lation between the potential and the
distance between the electrodes varies greatly, as we might expect, with
the current passing through the gas.

The connexion between the potential difference and the spark length has
been made the subject of a large number of experiments. The first
measurements were made by Lord Kelvin in 1860 (_Collected Papers on
Electrostatics and Magnetism_, p. 247); subsequent experiments have been
made by Baille (_Ann. de chimie et de physique_, 5, 25, p. 486), Liebig
(_Phil. Mag._ [5], 24, p. 106), Paschen (_Wied. Ann._ 37, p. 79), Peace
(_Proc. Roy. Soc._, 1892, 52, p. 99), Orgler (_Ann. der Phys._ 1, p.
159), Strutt (_Phil. Trans._ 193, p. 377), Bouty (_Comptes rendus_, 131,
pp. 469, 503), Earhart (_Phil. Mag._ [6], 1, p. 147), Carr (_Phil.
Trans._, 1903), Russell (_Phil. Mag._ [5], 64, p. 237), Hobbs (_Phil.
Mag._ [6], 10, p. 617), Kinsley (_Phil. Mag._ [6], 9, 692), Ritter
(_Ann. der Phys._ 14, p. 118). The results of their experiments show
that for sparks considerably longer than the critical spark length, the
relation between the potential difference V and the spark length l may
be expressed when the electrodes are large with great accuracy by the
linear relation V = c + blp, where p is the pressure and c and b are
constants depending on the nature of the gas. When the sparks are long
the term blp is the most important and the sparking potential is
proportional to the spark length. Though there are considerable
discrepancies between the results obtained by different observers, these
indicate that the production of a long spark between large electrodes in
air at atmospheric pressure requires a potential difference of 30,000
volts for each centimetre of spark length. In hydrogen only about half
this potential difference is required, in carbonic acid gas the
potential difference is about the same as in air, while Ritter's
experiments show that in helium only about one-tenth of this potential
difference is required.

In the case when the electric field is not uniform, as for example when
the discharge takes place between spherical electrodes, Russell's
experiments show that the discharge takes place as soon as the maximum
electric force in the field between the electrodes reaches a definite
value, which he found was for air at atmospheric pressure about 38,000
volts per centimetre.

_Very Short Sparks._--Some very interesting experiments on the potential
difference required to produce exc