Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/413

779.] Finding the values of A and B by substitution in the equation (3), we obtain Rh

The moment of the force with which the magnet acts on the coil $$L'$$, in which the current $$\dot{x}$$ is flowing, is Rh

Integrating this expression with respect to $$t$$, and dividing by $$t$$, we find, for the mean value of $$\Theta$$, Rh

If the coil has a considerable moment of inertia, its forced vibrations will be very small, and its mean deflexion will be proportional to $$\overline{\Theta}$$.

Let $$D_1, D_2, D_3$$ be the observed deflexions corresponding to angular velocities $$n_1, n_2, n_3$$ of the magnet, then in general Rh

where $$P$$ is a constant.

Eliminating $$P$$ and $$R$$ from three equations of this form, we find Rh

If $$n_2$$ is such that $$CLn_2^2=1$$, the value of $$\frac{n}{D}$$ will be a minimum for this value of n. The other values of n should be taken, one greater, and the other less, than $$n_2$$.

The value of $$CL$$, determined from this equation, is of the dimensions of the square of a time. Let us call it $$\tau^2$$.

If $$C_s$$ be the electrostatic measure of the capacity of the condenser, and $$L_m$$ the electromagnetic measure of the self-induction of the coil, both $$C_s$$ and $$L_m$$ are lines, and the product Rh and Rh

where $$\tau^2$$ is the value of $$C^2L^2$$, determined by this experiment. The experiment here suggested as a method of determining $$v$$ is of the same nature as one described by Sir W. R. Grove, Phil. Mag.,