6 Captain Sabine's experiments to determine the 
condition is not indeed a necessary one, but it is desirable to 
be accomplished, because it shortens the observations, as well 
as the calculation, from whence the dip is deduced ; its ful- 
filment may be ascertained with great precision by placing 
the needle on the agate planes before magnetism is imparted 
to it, and observing whether it returns to a horizontal direc- 
tion, after oscillation in each position of the axis ; if it does 
not, it may be made to do so at this time with no great 
trouble. 
With a needle in which this adjustment can be relied on, 
two observations made in the magnetic meridian are sufficient 
for the determination of the dip, the two faces of the needle 
being successively towards the observer, reversing the po- 
sition of the axis on its supports in such manner that the edge 
of the needle which is uppermost in the one observation be- 
comes lowermost in the other ; the angles which the needle 
makes with the vertical in these two positions being read, the 
mean of the tangents of those angles is the co-tangent of the 
dip. 
But when needles are used in which this adjustment has not 
been made, or where its accuracy cannot be relied on, four 
observations are required ; two being those which are already 
directed; the two others are similar to them, but with the 
poles of the needle reversed ; calling then the first arcs F and 
f, and those with the poles reversed G and g, and taking 
tang F + tan f = A 
tang F — tan f = B 
tang G + tang == C 
tang G — tan g = D 
TTT 13 b B + t) ~ tw * ce t ^ ie co-tangent of the dip. 
