+------+---------------------------------------------+ | Gas. | Electrode. | +------+---+---+---+---+---+---+---+---+---+-----+---+ | | Pt| Hg| Ag| Cu| Fe| Zn| Al| Mg| Na| Na-K| K | +------+---+---+---+---+---+---+---+---+---+-----+---+ |O2 |369| ..| ..| ..| ..| ..| ..| ..| ..| .. | ..| |H2 |300| ..|295|280|230|213|190|168|185|169 |172| |N2 |232|226| ..| ..| ..| ..| ..|207|178|125 |170| |He |226| ..| ..| ..| ..| ..| ..| ..| 80| 78.5| 69| |Argon |167| ..| ..| ..| ..| ..|100| ..| ..| .. | ..| +------+---+---+---+---+---+---+---+---+---+-----+---+ The dependence of the minimum potential required to produce a spark upon the metal of which the cathode is made has not been clearly established, some observers being unable to detect any difference between the potential required to spark between electrodes of aluminium and those of brass, while others thought they had detected such a difference. It is only with sparks not much longer than the critical spark length that we could hope to detect this difference. When the current through the gas exceeds a certain critical value depending among other things on the size of the cathode, the cathode fall of potential increases rapidly and at the same time the thickness of the dark spaces diminishes. We may regard the part of the discharge between the cathode and the negative glow as a discharge taking place under minimum potential difference through a distance equal to the critical spark length. An inspection of fig. 16 will show that we cannot regard the electric field as constant even for this small distance; it thus becomes a matter of interest to know what would be the effect on the minimum potential difference required to produce a spark if there were sufficient ions present to produce variations in the electric field analogous to those represented in fig. 16. If the electric force at a distance x from the cathode were proportional to [epsilon]^-px we should have a state of things much resembling the distribution of electric force near the cathode. If we apply to this distribution the methods used above for the case when the force was uniform, we shall find that the minimum potential is less and the critical spark length greater than when the electric force is uniform.