10 
DR. S. CHAPMAN ON THE SOLAR AND LUNAR 
into four groups only (as they were given in the 1902 paper), were treated by the 
method of least squares as before. While the resulting potential functions were not 
greatly different from those first obtained, the residuals for the given 18 stations 
were improved, without much affecting those for the other nine. The chief terms in 
the re-calculated functions are exhibited in Table D, § 10, in a form allowing 
comparison to be made with Schuster’s and the new results of this paper. 
Fritsche’s values, like those here found for the years 1902 and 1905, are much less 
than Schuster’s, for the reason already mentioned. But the agreement is more 
striking than the differences, considering the different material, epochs, and methods 
of analysis used in the various investigations. 
Fritsche treated the vertical force data from the same stations in a precisely 
similar way, and thus deduced from them a potential function which was independent 
of the horizontal force variations. In Table E, p. 26, the re-calculated results of 
his 1913 paper are compared with the corresponding results obtained in this paper. 
The two sets of figures generally agree in sign, but numerically the agreement is 
much less good than for the horizontal force data of Table D. I can only attribute 
the difference to the greater difficulty of obtaining reliable observations of the vertical 
force variations. # This renders it very necessary to use only the most modern and 
reliable data available. 
The calculation of a separate potential function from the vertical force data makes 
possible a more satisfactory estimation of the respectively external and internal parts 
of the magnetic variation field than Schuster’s limited material allowed. The 
method used by Fritsche, and also in this paper, is explained in §§ 8, 9, and only the 
results will be mentioned here. In place of Schuster’s value, 4:1, the ratio of the 
surface potentials of the outer and inner portions of the field was given as 1 '75 : 1 in 
the 1913 paper (in the 1902 paper the discordance was still greater, the stated 
ratio being 1*49 : l). Another method used by Fritsche for estimating the same 
ratio gave the results 1'59 : 1 (1913) or T44 : 1 (1902). He concluded that the 
internal field was too nearly equal to the external field to allow it to be regarded 
merely as an induction product of the latter. It need hardly be stated how much 
the difficulties in the way of an explanation of the phenomenon would be increased 
if such a conclusion were substantiated; two independent mechanisms would then 
have to be co-ordinated and accounted for. 
Fritsche did not discuss the phase relations of the internal and external potentials, 
nor did he consider Schuster’s theory of a non-uniformly conducting earth. In 
view of the new analysis of improved data in this paper, it does not seem necessary 
to complete Fritsche’s discussion in this respect. 
* An error of another kind which has to some extent affected earlier investigations of the present 
nature may be mentioned, viz., that by a mistake in the formulae of reduction the Batavian vertical force 
variations have been recorded at twice their true amount from their commencement in 1880 until the 
discovery of the error in 1913 (‘Batavian Observations,’ 35, 1912, Preface). 
