AND ON THE ELECTRIC FIELD OF THUNDERSTORMS. 
89 
the potential gradient at the earth’s surface at different distances due to a charge Q 
supposed concentrated at a point at a height of 2 km. : it represents the 
change produced in the potential gradient by the discharge of 20 coulombs from a 
height of 2 km. to earth. The curve II. represents similarly the potential gradients 
due to the same charge at a height of only 1 km. The difference between the 
ordinates of the two curves (curve III.), represents the change of potential gradient 
produced by a vertical discharge of the quantity Q from a height of 2 km. to a height 
of 1 km. The sign of the effect is reversed at a certain distance, the vertical electric 
force at the surface of the ground being, for a given charge Q at the lower level, 
greater than for the same charge at the higher level when the distance is small, but 
less when the distance is great. 
For a vertical discharge from a height H 2 to a height Hj, F, when L is large, 
becomes equal to 2Q (H 2 — EQ/L 3 , so that FL 3 = 2Q (H 2 —Hj) which may be defined 
as the electric moment of such a discharge. Thus when L is large FL 3 is equal to 
the electric moment of the discharge whether this reaches the earth or not. 
The effects at different distances of various kinds of double discharge are also 
readily obtained from inspection of the two intersecting curves of fig. 3. For example, 
a discharge from a height of 2 km. to a height of 1 km., followed by an equal 
discharge from the lower level to earth, would produce at the .surface of the ground 
two successive sudden changes of potential of the same or of opposite sign according 
as the distance exceeded or fell short of the above limit. Again if we consider a 
thunder-cloud of which the upper and lower parts are oppositely charged, and suppose 
that a discharge between the top of the cloud and the ground is followed by one 
between the ground and the bottom of the cloud, the two successive sudden changes 
of potential gradient would be of opposite sign, but their relative magnitude would 
depend on the distance of the place of observation from the discharges; at great 
distances the longer discharge, at small distances the shorter would produce the 
larger sudden change of potential gradient; while at some intermediate distance the 
two effects would be of equal magnitude. The various types of double discharge 
records shown in Plate 5 may perhaps be explained in this way; a given type of 
double discharge giving a considerable variety of effects on the trace according to its 
distance from the recording instrument. 
If the effects of individual discharges could simultaneously be recorded at several 
suitable distributed stations, we should be able to learn much about the quantities of 
electricity which pass and about the initial and final distribution of charges. It is 
especially useful to have measurements of the change of field (l) at points at a 
considerable distance from a discharge, since the electric moment 2QH or 
2Q (H 2 —Hj) may at once be deduced, and also (2) for points nearly below the centres of 
the regions discharged, where, in the case of discharges to earth, F approximates to its 
maximum value 2Q/H 2 . Knowing both 2Q/H 2 and 2QH we obtain both Q and H. 
When a single station only is available we have to be content with attempting to 
VOL. COXXI. — A. 
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