urves that for very short arcs the potential difference increases
continuously with the pressure, but for longer ones there is a
critical pressure at which the potential difference is a minimum, and
that this critical pressure seems to increase with the length of arc.
The nature of the gas also affects the potential difference. The
magnitude of this effect may be gathered from the following values
given by Arons (_Ann. der Phys._ 1, p. 700) for the potential
difference required to produce an arc 1.5 mm. long, carrying a current
of 4.5 amperes, between terminals of different metals in air and pure
nitrogen.

+-----------+------+-----------+
| Terminal. | Air. | Nitrogen. |
+-----------+------+-----------+
| Ag | 21 | ? |
| Zn | 23 | 21 |
| Cd | 25 | 21 |
| Cu | 27 | 30 |
| Fe | 29 | 20 |
| Pt | 36 | 30 |
| Al | 39 | 27 |
| Pb | .. | 18 |
| Mg | .. | 22 |
+-----------+------+-----------+

Thus, with the discharge for an arc of given length and current, the
nature of the terminals is the most important factor in determining
the potential difference. The effects produced by the pressure and
nature of the surrounding gas, although quite appreciable, are not of
so much importance, while in the spark discharge the nature of the
terminals is of no importance, everything depending upon the nature
and pressure of the gas.

The potential gradient in the arc is very far from being uniform. With
carbon terminals Luggin (_Wien. Ber._ 98, p. 1192) found that, with a
current of 15 amperes, there was a fall of potential of 33.7 close to
the anode, and one 8.7 close to the cathode, so that the curve
representing the distribution of potential between the terminals would
be somewhat like that shown in fig. 21. We have seen that a somewhat
analogous distribution of potential holds in the case of conduction
through flames, though in that case the greatest drop of potential is
in general at the cathode and not at the anode. The difference between
the changes of potential at the anode and cathode is not so large with
Fe and Cu terminals as with carbon ones; with mercury terminals, Arons
(_Wied. Ann._ 58, p. 73) found the anode fall to be 7.4 volts, the
cathode fall 5.4 volts.

The ca