Terrestrial Magnetism. 163 
Let »/ and »” be the moments of the two fixed counterpoises, and @ and 6" the 
corresponding inclinations of the needle to the horizon: then, substituting in 
equation (1), 
nw =o (sin —cos o tan), pw = o (sin 6—cos 6 tan @”). 
We have thus two equations containing % and 8, from which these quantities may be 
obtained by elimination. To effect this, let the former be divided by the latter, and 
we find 
me tan 6—tan 4 ! a pw tan = tan 6’ : 
nw” tand—tan 6 wap 
y 
And denoting the constant factors ar and gee by v' and v’, 
we have finally, 
tan =v’ tan 0” —v” tan 0’. (3) 
If we eliminate 8 between this equation and either of the two equations given above, ° 
we readily obtain an expression for @ in terms of /, 1’, and @, 0”; but as the result- 
ing expression is somewhat complicated, it will be much simpler in practice to obtain 
the dip, in the first instance, from the equation last deduced, and to substitute its 
value in the formula 
pcos 0 
Ke o sin (0 Liiy 
The quantity o, in this formula, depending on the law of distribution of the magnetic 
fluid in the needle employed, is unknown ; and, consequently, the absolute intensity 
of the terrestrial magnetic force cannot be determined without some other artifices. 
In general, however, the ratio of this force at different parts of the earth’s surface is 
alone required ; and for this purpose the force at some given place (usually the mag- 
netic equator) is taken as unity, and the force at other places determined by compa- 
rison. Let ¢, be the force at the given place, and 6, @ the corresponding values of 
8 0, then 
_ cos 8, 
‘~gsin(8,—0) ” 
and dividing 
i ere vee 
¢, sin (8—6) cos 0,” (4) 
