12 
DR. S. CHAPMAN ON THE SOLAR AND LUNAR 
by Walker agree in order of magnitude with those tabulated, although his value for 
C 3 2 is rather small. Since his data refer to the mean of a year, and are drawn almost 
entirely from the Northern hemispheres, the unsymmetrical terms in his analysis are 
not comparable with any results of this paper. 
With regard to the vertical force data, Walker showed that the 24-hour terms in 
the horizontal force potential would fit the vertical force observations if it was 
assumed that the internal and external fields agree in phase, and that their 
amplitude ratio, in the case of the second degree harmonics, is that found by 
Schuster, viz., 4:1; the internal contribution to the harmonic of the first degree was 
taken to be nil. The 12-hour component was examined in more detail, and it was 
estimated that the internal contribution to the harmonics of degree three was about 
one-quarter the external, and that a phase difference between the two would improve 
the agreement with the vertical force data; as before, the minor harmonic (in this 
case Qi 1 ) was assumed to be entirely external. The phase differences alluded to 
amounted to 35 degrees in the case of Q 3 2 , and 54 degrees in the case of Q 3 3 , the 
internal field being in advance of the external. Fritsche’s data indicate a phase 
difference of smaller amount in the contrary sense. The theoretical significance of 
these differences was not considered, perhaps because the phase difference seemed to 
be absent in some cases and present in others. The data of the present paper 
indicate that in all the important, well-determined harmonics, both in the solar and 
lunar diurnal variations, the phase of the internal field is in advance of the external 
phase by amounts of the order of 20 degrees. In §§ 15-17 it is shown how these 
phase differences and the amplitude-ratios can be accounted for by a modified form 
of Schuster’s hypothesis of a non-uniformly conducting earth. 
§ 5. Van Bemmelen’s Study of the Lunar and Solar Semi-diurnal Magnetic 
Variations (1912). 
While the lunar diurnal magnetic variation has often been studied, and from 
many points of view, van Bemmelen was the first to investigate it as a world-wide 
phenomenon after the manner of Schuster and Fritsche. His data consisted 
of the Fourier coefficients a 2) h * for the lunar semi-diurnal variations of the 
geographical components of magnetic force, taken separately over the summer and 
winter half-years, from fifteen observatories. The latitude range of these was 60° N. 
to 43° S. The material was somewhat heterogeneous, relating to different epochs, 
and calculated in different ways from unequal periods of observation; but a careful 
* The first harmonic coefficients «i, bi were also calculated and tabulated, but it was stated that they 
were irregular, and probably not a real part of the phenomenon. This is the case when they are 
calculated directly from the mean of a month, as for the semi-diurnal variation. A later paper (‘ Phil. 
Trans.,’ A, vol. 213, p. 279, 1913) showed, however, that a real 24-hour component exists, which can be 
calculated only by separately considering the days of different lunar phase. 
