104 
MR. C. T. R. WILSON: INVESTIGATIONS ON LIGHTNING DISCHARGES 
the electric field where it approached the sparking limit, 100 in E.S. measure, would 
amount to 2500 dynes, i.e., to more than twice its weight. As pointed out by 
Simpson, # 10 E.S.U. is the largest charge per cubic centimetre of water consistent 
with its falling in an opposing electric field of 100 E.S.U. (on one occasion rain actually 
was found by him to carry a charge exceeding 10 E.S.U. per cubic centimetre). 
In the same paper Simpson draws attention to the very considerable accumulation 
of water that must occur in thunder-clouds through lagging of the larger drops 
behind the uprushing air. Thus the charge per cubic centimetre of water does not 
necessarily reach the above high values : and indeed the electric force opposing the 
fall of the large drops associated with the lower pole of the cloud cannot, as a rule, 
exceed their weight, since it is by the fall of these drops that the field is maintained. 
But there will be less concentration of water on the smaller drops associated with 
the upper charge, and densities exceeding 10 E.S.U. per cubic centimetre in the 
upper part of the cloud are not unlikely. 
The drops in the head of a thunder-cloud may thus in virtue of their mutual 
repulsion have radial velocities which near the boundary may be comparable with the 
terminal velocity which the drops would acquire if falling freely through the air. 
Drops of 10 -3 cm. in radius would have a maximum radial velocity of a few centi¬ 
metres per second: if the radius were as large as 5xl0~ 3 , the charge per cubic 
centimetre of water remaining the same, the radial velocity would be of the order of 
1 metre per second. The characteristic bulging form of the heads of a, developing 
cumulo-nimbus cloikl may possibly lie partly due to mutual repulsion of the charged 
droplets. 
XIV. Disruption of Drops by the Electric Field. 
It was shown by Lord Rayleigh! that a charged spherical drop must become 
unstable if Q 2 exceeds 167r« 3 T, where Q is the charge, a the radius of the drop and 
T the surface tension. If the charge per cubic centimetre of the water in the cloud 
is p and is equally distributed among the drops, so that Q = -f -7 ra 3 p, then the spherical 
form will be stable so long as p 2 a z does not exceed 9 T/t r, i.e., about 225 in the case of 
water drops. The limit fixed in this way for the maximum charge per cubic centimetre 
of water, even for rain-drops as large as 3 cm. in radius (for which it amounts to 
more than 70 E.S.U.), is too high to be of importance in the thunder-cloud problem. 
Of much greater importance is the effect, upon the stability of the drops, of the 
electric field in which they are suspended, or in other words of the induced charges on 
the two halves of each drop. 
If it is as a result of the electric force within or at the boundary of a cloud that 
a lightning flash occurs, then it becomes an interesting question whether under 
certain conditions disruption of the drops may not occur before the conditions for 
* Simpson, loc . cit . 
t Rayleigh, ‘Phil. Mag.,’ vol. 14, p. 184, 1882. 
