in the recognition and execution of the duty of forwarding science in general by national exertions. For at most of the magnetic observatories, meteorological observations are also carried on; and such observations, being far more extensive, systematic, and permanent than those which have usually been made, can hardly fail to produce important additions to science. But at any rate they do for science that which nations can do, and individuals cannot; and they seek for scientific truths in a manner suitable to the respect now professed for science and to the progress which its methods have made. Nor are we to overlook the effect of such observations as means of training men in the pursuit of science. “There is amongst us,” says one of the magnetic observers, “a growing recognition of the importance, both for science and for practical life, of forming exact observers of nature. Hitherto astronomy alone has afforded a very partial opportunity for the formation of fine observers, of which few could avail themselves. Experience has shown that magnetic observations may serve as excellent training schools in this respect.”[27]]