AND ON THE ELECTRIC FIELD OF THUNDERSTORMS. 
101 
diminished by the action of the induced charge, i.e., virtually by the image of the 
lower charge. An .extreme case is that in which the lower charge, carried largely by 
rain below the actual cloud, extends to the ground. Here the maximum value of the 
electric force would be at the surface of the ground ; and, if the charge be assumed to 
be distributed uniformly throughout a region of which the vertical and horizontal 
dimensions are approximately the same, the maximum vertical electric force would 
not differ much from 2Q/R 2 , where R is the height of the centre of the lower charge. 
In this case the field will be locally intensified at the surfaces of projecting parts of 
earth-connected conductors, and discharges (not necessarily developing into lightning 
strokes) will occur from such points long before the electric force over flat ground 
reaches the sparking limit. 
X. Dimensions of the Regions Discharged by Lightning Flashes. 
It has been shown that the quantity of electricity which passes in an average 
lightning discharge—if the thunderstorms investigated may be taken as typical—is 
of the order of 20 coulombs. In this and the following sections, X. to XYIL, are 
considered some of the consequences which follow if the quantity discharged by a 
lightning flash is taken as 20 coulombs. 
Consider a thunder-cloud of the bipolar type and assume that a discharge takes 
place when the electric force at the boundary of either the upper or the lower charge 
reaches the sparking limit F 0 . To get an idea of the order of magnitude of the 
effects, let us assume that the charge is contained within a sphere of radius ft, at a 
distance from the ground and from other charged masses, and that it is distributed 
symmetrically in such a way that the maximum radial electric force is at the boundary. 
A discharge will occur when Q/R 2 = F 0 . Thus, if Q = 20 coulombs = 6 x 10 10 E.S.U. 
and F 0 = 30,000 volts per centimetre = 100 E.S.U. (its value at ground level) then 
R = 250 metres. If F„ = 50, its value at a pressure of half an atmosphere, 
R = 350 metres. If an equal and opposite charge (the other cloud-charge or the 
image of the first in the ground) were similarly distributed within a sphere of the 
same radius in contact with the first, we should have at the moment of discharge 
2Q/R 2 = F 0 ; and the values found for R would be y/ 2 times as great as in the case 
considered, i.e., 350 and 500 metres respectively. 
A similar result is obtained if, instead of assuming the charge to have been 
distributed in a sphere, we suppose the vertical thickness of the charged portion of 
the cloud to have been small compared with its horizontal dimensions. Consider for 
example the case in which there are frequent flashes between the earth and the base 
of the cloud. We may picture the charged rain escaping from the base of the cloud 
as forming a charged layer which increases in thickness at a rate equal to the down¬ 
ward velocity of the drops. The vertical electric force at the upper and lower 
boundaries of the charged layer, due to its charge, will amount to 2-7T pd where p is the 
