DISRUPTIVE DISCHARGE OF ELECTRICITY. 639 
a test of the accuracy of the experiments. The mean equation, 
V = 66'940,/ {s’ + :20503s| , 
is drawn on fig. 1, so that it may be compared with the equation which passes 
through the points of observation. Assuming, then, that the above mean 
equation is true when the discs are of infinite extent, the equation for the 
electrostatic force is 
R= 66-940 {1+ -20503'} > 
where R denotes the electrostatic force, and s the length of the spark. 
The values of R for several values of s are given in Table VIII, and the 
curve is drawn in fig. 2. Plotted along with it are several values for R, pub- 
lished by Sir WittrAm Tuomson, p. 252 of ‘‘ Papers.” His measurements do 
not extend beyond 1°5 centimetre ; the parts in common agree very well. From 
his observations, he concluded that the limiting value of R was something not 
much less than 130; the above equation gives 66°94. 
According to the mathematical theory of electricity, if the conductors are 
in the form of two infinite parallel plates, then R is constant. The above 
function would give R constant were it not for the term involving s; in the 
above example 889°52s. It is probable, then, that there is a physical condition 
which the mathematical theorem in question assumes implicitly, but which is 
not fulfilled in the conditions of the experiment. Professor CLERK MaxweE.Lu 
: Says with reference to this (p. 56 of “ Electricity and Magnetism ”)— 
“Tt is difficult to explain why a thin stratum of air should require a greater 
_ force to produce a disruptive discharge across it than a thicker stratum. Is it 
possible that the air very near to the surface of dense bodies is condensed, so 
as to become a better insulator? or does the potential of an electrified con- 
ductor differ from that of the air in contact with it by a quantity having a 
maximum value just before discharge, so that the observed difference of poten- 
tial of the conductors is in every case greater than the difference of potentials 
on the two sides of the stratum of air by a constant quantity, equivalent to the 
_ addition of about ‘005 of an inch to the thickness of the stratum ?” 
Several of the series of observations in the succeeding tables were made to 
‘decide between these two hypotheses ; the results fully establish, in my judg- 
ment, the former. The quantity (005 inch, that is, ‘(0127 centimetre) is con- 
siderably less than the quantity above denoted by a. But if the two curves for 
R, fig. 2, are similar, the equation for Sir W1Lt1Am THomson’s curve is 
‘073718 
an equation satisfying well the given values, and according to it the value of a is 
, 037 centimetre. 
The observations recorded in Table IX. were made with discs of much 
