AND ON THE ELECTRIC FIELD OF THUNDERSTORMS. 
91 
are included the mean is 11'8 x 10 5 volts per metre x kilometres 3 . Data for negative 
discharges between 10 and 15 km. are almost lacking. 
These numbers leave little room for doubt as to the order of magnitude of the 
average electric moments of the discharges. Distances below 5 km. are too small in 
comparison with the probable lengths of the discharges for FL 3 to serve as a measure 
of the electric moment. We may assume that the value of FL 3 for a discharge at a 
distance of 10 km. or more approximates to its electric moment. The mean value of 
the electric moment for both positive and negative discharges may be taken as not 
differing much from 10 6 in volts per metre x kilometres 3 = 3 x 10 16 E.S.U. x centimetres 
or about 100 coulomb-km. 
Higher values for the mean electric moment are obtained, as is evident from Table I., 
if the data from discharges at greater distances than 15 km. are used. The records 
of discharges at great distances may possibly give disproportionately large values for 
the mean electric moment for two reasons: (l) because at these distances discharges 
of small electric moment are unrecorded on account of the small magnitude of the 
charges of potential gradient produced by them ; and (2) because it is only at great 
distances that discharges, which do not reach the earth and which may be of great 
vertical length and have large electric moments, produce effects proportional to their 
moments. The sign of the effect of such discharges is in fact reversed at small 
distances, and the magnitude of the sudden change of potential gradient produced 
becomes more nearly proportional to the height of the lower end of the discharge 
than to its vertical length (fig. 3). 
Some additions to the data of Table I. were furnished by the storm of June 17, 
1917, in which the distance and frequency of the flashes were too great to admit of 
the distances of the individual discharges being estimated. There was in this case 
(see p. 80) independent evidence as to the approximate distance of the storm when 
the trace containing records of 95 positive and 40 negative discharges within 10 
minutes was obtained. Assuming the distance of the discharges to have been 17 km. 
we obtain for the mean value of FL 3 , in volts per metre x kilometres 3 , 5*8 x 10 5 for the 
95 positive discharges and 3‘9xl0 5 for the 40 negative, corresponding to electric 
moments 2QH of l'9xl0 16 E.S.U. x centimetres = 63 coulomb-km. and l'3xl0 16 
E.S.U. x centimetres = 43 coulomb-km. respectively. The discharges were observed to 
be approximately vertical and to pass between the base of the cloud and the earth. 
VII. Quantity of Electricity Discharged in an Average Lightning Flash. 
When the electric moment of a discharge is known, the order of magnitude of the 
quantity of electricity which passes in the discharge may be roughly estimated. We 
may assume that the average vertical length of any ordinary discharge is likely to be 
between 1 and 5 km. Thus if the average electric moment 2QH is 100 coulomb-km., 
we may estimate the average quantity discharged in a flash as being between 10 
and 50 coulombs. 
o 2 
