31 
on, that he still does the same tiling"^ after having expressly 
put sin(0-- 30° + A) in the place previously occupied by T. 
We now come to the writer’s principal undertaking— the 
proof that the seat of the magnetic variations lies outside 
the earth. To adapt our formulse to his convention that 
the time (t) should be reckoned from two o’clock in the after- 
noon on the initial meridian we must take p = -30^ when 
(^-pX) = (0- 30° + A). He first assumes that, with an 
ax’bitrary unit, Y = cosucos(^ -f X) ; and then deduces 
X = cos2usin(^-hX), 
and the surface potential V = -asinucosxtsin(i^-j-X). 
This gives for the vertical force inequality — ■ 
Z = - ^ = sm2x^sin(t + X) (10) 
dr 
Z = - ^ = - |sin2wsin(^ + X) (11) 
according as the region of origin of the forces is wholly 
outside or wholly inside the earth. 
In comparing the deduced expression for X with observa- 
tions, the writer says, 'Hf our equation is approximately 
right, the northerly force ought to be a maximum in the 
morning, a minimum in the afternoon in the equatorial 
regions, where cos2u is negative ; while in latitudes above 
45° the minimum ought to take place in the morning. This 
is exactly what happens, with the exception that the change 
seems to take place in latitudes smaller than 45°. At 
Bombay the maximum of horizontal force takes place 
at 11 a.m. At Greenwich the minimum takes place a 
little after that time. At Lisbon (u = 51°) the minimum 
lies, as at Greenwich, in the morning, but the range is con- 
siderably reduced;” and he concludes, without any further 
evidence, that the equation represents surprisingly well the 
general character of the horizontal force variation, both in 
Pages 125 to 127 of the paper. 
