408 DR. G. C. SIMPSON ON THE ELECTRICITY OF 



ascending current had a velocity of only 8 metres a second enough water would be 

 deposited for a considerable breaking up of drops. 



Turning now to the second point which the theory has to consider, a rough 

 estimate will be made of the amount of electricity which could be separated under 

 such conditions. For this purpose it will be necessary, in order to simplify the 

 reasoning, to make several somewhat artificial assumptions. It will be assumed that 

 the ascending current extends over a fairly large area, so that vertical distances may 

 be considered as small in comparison with horizontal ones ; that the separation of 

 electricity takes place uniformly over a horizontal plane ; and that all the positive 

 electricity remains in the water near the place of separation, while all the negative is 

 carried vertically upwards in the air stream. We will first consider how many drops 

 must be broken in order to set up the potential gradient of 30,000 volts per 

 centimetre which is necessary for a lightning discharge. This field is set up between 

 two parallel plates having a surface density of 8 els. units per square centimetre. 

 Thus sufficient drops must break over each square centimetre to provide 8 els. 

 units before a discharge can take place, and as the breaking of each drop 



Q 



provides 5X 10~ ;t els. unit, this will occur when ,, or 1GOO, drops have broken. 



u X 1 U 



Thus if 1 drop breaks over each square centimetre every second, a discharge can 

 take place after 27 minutes; or, if 27 drops break, after 1 minute. Now it has 

 already been shown that under certain conditions which are not at all improbable, 

 30 drops of water, eacli large enough to be broken up, will have accumulated in the 

 course of 1 minutes over eacli square centimetre of the ascending current ; hence, 

 it does not seem at all improbable that with even moderate values of the ascending 

 current sufficient breaking of drops could take place to give the rapid electrical 

 discharges observed in thunderstorms. In this connection it is important to realise 

 that each electrical discharge in a thunderstorm only neutralises the electricity over 

 a small area of the region in which separation takes place. Thus suppose that the 

 ascending current is 4 kilometres in diameter, and that each discharge neutralises the 

 charge over 1 square kilometre of area, then it would take 12 discharges to neutralise 

 the whole electricity over the whole surface. Under these conditions, if the potential 

 gradient were being created at the rate of 30,000 volts per centimetre every minute, 

 the lightning discharges would occur on the average every 5 seconds. 



It may also be considered how many times a given mass of water would have to 

 be broken up in order to give to the rain which falls from the cloud the charges of 

 electricity which are actually measured. The case of rain positively charged will 

 be considered first. From Table III, p. 388, it will be seen that the positive 

 charge carried down by the rain is of the order of magnitude of 1 els. unit per cubic 

 centimetre of water. The laboratory experiments showed that water which has 

 splashed once has a charge of the order of magnitude of 10 X 10~ 6 els. unit per cubic 

 centimetre. Thus the water on the average would have to splash something like 



