38 
DR. S. CHAPMAN ON THE SOLAR AND LUNAR 
A brief inspection of Tables I and K suffices to show that no single value of p can 
be found for which the calculated and observed values of f and a are in agreement. 
Indeed, even if we leave out of account the constancy of p for the different harmonics, 
no calculated values of f and a. are to be found in Table Iv which agree with those 
which are deduced from observation. Thus, considering only the mean results for the 
“ annual” harmonics Q n n+1 , we may notice the following comparative figures :— 
Table L.—Illustrating the Failure of the Hypothesis of a Uniformly Conducting 
Earth. 
Harmonic. 
Theoretical a 
(corresponding to 
observed /). 
Observed a. 
Theoretical f 
(corresponding to 
observed a). 
Observed /. 
; Qff 
0 
37 
13 
1-9 
2-8 
i Qs 3 
30 
18 
1-8 
2 * 2 
Qd 
39 
21 
1-8 
2-5 
Q.5 4 
13 
23 
1-8 
2-7 
These figures indicate clearly that the observed relations between the external and 
internal fields could not arise from a uniformly conducting earth whatever its 
conductivity. The observed phase differences are smaller than the amplitude ratios 
would suggest on this assumption. The discrepancy is in the same sense as in 
Schuster’s paper, where no observed phase difference was found; but as his 
determination of the amplitude ratio was also larger than those of this paper, his 
data indicated a more outstanding failure of the hypothesis than do our present 
results. 
§17. The Hypothesis of a Non-uniformly Conducting Earth. 
The simplest form of non-uniformly conducting earth which we can consider is 
that discussed by Schuster in his first paper, viz., a sphere containing an inner 
core of one degree of conductivity and an outer concentric layer of another degree. 
There is observational evidence for the belief that the outer crust of the earth, down 
to a depth which is considerable in comparison with that of the oceans and of the 
surface inequalities, possesses high electrical resistance. For this reason, and because of 
the mathematical simplicity of the hypothesis, we shall suppose that the outer layer of 
the earth is an absolute non-conductor. If It c is the radius of the inner core, and p its 
resistivity, the theory referred to in § 16 will, as before, enable us to calculate 
the amplitude ratio f and phase difference a between the potentials of the 
primary external, and induced internal, fields, at the surface of the inner core 
(B = B c ). Corresponding to a harmonic of degree m, however, the earth-surface 
potential of the primary external field will at the surface of the inner core be reduced 
