VARIATION OF TERRESTRIAL MAGNETISM. 
497 
Table XXL—Comparison of the magnetic force due to a varying potential repre¬ 
sented by a solid harmonic of degree 4 with the corresponding forces due to 
currents induced inside the Earth. 
s. 
c. 
Eatio of normal 
forces due to 
secondary and primary 
variation. 
c'. 
Ratio of tangential 
forces due to 
secondary and primary 
variation. 
a. 
Difference of phase. 
Corresponding value of p. 
I 
- -0101 
4- •0081 
8°9 01 
3-70 X 10^1 X m. 
10 
•0992 
•0794 
80 21 
3-70 X 1013 
100 
•5149 
•4119 
37 50 
3-70 X 1012 
Tables XX. and XXL cannot, however, be used to compare our calculated and 
observed results, but form only an intermediate step. 
We observe on the Earth the resultant of the outside and inside effect, and we 
have calculated the vertical force on the assumption that the whole horizontal force 
is due to outside effect. 
In hg. 11 , let OH^ represent that part of the horizontal force which is due to the 
Fig. 11. 
outside effect, and OHg the corresponding force in phase and amplitude which is due 
to the induced effect. The observed horizontal force will be the resultant OK. Let 
OV^ be the magnitude of the vertical force due to the outside currents, and OV 3 the 
vertical force in phase and amplitude due to the induced effect. The observed 
vertical force will be ON. If we calculate the vertical force on the assumption that 
the resultant OK is due entirely to the outside, we should obtain a force OK, such 
that OK : OK ; : OV^ : OHj. Our calculated value of vertical force will be OK, and 
our observed value ON. We require the ratio of lengths of these lines and the angle 
between them. 
MDCCCLXXXIX.-A. -3 S 
