422 
MR W. CAUR ON THE LAWS C40VEENIN0 
normal state, and that therefore no discharge could occur until the correct potential 
difference was reached. 
After discharge did occur the gas was allowed to stand for a considerable time 
before the operation was repeated. 
On account of the ‘'delay” in the discharge, already referred to, special care was 
taken at the critical pressure to see that no voltage applied to the electrodes was 
replaced by a higher one, until a sufficient time had elapsed to make sure that 
discharge would not occur with the lower voltage. 
VIII. Connection between Spark Lengths and Simrk Potentials. 
In the preceding experiments the spark potentials and corresjjonding pressures have 
been found for spark lengths I'anging from 1 to 10 millims. It is evident from Paschex's 
laAv, which has been shown to govern these discharges, that the different curves in 
tigs. 2, 4 or 6 are interdependent, and that if one were given in each figure all the 
others could be deduced. It is clear, too, providing Paschex’s law applies, that curves 
can be deduced for spark lengths not included within these limits. This has been 
done in fig. 8, where curves corresponding to a number of spark lengths, in air, 
ranging from 1 millim. down to 5 micra^^ have been plotted. 
The numbers corresponding to these curves were calculated by Paschex’s law from 
the experimental results obtained with a S23ark length of 1 milhm. The values for 
spark lengths shorter than 5 micra have not been calculated, as there is evidence to 
show that Paschen s law does not ajiply beyond this point. It can be seen that as 
the spark length is gradually decreased a length will be reached finally when the gas 
between the electrodes will consist of but two surface layers. It will then be subject 
to special molecular forces and, in all probability, a departure from the laws governing 
electric discharges in a gas under normal conditions will appear when this limiting 
spark length is reached. 
I his point has been well brought out by EarhartI' in a paper on spark potentials 
for very short distances. Pie has shown, for a series of pressures, that a direct 
proportionality exists between s])ark potential and spark length, down to a spark 
length of about 5 micra. For shorter lengths than this he has shown that, while 
a law of proportionality still holds between spark potentials and spark lengths, the 
spark 23otentials diminish more rajjidly for the same change in the spark length than 
they do in the range of longer distances. 
It is true this critical sj^ark length of 5 micra is of a higher order than most of the 
values found by a number of experimenters for the distance over which molecular 
foices act. I he value of this distance given by Quincke,| deduced from the results 
* 1 micron = -001 millim.; PIarhart, ‘Phil. Mag.,’January, 1901. 
t Earhart, ‘Phil. Mag.,’January, 1901. 
t Quincke, ‘Pogg. Ann.,’ 1809, vol, 137, p. 402. 
