Terrestrial Magnetism. 165 
It now remained to take a series of observations, with the common as well as the 
counterpoised needle, and to compare their results. The following tables contain the 
results of two such series. The first series of observations was taken at places differing 
in dip: the second series at the same place. The poles of the counterpoised needle 
were not reversed, as such a process would be incompatible with one of the objects of 
the needle—namely, the determination of the variations of terrestrial intensity ; and it 
fortunately happens, that this troublesome operation is, in the present method, wholly 
unnecessary. The use of reversing the poles in the common needle, it is well known, 
is to correct for the moment of the needle itself. If the centre of gravity of the 
needle deviates at all from the centre of motion, in the direction of its length, 
the moment of the needle will increase or diminish its inclination to the horizon, 
according as the deviation is towards the north or south pole; and this error 
can only be corrected by reversing the poles of the needle, so that its moment may 
act in opposite directions in the two cases.* But, in the needle proposed in these 
pages, the centre of gravity of the whole is made intentionally to deviate from the 
axle, and the dip determined from the altered inclinations. In this case, accordingly, 
the moment of the needle, if any, simply increases or diminishes the moments of the 
actual counterpoises ; and, as these are determined a posteriori, the moment of the 
needle itself will of course be included in the determination. 
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* It may be readily shown, that the tangent of the true dip, is the arithmetical mean between the 
tangents of the observed inclinations of the needle, when the same end is a north and south pole. But 
when the difference of the observed inclinations is small, we may, without much error, suppose the same 
relation to hold amongst the angles themselves. 
