VARIATION OF TERRESTRIAL MAGNETISM. 
489 
Table XV.—Comparison between the observed and calculated coefficients a^, h^, a^, 
on the assumption that the disturbing force is outside the Earth. 
a-i- 
h- 
a^. 
b- 
Calculated. 
Observed. 
Calculated. 
Observed. 
Calculated. 
Observed. 
Calculated. 
Observed. 
Bombay. 
+ 66 
- 10 
+ 22 
+ 35 
-b 18 
+ 3 
+ 
24 
+ 
16 
Lisbon. 
- 134 
- 81 
+ 125 
+ 12 
- 8 
- 21 
+ 
18 
+ 
11 
Greenwich. 
- 70 
- 24 
-b 38 
+ 3 
- 25 
- 8 
33 
+ 
3 
St. Petersburg.... 
- 7 
- 12 
+ 16 
- 8 
- 20 
- 18 
I 
+ 
27 
— 
1 
Confining ourselves in the first place to the first four coefficients, we find that out 
of twenty coefficients eighteen have the wrong sign on the hypothesis of an internal 
cause, while only two have the wrong sign on the hypothesis of an external cause, 
and those two belong to St. Petersburg, to which station, as was pointed out, we cannot 
attach much value. If instead of the numbers given for 1870 we take the numbers 
given at the same station for 1878, the agreement becomes better, even for St. 
Petersburg. The coefficients a^, 63 , a^, are of course more uncertain ; but even 
here the evidence is strongly in favour of the external cause. Out of twenty 
coefficients seventeen agree in sign with that hypothesis. 
A better comparison can perhaps be obtained in a different way : the two terms 
can be written 
cos nt + h sin nt 
cos n{t — t,), 
where r„ is the amplitude of the oscillation, and C the time at which the maximum 
elongations take place. 
Tables XVI. and XVII. contain the results for t„, and from these tables I think it 
will clearly appear that the phase of the vertical force completely agrees with tlie 
assumption of an external cause and completely disagrees with the assumption of an 
internal cause. 
For Lisbon, our principal station of comparison, the phase in Table XVI. agrees 
for both the diurnal and semi-diurnal variation within four minutes of time. For 
Bombay the diurnal variation agrees within three minutes, and the semi-diurnal 
variation within 36 minutes. For Greenwich, the semi-diurnal variation, which we 
have seen differs little from year to year, agrees closely, while the diurnal variation 
shows a greater difference. In all these cases the phases, as calculated in Table XV., 
are in as great a disagreement as possible. St. Petersburg gives less decisive results, 
but they still go in the same direction, especially if we take the observations of 1878 
to represent the type of vertical variation. 
MDCCCLXXXIX.- 3 R 
