124 
tilde measured towards the east. If ib is the colatitude we 
have, assuming the existence of a potential — 
d , dX dX 
Y, considered as a function of the time, is nearly of the same 
type at places differing widely in latitude, and we may, 
therefore, as a first approximation, put Y equal to the pro- 
duct of two quantities, one depending on the latitude, the 
other on the time only. This seems true approximately, 
but only approximately. Writing therefore — 
Ysimj = U^ 
dt 
where U is a function of ^6, and T a function of the time, 
we get— X = T— 
du 
where no constant is added, as we only consider periodic 
terms. 
The result I wish to draw from this equation, which can 
easily be tested, is this : If our assumptions are all justified, 
X will be a maximum or a minimum as far as the time is 
concerned, whenever T is a maximum or a minimum, that 
is to say, whenever — and therefore also Y vanishes. In 
etc 
other words, the northerly component of horizontal force 
ought to be a maximum and a minimum, whenever the 
westerly component vanishes. 
At Greenwich X has a maximum at seven o’clock in the 
evening, and a minimum at noon ; while Y vanishes a little 
after seven o’cloS^ and between twelve and one in the 
afternoon. 
At Bombay the declination needle seems to pass its mean 
position on the average a little after ten in the morning, and 
about ten in the evening. The horizontal force has its 
maximum a little after eleven in the morning, and the 
minimum at a quarter past nine o’clock in the evening. 
