92 
MR. C. T. R. WILSON: INVESTIGATIONS ON LIGHTNING DISCHARGES 
We get some further information about the discharges by considering the way in 
which F varies with L (fig. 2). The charge which feeds a lightning flash is evidently 
not generally derived from a widely extended horizontal sheet, as is shown by the 
rapid falling oft 1 in F at comparatively short distances from the discharge. 
The curve shown in fig. 2 represents the relation which would hold between F 
and L in the case of the discharge of 20 coulombs to earth from a point at a height of 
2 km. ; the charge may be considered to have been distributed symmetrically within 
a sphere around this point. The curve represents the mean of the observations fairly 
well, except in the case of discharges at great distances. 
The average magnitude of the sudden change of field produced by lightning 
discharges at any distance may be roughly calculated by assuming that the average 
lightning flash consists of a discharge of 20 coulombs to earth from a height of 2 km. 
The average change produced in the potential gradient by a discharge at a distance 
of 10 km. is, it will be noticed, of the order of 1000 volts per metre, and for 
moderate distances beyond this it probably falls off approximately according to the 
inverse cube law. (It should perhaps be pointed out that the change of field referred 
co here is merely the difference between the initial and final values, before and after 
the passage of a single discharge. At distant points the amplitude of the short 
period oscillations will greatly exceed the difference between the initial and final 
magnitudes of the field. Such oscillations—the ordinary “ atmospherics ” or 
“ strays ”—are of too short period to be recorded by the methods of this research). 
Discharges may be expected to occur (l) between the ground and the lower part of 
a thunder-cloud ; (2) between the upper and lower parts of the cloud; (3) between 
the upper part of the cloud and the ground ; and (4) upwards from the top of the 
cloud. Great differences in the vertical lengths and in the electric moments of 
discharges are therefore to be expected, and the manner in which F varies with L in- 
the different storms furnishes some evidence of such differences. When, as in the 
records of June 12, 1917, FL 3 varies little with the distance and is besides relatively 
small, one is tempted to conclude that the vertical length of the discharges was small, 
that, for example, they passed between the ground and the base of the cloud. When 
on the other hand, as on August 15, 1915, or August 15, 1917, FL 3 continues to 
increase with increasing distance and reaches very high values, great vertical lengths 
would appear to be indicated for the discharges. Possibly the discharges of greatest 
vertical length may be those between the top of a thunder-cloud and higher levels of 
the atmosphere. 
It is unfortunate that no records were obtained of the effects of discharges from 
clouds immediately overhead; such observations of the maximum values of F would 
have given useful evidence bearing on the height from which the discharges came. 
A. dischai-ge of 20 coulombs from a height of 2 km. would cause at the ground a 
maximum change of potential gradient of nearly 100,000 volts per metre. 
Comparatively few determinations appear to have been made of the dimensions of 
