Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/128

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96
MAGNETIC MEASUREMENTS.
[452.

The reading of the torsion circle should now be adjusted, so that the coefficient of may be as nearly as possible zero. For this purpose we must determine , the value of when there is no torsion. This may be done by placing a non-magnetic bar of the same weight as the magnet in the stirrup, and determining when there is equilibrium. Since is small, great accuracy is required. Another method is to use a torsion bar of the same weight as the magnet, containing within it a very small magnet whose magnetic moment is of that of the principal magnet. Since remains the same, will become , and if and are the values of as found by the torsion bar,

(12)

Subtracting this equation from (11),

(13)

Having found the value of in this way, , the reading of

the torsion circle, should he altered till

(14)

as nearly as possible in the ordinary position of the apparatus.

Then, since is a very small numerical quantity, and since its coefficient is very small, the value of the second term in the expression for will not vary much for small errors in the values of and , which are the quantities whose values are least accurately known.

The value of , the magnetic declination, may be found in this way with considerable accuracy, provided it remains constant during the experiments, so that we may assume .

When great accuracy is required it is necessary to take account ot the variations of during the experiment. For this purpose observations of another suspended magnet should be made at the some instants that the different values of are observed, and if are the observed azimuths of the second magnet corresponding to and , and if and are the corresponding values of , then

(15)

Hence, to find the value of we must add to (11) a correction

(15)

The declination at the time of the first observation is therefore

(16)