ANI) ON THE ELECTRIC FIELD OF THUNDERSTORMS. 
99 
value and will continue to do so as the track lengthens, so that the discharge may 
finally extend far beyond the boundary of the region in which the critical electric 
force was originally exceeded. Consider a stratiform cloud in which vertical separation 
of positive and negative electricity is taking place so that opposite charges are 
accumulating in the upper and lower portions of the cloud. Let us suppose that 
these charges remain approximately equal. There will be a vertical electric force 
within the cloud reaching a maximum in the central neutral zone of the cloud ; the 
vertical electric force at the ground will be small and the conditions for discharge 
will he first reached within the cloud. Discharge will occur when the maximum 
vertical electric force within the cloud reaches its critical value; this amounts 
to about 30,000 volts per centimetre (= 100 electrostatic units) at a pressure of one 
atmosphere and is proportional to the pressure. 
It is perhaps doubtful whether the vertical potential gradient within a cloud has 
necessarily to reach the above value of 3,000,000 volts per metre, in order that a 
discharge may begin, since an electric force amounting to one-third of this would be 
sufficient to bring the maximum electric force at the surface of a suspended drop, 
assumed spherical, to the above value. It must however be remembered that the 
critical value of the electric force at a curved surface of a conductor increases rapidly 
with the curvature and that only drops of the largest size will have any marked 
effect in assisting discharge. * 
The discharge may extend considerably beyond the limits of the zone in which the 
vertical electric force originally reached the critical value. It is possible that it might 
extend even beyond the upper and lower boundaries of the cloud, for the ends of a 
linear vertical discharge would, as it lengthened, be continually penetrating into 
regions of a greater potential difference until they reached the limits of the charged 
portions of the cloud, so that the density of electrification and maximum electric 
force at the ends of the conducting track, and the consequent tendency to further 
lengthening of the discharge, would be increasing up to this point. 
The end of an initial discharge which has penetrated into a region where there is 
little electric force to guide it will tend to branch or to expand into a brush. The 
potential may thus finally be approximately equalised throughout a considerable 
volume at each end of the discharge, the effective electric capacity of the expanded 
ends of the discharge and the original difference between the potentials of the regions 
thus connected will determine the quantity of electricity discharged by the complete 
flash. 
If the lower charge of the stratiform cloud reaches nearly or quite to the ground 
* The electric force at the surface of a conducting sphere 6 mm. in diameter has to reach about 
260 E.S.U. (a value equal to nearly three times the sparking limit for a uniform field) in order that a 
spark may pass. (Schuster, ‘Phil. Mag.,’ vol. 29, p. 182, 1890.) Drops of this size—which is little 
short of the maximum attained by rain drops—will only slightly assist discharge in an electric field in 
which they are suspended, and drops smaller than 3 5 mm. will not assist discharge at all. 
P 2 
