8 
DR. S. CHAPMAN ON THE SOLAR AND LUNAR 
magnitude of Schuster’s results is in nearly every case greater than those here 
obtained, even for the year of sunspot maximum. This was to be expected in view 
of the exceptional character of the year 1870. 
Having obtained a potential function which would account for the horizontal force 
variations, Schuster compared the observed vertical force variations with those 
calculated from this function on the respective hypotheses that its origin was (a) 
external, (b) internal to the earth. Only from one of the four stations (Lisbon), 
unfortunately, were satisfactory vertical force data available for the year 1870. For 
the other three observatories data relating to later years had to be taken. # 
It appeared that the phase of the observed vertical force variations agreed 
completely with the assumption of an external cause (and was therefore opposite to 
that corresponding to the second hypothesis), but that the observed amplitude was 
only about half the calculated amplitude. This was explained by supposing the 
primary varying magnetic field, above the earth’s surface, to be accompanied by a 
secondary field within the earth due to electric currents induced by the primary field. 
The secondary field would reinforce the horizontal force variations due to the 
primary, and would partly neutralize the vertical force variations. But an accom¬ 
panying phase difference was to be expected between the calculated and observed 
vertical force results, and this appeared not to exist. Certain researches by Lamb,! 
indeed, indicated that if the earth were assumed uniformly conducting, a reduction of 
the amplitude of the vertical force variations by one-half (as in the Lisbon data) 
should be accompanied by a phase change of about 40 degrees. This difficulty was 
surmounted, however, in pursuance of a suggestion by Lamb, by assuming that the 
conductivity of the inner core of the earth exceeds that of the upper layers. In his 
second memoir (p. 169) Schuster roughly estimated the thickness of the outer non¬ 
conducting crust to be about 1000 km. 
The general conclusion as regards the diurnal and semi-diurnal components ol 
the solar diurnal magnetic variation was that the potential of the external field 
agrees in phase with, but is four times the magnitude of, that for the internal field4 
The components of shorter period were hardly at all discussed in either of his 
memoirs. The character of the vertical force data used, and the presence of local 
irregularities in the variations at single stations, naturally suggest that this 
separation of the internal and external fields may be somewhat uncertain. Fritsche’s 
and van Bemmelen’s results are considerably different, and those also of the present 
paper, while confirming Schuster’s main conclusions, differ from his results in some 
important respects. 
* As regards Greenwich and St. Petersburg this was because the temperature corrections to the 
vertical force records were not properly known in 1870. The vertical force magnetograph at Bombay did 
not come into operation till after 1870. 
t Lamb, ‘ Phil. Trans.,’ 1883, p. 536; also the appendix to Schuster’s memoir of 1889. 
\ Cf. p. 170 of the second memoir : this conclusion was not explicitly stated in the first memoir. 
