100 
ME, C. T. R. WILSON: INVESTIGATIONS ON LIGHTNING DISCHARGES 
(as will generally be the case when rain is falling), or if its charge is considerably 
smaller than the upper charge, then the initial discharge is likely to extend downwards 
till it reaches the ground; it will form then a conducting path for the main 
discharge, which may be regarded as reducing approximately to zero the whole 
discharge track and its ramifications. 
If the potential gradient at the ground reaches a value amounting to any 
considerable fraction of that in the cloud, if for example, the upper and lower charges 
of a stratiform cloud are very unequal, then the critical value of the electric force is 
likely to be first reached, and the initial discharge to begin, at the surface of a 
projecting earth-connected conductor. 
Let us next assume—and this perhaps represents more nearly the conditions which 
hold in an ordinary thunder-cloud—that the vertical separation of the centres of the 
charges is as great as the horizontal dimensions of the charged portions of the cloud. 
Consider for example a charge to accumulate in the head of a cumulo-nimbus cloud 
until the conditions for the passage of a lightning discharge are reached. To get an 
idea of the order of magnitude of the quantities involved let us assume that the 
charge is distributed symmetrically about its centre within a sphere of radius R, the 
maximum electric force being at the boundary of the sphere. If the total charge of 
the sphere is Q, the radial electric force exerted at its surface by the charge is Q/R 2 
and is there a maximum. A radial discharge will therefore begin at a point on the 
boundary of the sphere when F exceeds the critical value and will be continued inwards 
towards the centre and outwards approximately along a line of force. The charge of 
opposite sign in the lower part of the cloud will increase the electric force below and 
diminish it above the upper charge; the effect will however be small if the lower 
charge is small or if it is situated at a height small compared with that of the upper 
charge ; in the latter case the effect of the lower charge is largely neutralised by the 
force due to its image. On the other hand on account of the diminished pressure at 
the greater height a smaller electric force is required to start a discharge from the 
upper than from the under side of the upper charged portion of the cloud. 
Thus discharges may be expected to start not only downwards but also upwards 
and laterally from the charged head of a thunder-cloud. The path of discharge is 
likely to follow approximately a line of force which may belong to any of the classes 
of Section VIII. Discharges such as that of fig. 4, or even discharges upwards into a 
cloudless sky, such as have sometimes been observed, are not unlikely occurrences. 
If an initial discharge from the charged head of a cloud reaches the ground, thus 
opening up a conducting path to earth, an approach to complete discharge is probable, 
so that the quantity of electricity which passes in the lightning flash may be taken 
as a measure of the charge which had accumulated in the head of the cloud. 
A discharge originating in the region surrounding the lower pole of a cumulo¬ 
nimbus cloud is more likely to begin in the lower rather than the upper boundary of 
the charged region ; since the electric force below will be increased, and that above 
