LONDON. Royal Society, May 9.—Sir J. J. Thomson, president, in the chair.—Major P. A. MacMahon and H. B. C. Darling: Contribution to the theory of attraction when the force varies as any power of the distance.—Sir George Greenhill: Electromagnetic integrals. Starting with Maxwell's M, mutual inductance of two coaxial circular currents, a straightforward integration will lead to the analytical expressions arising in the theory of the ampere-balance current-weigher, described in Phil. Trans., 1907, by Ayrton-Mather-Smith, and the complicated dissections are not necessary, employed by Viriamu Jones, Minchin, and other writers. The elliptic integrals which occur are then reduced to a simple standard form, capable of use with Legendre's tables of the elliptic function; and the quadric transformation is explained geometrically, required to reconcile the conflicting notation of previous treatment. A re-drawing is submitted of Maxwell's figure XVIII of the curves of constant, employing the co-ordinates of the confocal conies on Weir's chart: The same co-ordinates are applied to a state of uniplanar liquid motion, where they appear appropriate, as well as to Euler's problem of the orbit under two centres of force.—Dr. T. R. Merton and Prof. J. W. Nicholson: Intensity relations in the spectrum of helium. The paper contains the results of an experimental investigation of the variations in distribution of intensity among the lines of the helium spectrum under various conditions of excitation. The intensities have been examined quantitatively, according, to the method described in previous memoirs, at various assigned positions in the cathode dark space and beyond, so that the variations can be determined as definite functions of cathode distance. It is found that the relative intensities of lines in the diffuse series of helium and parhelium remain essentially the same at all distances, but that striking variations occur in other types of series. The results are discussed (1) from the point of view of selective transfer of energy in any one series; (2) in relation to type of series—diffuse, sharp, or principal; and (3) in relation to the relative behaviour of the doublet and single-line spectra. The spectra of mixed gases—hydrogen and helium—have also been studied in the same way, and it has become apparent that the phenomena presented by the presence of a spectroscopic trace of one of the gases are essentially different in character from those presented when the gases are mixed in comparable amounts. The low-pressure spectrum of helium has been investigated quantitatively, and the results have been discussed with special reference to the reproduction in the laboratory of the abnormal intensity relations found in the spectra of the nebulae. It is shown that the nebular spectrum of helium would be obtained very closely by a combination of the conditions belonging to the condensed discharge and to the low-pressure spectrum.—Dr. S. Chapman: The outline of a theory of magnetic storms. The average characteristics of magnetic storms are separated into two parts, depending respectively upon time measured from the commencement of the storm and upon local time. In the former the horizontal force is the element chiefly affected, a brief initial increase being followed by a much larger decrease, extending over several hours. Afterwards, during a period of days, the force slowly returns to its normal value. The. local-time changes, after the ordinary diurnal magnetic variations have been removed, are approximately simple sine or cosine weaves in all three elements. Their mutual relations in phase, and the dependence of their amplitudes upon latitude, are determined for twelve observatories from the mean of forty storms. The two sets of variations are interpreted in terms of electric current systems circulating in the upper atmosphere (with corresponding earth currents). These, again, are referred to the inductive action of a system of atmospheric motions. These motions are primarily vertical, though the unequal distribution of vertical velocity introduces horizontal movements also. The atmospheric motions are explained as the result of the precipitation of electric particles from the sun into the earth's atmosphere. A depression of the absorbing layer (which becomes ionised) is first. produced. This is succeeded by a general upward expansion, due to the mutual repulsion of the particles (which are mainly of one sign of charge) which are entangled in the layer. The stratum in which these, actions occur is considered to be above that in which the ordinary diurnal magnetic variations are produced, and the ionisation in the latter layer is attributed to the action of ultra-violet light from the sun.