AND ON THE ELECTING FIELD OF THUNDERSTORMS. 
103 
If Q = 20 coulombs = 6x 10 10 E.S.U. and F 0 = 50 E.S.U. the potential at the 
surface of the sphere before discharge must reach 1'7 x 10 6 E.S.U. = 5 x 10 8 volts. 
We may take 10 9 volts as giving the order of magnitude of the potential reached 
in a thunder-cloud before the passage of a discharge of 20 coulombs. 
The order of magnitude of the potential required to cause a discharge remains the 
same even if the spherical distribution of the charge is departed from : the horizontal 
dimensions might, for example, considerably exceed the vertical so long as they did 
not much exceed the height of the charge above the ground. 
Suppose next that there is a stratiform distribution of charges over a wide area, so 
that the lines of force are vertical. The conditions of discharge have already been 
discussed in Section IX. 
If we assume that the mean vertical electric force along the whole length of the 
line of discharge initially approached the value F 0 ( = about 3x 10 6 volts per metre) 
and that this length is 2 km., the potential difference between the levels connected 
by the discharge must have been about 6xI0 9 volts. But, as was pointed out in 
Section IX., the discharge may extend much beyond the regions in which the vertical 
electric force had originally attained the sparking limit F 0 ; the discharge might, for 
example, extend from the region of the upper charge of the cloud to the ground, 
although the electric field did not originally extend to the ground. The potential 
difference required to produce a vertical lightning flash 2 km. long from a cloud of 
this type may thus be considerably less than 6 x 10 9 volts, but it is not likely to be so 
small as 10 9 volts. 
XII. Mean Density of the Charge in a Thunder-cloud immediately before Discharge. 
If we assume that a charge of 20 coulombs is concentrated within a sphere 
500 metres in radius, the charge per cubic metre is about 120 E.S.U. 
In the case of a stratiform distribution of charges we have immediately before 
discharge 4 tt<t = F 0 (Section X.). If uniform density y be assumed for the charge 
throughout a layer of thickness d, then yd = F 0 /47r = about 8 E.S.U. If d be taken 
as equal to 1 km., y = 8x 10~ 5 E.S.U. per cubic centimetre (=80 E.S.U. per cubic 
metre). Concentration of the charge within a smaller thickness is probable, with a 
corresponding increase in the density of the charge. 
The mean density of the charges in thunder-clouds is thus likely to reach values of 
the order of 100 E.S.U. per cubic metre. 
XIII. Charge Associated with 1 c.c. of Water. 
If the amount of water in the charged portion of a thunder-cloud were no greater 
than in ordinary clouds (about 4 gm. per cubic metre), the average charge per gramme 
of water would be about 25 E.S.U. ; the force exerted on each gramme of water by 
