IX. On the lunar diurnal variation of the Earth's magnetism at Pavlovsk and Pola (1897-1903)

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1. The present paper contains an account of the methods and results of an investigation into the lunar diurnal magnetic variations at the observatories of Pavlovsk and Pola (1897-1903). This work is part of a larger undertaking, now in progress, by which I hope to obtain the data necessary for the discussion of the lunar diurnal magnetic variations over the whole earth, using the method of the Gaussian potential in a manner similar to that in which Schuster applied it to the solar diurnal magnetic variations. For this purpose data will be computed from at least three or four other observatories. The labour of computation involved is very large, and in the present instance has been executed partly by the aid of a grant from the Government Grant Committee of the Royal Society, and partly by assistance put at my disposal by the Astronomer Royal and Dr. Schuster. While the data thus obtained will, I trust, throw much new light on the theory both of the lunar and solar diurnal magnetic variations, the investigation has been undertaken not with any thought of finality in itself, but rather as an incentive to the provision of data for a more accurate and detailed discussion by subsequent workers. The reduction of the observations to the required form is, in fact, almost too great a labour for a single person to undertake if it is to be done on an adequate scale and in a reasonable time. It is in the hope, therefore, that a number of directors of magnetic observatories may be induced to carry out the reductions for their own stations that I have, in this paper, indicated what seems to me to be the simplest and most suitable method of computation for the purpose, and also some of the lines along which the discussion of the results from a single observatory should proceed. In a later paper some further points will be dealt with, in addition to the final discussion of the collected results from several observatories ; for a general review of the subject, reference may be made to my recent discussion of the previously existing data for Batavia, Bombay, and Trevandrum. A few of its main points are summarized below for the better understanding of the object of the present paper. 2. The magnetic elements undergo regular variations with the period of a lunar day, just as they do in the course of a solar day; the latter variations are much the larger of the two. The lunar diurnal changes are the simpler in character, however, taking the form, when averaged over a whole lunation, of a purely semi-diurnal wave. But if the variation is computed from a number of days all at the same lunar phase ( i. e ., when there is a definite angular distance between the sun and moon), the solar diurnal variation having first been eliminated from the observations, harmonic components of other frequencies in the lunar day are also found to be present. The epoch of the component of frequency 2 (the semi-diurnal term) remains constant throughout the lunation, but the epochs of the terms of frequency 1, (2), 3, 4, ..., n change regularly during the lunation by amounts —2π, (0), 2π, 4π, ..., 2( n - 2) π respectively. Moreover, the epochs of the various components generally seem to be nearly or quite the same at the time of new moon, when the sun and moon are on the same meridian. This law of phase change was discovered and verified by a study of the first four harmonic components; it explains the disappearance of all components of frequency other than 2 from the variation computed from a whole lunation. The phenomenon clearly suggests a solar action modifying a regular semi-diurnal lunar variation. In the paper referred to, I have shown that the law according to which the epochs of the several harmonic components change during a lunation is in accord­ance with the theoretical consequences of such a solar action. While the proof of this theorem might easily be stated in terms which imply no special hypothesis as to the manner in which the action takes place, it was actually given in terms of a parti­cular theory, viz., that the effect is due to a variation, periodic in a solar day, of the electrical conductivity of the medium in which flow the currents to whose magnetic potential is attributed the variable field put in evidence by the observations. The dependence of the electrical conductivity upon solar time is accounted for if we suppose that all or part of this conductivity is due to some ionizing influence from the sun. So far as regards the facts thus mentioned, this assumption fits in naturally with a view that the lunar magnetic variations arise from the lunar tide in the earth’s atmosphere in the same way as, according to Schuster’s well-known theory, the solar diurnal magnetic changes arise from the ordinary daily atmospheric motions which are indicated by the barometer.

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