108 
MR. C. T. R. WILSON: INVESTIGATIONS ON LIGHTNING DISCHARGES 
The value of T = F 
, where F is the instantaneous change recorded and clF/clt 
the initial rate of recovery immediately after the discharge, has been deduced from 
the recovery curves in the case of 34 discharges. We may regard T as the time 
which would have been required to re-charge the cloud to the sparking limit had 
there been no neutralising process due to the action of the electric field of the cloud. 
The values of T vary between 1‘5 seconds and 30 seconds, the mean of 64 measure¬ 
ments giving 6'9 seconds; in more than half the cases examined T lies between 4 and 
10 seconds. These times are generally only a small fraction of the actual intervals 
between the flashes: on June 17, however, in a record (Plate 3, fig. 5) showing more 
than 100 flashes in 10 minutes—-so that the average interval between the flashes was 
less than 6 seconds—the average value of T exceeded half this interval. 
Some of the recovery curves, as, for example, that of June 12, shown in Plate 4, 
fig. 11, approximate very closely to the exponential form, so that the charge which 
has been regenerated when a time t has elapsed after the discharge may be represented 
by Q = Q 0 (l— e~ H ). Such a curve suggests that the charge of the thunder-cloud is 
being regenerated at a constant rate, and that it is at the same time being dissipated 
at a rate which is at any moment proportional to the charge. It might also however 
be interpreted as representing the regeneration of the charge by a constant E.M.F. 
in the cloud, the current through the cloud being proportional to the difference 
between this E.M.F. and the opposing potential difference produced by the charges 
separated ; there would be no current when the charges reached a steady value. If 
dissipation of the accumulated charges is taken into account the recovery curve still 
remains of the same type ; if the dissipation is large, or, in other words, if the 
internal resistance of the thunder-cloud, regarded as a generator of constant E.M.F., 
is large compared with that of the external circuit, the current through the cloud is 
constant, and we have again the case first considered. 
The rate of regeneration of charge per second, in other words the vertical current 
through the cloud, immediately after a discharge varies between -§ and ^ of the 
charge removed by the flash, the mean being about If we assume a discharge to 
convey a quantity of the order of 20 coulombs, the mean current through the cloud, 
immediately after a discharge, is of the order of 3 amperes. 
It is not at all impossible that this is also the order of magnitude of the vertical 
current through a thunder-cloud at other times than immediately after a lightning 
discharge, and even when an approximately steady condition of the field has been 
reached. Consider, for example, the charge in the head of a thunder-cloud which 
reaches to a great height. The conductivity of the atmosphere has been found by 
Gerdien and by Wiegand # to increase rapidly with the height, the former having 
found at 6 km. a conductivity more than 20 times as great, and the latter at 
8865 metres a conductivity about 40 times as great as the normal conductivity near 
* Wiegand, ‘ Deutsch. Physik. Gesellschaft,’ February 29, 1914. 
