42 
mum of the whole variation, so that it became a matter of 
no importance which was taken. If, however, Mr. Chambers 
wishes to test the formulse by means of the diurnal 
period as distinguished from the semi-diurnal period, he 
ought also to have chosen the origin of the time, so as 
best to suit the observations on declination. Had he done 
so, he would have found that the greatest discrepancy in the 
time at which the maximum of vertical force takes place 
amounts to about two hours, and a few words are necessary 
why I did not consider that such a discrepancy seriously 
affected my argument. 
No one who has realised the meaning of the two first 
equations (3) can doubt that the expression for the potential, 
from which they are derived, constitutes an important term 
in the general expansion of that potential. They give a 
periodic variation, which contains all the characteristic facts 
of observation. The first equation gives a change in declina- 
tion gradually increasing in amplitude from the equator 
towards both sides, the change being such that, whenever the 
needle deviates towards the east in the northern hemisphere, it 
deviates towards the west in the southern hemisphere, and 
vice, versa. The second equation gives a horizontal force 
variation, diminishing from the equator to a latitude of 45°, 
and then again increasing, the phase being the same for the 
same latitude, north and south of the equator. 
But if there is a term — 
V = “ (%sin2icoswsin(i( + \) (4) 
in the full expansion for the potential, the corresponding term 
for vertical force must be, if the cause is inside the earth — 
sin2^^sm(^ + X) (5) 
and if outside — 
3 
- 2sin22isin(^ + X) (6) 
According to Mr. Chambers, the phase of the expression (5) 
