AND ON THE ELECTRIC FIELD OF THUNDERSTORMS. 
87 
peal of thunder heard was marked on the trace by momentarily cutting off the light 
as described in Section I. It was by no means always possible to be certain which 
peal of thunder recorded was caused by the lightning discharge responsible for a 
given sudden disturbance of the field ; when the storm was a distant one with very 
frequent lightning flashes there might be several subsequent discharges between the 
passage of a flash and the arrival of the sound of its thunder. There appeared to be 
no ambiguity in the case of about 120 discharges recorded in 1917 ; the approximate 
distance L of each of these discharges and the sign and magnitude of the resulting 
sudden change of field F are shown in fig. 2, which includes also the eye observations 
of 1914 and 1915. When the records show two or more sudden changes of field 
within a fraction of a second it is the largest of these which is recorded in fig. 2 ; it 
was considered that if the component discharges of the multiple flash were not all at 
the same distance, the one which produced the largest effect was likely to be the 
nearest, and therefore that of which the distance was deduced from the interval 
elapsing between the discharge and the beginning of the thunder. 
V. Effects to be Expected from Different Kindis of Discharges at Different 
Distances. 
A lightning flash may consist in the passage of a charge Q from a certain region A 
of the atmosphere to earth, or from a region A] to another A 2 both in the 
atmosphere ; A x and A 2 may be in the upper and lower parts of the same thunder¬ 
cloud with their centres near the same vertical line, or they may be at a considerable 
horizontal distance apart. 
Let a charge Q derived from a certain region A of the atmosphere pass to earth. 
The change in the electric field may be considered as due to the removal of the charge 
Q from A and of an equal and opposite charge — Q from A' the image of A. Just as 
for many purposes no sensible error is made by assuming the magnetism of a bar 
magnet to be concentrated at two definite points, the poles of the magnet, so in the 
present case the charges Q and — Q may be regarded as being concentrated at two 
points p and p'. These points are situated at a height H above and at an equal 
depth below the surface of the ground, such that 2QH = 2 Hqli = M, the electric 
moment of the discharge q being the charge derived from a small element of 
volume at a height h. In calculating the change produced in the electric field at 
distant points by the passage of the discharge, no sensible error will be made by 
making this substitution, and even at points at no great distance from the axis pp' ', the 
error will be small if there has been any approximation to a symmetrical distribution 
of the charge in a sphere surrounding p. 
* In the present paper 2qh, not qh as in the previous paper, is taken as the electric moment of the 
discharge of a quantity q from a height h to earth, the moment with which we are concerned being that 
of charge q at a height h together with that of its image -q at a height - h. 
