Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/275

627.] We have already considered the products of the pairs of these quantities in the order in which they stand. Their ratios are in certain cases of scientific importance. Thus

	Symbol.	Electrostatic System.	Electromagnetic System.
${\frac {e}{E}}={}$ capacity of an accumulator	$q$	$[L]$	$\left[{\frac {T^{2}}{L}}\right]$.
${\frac {P}{C}}={}$ coefficient of self-induction of a circuit, or electromagnetic capacity	$L$	$\left[{\frac {T^{2}}{L}}\right]$	$[L]$.
${\frac {\mathfrak {D}}{\mathfrak {E}}}={}$ specific inductive capacity of dielectric	$K$	$[0]$	$\left[{\frac {T^{2}}{L^{2}}}\right]$.
${\frac {\mathfrak {B}}{\mathfrak {H}}}={}$ magnetic inductive capacity	$\mu$	$\left[{\frac {T^{2}}{L^{2}}}\right]$	$[0]$.
${\frac {E}{C}}={}$ resistance of a conductor	$R$	$\left[{\frac {T}{L}}\right]$	${\frac {L}{T}}$.
${\frac {\mathfrak {E}}{\mathfrak {C}}}={}$ specific resistance of a substance	$r$	$[T]$	$\left[{\frac {L^{2}}{T}}\right]$.

628.] If the units of length, mass, and time are the same in the two systems, the number of electrostatic units of electricity contained in one electromagnetic unit is numerically equal to a certain velocity, the absolute value of which does not depend on the magnitude of the fundamental units employed. This velocity is an important physical quantity, which we shall denote by the symbol $v$.

Number of Electrostatic Units in one Electromagnetic Unit.

For $e$, $C$, $\Omega$, ${\mathfrak {D}}$, ${\mathfrak {H}}$, $C$, …… $v$.

For $m$, $p$, $E$, ${\mathfrak {B}}$, ${\mathfrak {E}}$, ${\mathfrak {A}}$, …… ${\frac {1}{v}}$.

For electrostatic capacity, dielectric inductive capacity, and conductivity, $v^{2}$.

For electromagnetic capacity, magnetic inductive capacity, and resistance, ${\frac {1}{v^{2}}}$.

Several methods of determining the velocity $v$ will be given in Arts. 768–780.

In the electrostatic system the specific dielectric inductive capacity of air is assumed equal to unity. This quantity is therefore represented by ${\frac {1}{v^{2}}}$ in the electromagnetic system.