36 
DR. S. CHAPMAN ON THE SOLAR AND LUNAR 
still lower values, both for the solar and lunar semi-diurnal variations. Hitherto 
the evidence afforded, by the third and fourth harmonics has never been examined. 
There seems now no reason to doubt that the internal field is merelv an induction 
* 
product of the external field. 
If the latter be so, the mechanism by means of which the internal solar variation 
field is produced must also be that responsible for the internal lunar variation field, 
and the relation between the external and internal fields will be very similar in the 
two cases. Table J does, indeed, show results very similar, in general, to those of 
Table I, especially when the small magnitude and accidental error of the determined 
lunar variation are considered. The mean amplitude ratio of the external and 
internal fields in the lunar case is 2‘3, while the mean of the phase differences (all 
of which, save one, have the negative sign) is —21 degrees. The results for the 
mean of the corresponding solar variation fields are 2'4 and —19 degrees. There 
seems, therefore, no reason to question the similarity of the two phenomena in this 
respect, although a more precise discussion of the point, with more adequate data, 
would be of value. 
As might be anticipated, the results of Tables I and J show little dependence on 
season or on solar activity. The only notable difference between 1902 and 1905 is 
found in connection with the diurnal “annual” harmonic .Q 2 X , for which the mean 
phase differences are —4 degrees (1902) and —21 degrees (1905). The solstitial and 
equinoctial results separately indicate these divergent differences, and thus tend to 
* 
establish the reality of the divergence. It remains to be seen whether other pairs of 
years will manifest the same result, but for the present no theoretical explanation of 
it will be attempted. Only the mean of the two values of e 2 x — i 2 x will be used, but 
the uncertainty of this mean should be kept in mind during the discussion. 
§ 16. The Hypothesis of a Uniformly Conducting Earth. 
In § 2 a brief account has already been given of the theory proposed by Schuster 
to explain the results of his separation of the external and internal solar diurnal 
magnetic variation fields. At that time the problem was to account for the induction 
of an internal field of one-quarter the magnitude of the primary without the 
production of a phase difference. It now appears that a phase difference does exist, 
and it may be expected that the difficulty of explanation will be lessened. The sign 
of the difference agrees with that predicted by the theory of induction in a uniformly 
conducting sphere, as Prof. Lamb’s researches* show (and this was kindly confirmed 
by him on enquiry). The hypothesis of induction being so far substantiated, it 
remains to consider the actual numerical relations between the external and 
internal fields; the theory can be regarded as completely satisfactory only when the 
same amount and distribution of conducting matter in the earth will suffice in 
relation to all the harmonics of the many periods and degrees concerned. 
* Of. the appendix to Schuster’s first memoir, p. 513, and also ‘ Phil. Trans.,’ 1883, p. 526, 
