Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/411

 

The condition of no final current is, as in the ordinary form of Wheatstone's Bridge,

$QR=SP$.

(5)

The condition of no current at making and breaking the battery connexion is

${\frac {L}{Q}}=RC$.

(6)

Here ${\frac {L}{Q}}$ and $RC$ are the time-constants of the members $Q$ and $R$ respectively, and if, by varying $Q$ or $R$, we can adjust the members of Wheatstone's Bridge till the galvanometer indicates no current, either at making and breaking the circuit, or when the current is steady, then we know that the time-constant of the coil is equal to that of the condenser.

The coefficient of self-induction, $L$, can be determined in electromagnetic measure from a comparison with the coefficient of mutual induction of two circuits, whose geometrical data are known (Art. 756). It is a quantity of the dimensions of a line.

The capacity of the condenser can be determined in electrostatic measure by comparison with a condenser whose geometrical data are known (Art. 229). This quantity is also a length, $c$. The electromagnetic measure of the capacity is

$C={\frac {c}{\nu ^{2}}}$.

(7)

Substituting this value in equation (8), we obtain for the value of $\nu ^{2}$

$\nu ^{2}={\frac {c}{L}}QR$,

(8)

where $c$ is the capacity of the condenser in electrostatic measure, $L$ the coefficient of self-induction of the coil in electromagnetic measure, and $Q$ and $R$ the resistances in electromagnetic measure. The value of $\nu$, as determined by this method, depends on the determination of the unit of resistance, as in the second method, Arts. 772, 773.

 

V. Combination of the Electrostatic Capacity of a Condenser with the Electromagnetic Capacity of Self-induction of a Coil.

779.] Let $C$ be the capacity of the condenser, the surfaces of which are connected by a wire of resistance $R$. In this wire let the coils $L$ and $L^{\prime }$ be inserted, and let $L$ denote the sum of their capacities of self-induction. The coil $L^{\prime }$ is hung by a bifilar suspension, and consists of two coils in vertical planes, between which