Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/140

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magnetic measurements.

[459.

To find the value of $L$ we have the equations of moments

Qh=W.AB=W'.A'B'

,

(2)

and the geometrical equation

(AB+A'B')PP'=ab\sin(\alpha -\beta )

,

(3)

whence we obtain,

L=Q.PP'={\frac {ab}{h}}{\frac {WW'}{W+W'}}\sin(\alpha -\beta )

(4)


Fig. 18	Fig. 17.

If $m$ is the mass of the suspended apparatus, and $g$ the intensity of gravity,

W+W'=mg

.

(5)

If we also write

W-W'=nmg

,

(6)

we find

L={\frac {1}{4}}(1-n^{2})mg-{\frac {ab}{h}}-\sin(\alpha -\beta )

.

(7)

The value of $L$ is therefore a maximum with respect to $n$ when $n$