280 DR S. CHAPMAN ON THE DIUENAL VARIATIONS OF THE 



x iol,-t radiation from the sun.* The fundamental assumptions are in accordance with 

 S. HI-SIKH'S demonstrationt that the magnetic variations are principally due to a 

 system of currents above the earth's surface. In order to explain the relative 

 magnitudes of the diurnal and semi-diurnal terms in the magnetic potential, it is 

 necessary to suppose that the conductivity of the atmosphere varies with the solar 

 hour angle, which is certainly a priori probable : the great excess of the summer 

 variation over the winter variation is unexplained, however, as the usual rapid rate 

 of recombination of ions makes it difficult to believe that the solar ionization is slowly 



cumulative. 



There is at present much uncertainty as to the numerical constants of the potential 

 of the magnetic field responsible for the solar diurnal variations, as the only two 

 calculations yet madej show serious disagreement. A new determination of this 

 potential is now in progress at the Royal Observatory, Greenwich. Whatever be the 

 result of this calculation, however, there will remain several important features of the 

 phenomenon which require explanation in particular, the seasonal changes. By 

 the elucidation of these difficulties, terrestrial magnetism may throw light on the 

 ionization of the upper atmosphere. The variables at disposal in the theory are, 

 unluckily, too numerous to get very definite knowledge of any one of them from a 

 single source, and therefore it is peculiarly fortunate that there is a kindred but 

 independent set of phenomena, produced by the moon jointly with the sun, which 

 promises very valuably to supplement the knowledge furnished by the solar diurnal 

 variations. It should be specially instructive to compare the seasonal changes of the 

 two sets of phenomena. 



2. The general outlines of this paper may be briefly indicated here. The principal 

 known facts regarding the lunar magnetic variation are first summarized, and it is 

 shown that, so far as they go, they seem most easily explicable in the manner 

 proposed by SCHUSTER for the solar diurnal variations. Nothing in the nature of a 

 proof is yet possible however. Some new facts, deduced by harmonic analysis of 

 existing material for the lunar variation at the separate phases of the moon, are then 

 described, and it is pointed out how they confirm the hypothesis of the variable 

 conductivity of the atmosphere in a very direct way, and provide a powerful means 

 of quantitatively investigating the changes of the conductivity. The details of the 

 calculation of these new harmonic terms in the lunar variation, and the actual tables 

 of results, are collected in Part III. of the paper. In order to discuss the bearing of 

 these observational results on the theory, it is necessary to extend SCHUSTER'S 

 calculation of the effect of an atmospheric oscillation, under the influence of the 

 earth's radial magnetic forces and the variable conductivity of the air, in producing 



* That there is a highly conducting layer in the upper atmosphere is also indicated by the bending of 

 electric waves round the earth. 



t ' Phil. Trans.,' A, vol. 180, p. 467. 



J SCHUSTER, ' Phil. Trans.,' A, vol. 180, p. 467 ; and FRITSCHE, St. Petersburg, 1902. 



