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bay the maximum of horizontal force takes place at eleven 
o’clock 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.* 
It is surprising that the above equation represents so well 
the general type of character of the horizontal force variation, 
both in the northern and southern hemispheres. Conside- 
rable importance is to be attached to the fact that the maxima 
and minima of horizontal force agree in sign with the observed 
phenomena, for as regards magnitude all these variations 
might equally well be due to currents crossing the surface of 
earth, but the sign of X would have to be reversed, so 
that the minima and maxima would be inverted. This is 
another argument in favour of the supposition that no 
appreciable part of the diurnal variation is due to currents 
crossing the surface of the earth. 
Now as regards the vertical force and the localisation of 
the currents, we must, in the first place, obtain an expression 
for the potential V. We may take 
either 
dY 
adu asinii(iX 
where a is the radius of the earth, and find 
V = - asinz« cosw sin(^ + X). 
This expression for V happens to be a tesseral harmonic, 
and the potential if it exists must therefore be 
either 
or 
iyi2 
^ V = — sin'M cosw sin(^ + X) 
a ' ' 
- V’ = com sin(^ + X). 
For the vertical force we obtain in the first case, putting 
r — a^ 
*** 1 And since writing the above that in the winter months Lisbon agrees in phas 
with Bombay j so that it is very likely near the line at Avhich the change takes place. 
