Theory of Thunder storm Electricity. 625 



We will now consider how long il will take for electricity 

 accumulating at such a rate at a certain layer in the atmosphere 

 to give rise to a lightning discharge. 



We have assumed that the whole of the negative ions are 

 separated at the condensation layer, and that the positive 

 ones are carried up above. Thus we have got a charged 

 layer with the corresponding quantity of electricity in the 

 space above. Let cr= the charge on each sq. cm. of this 

 layer at any time t seconds after condensation first started, 

 then the field above the layer will be 



dY els. units 



alt cm. 



or if V is measured in volts 



<W oaa a v °l ts 



— = 300 x 47ro- • 



ah cm. 



cm. 

 Now it was shown above that 



approx. 



a = 2xlO-'U els. unit. 

 Therefore the potential gradient produced would be 



^-=3-8xl0 3 x2xlO-^ V ° Its 

 an cm. 



cm. 



That is, the potential gradient above the condensation layer 

 would grow at the rate of 8 volts/cm. per second. Now air 

 at atmospheric pressure can resist an electric stress of about 

 30,000 volts per cm.; hence it would take ^j™ sec . = 53 

 minutes for the potential gradient to grow sufficiently great 

 for a lightning discharge to take place. Thus the first 

 lightning discharge could not, under the favourable con- 

 ditions we have assumed, occur until nearly an hour after 

 the supersaturated stratum had extended from the cloud to 

 the condensation layer. This first lightning discharge would 

 travel between the condensation layer and the positive charge 

 which had been separated and carried upwards, and would 

 more or less completely conduct away the negative electricity 

 from the portion of the layer affected. In other words, the 

 discharge would neutralize the negative electricity contained 

 in a portion of the layer and destroy the field above it. Thus 



Phil. Mag. S. 6. Vol. 17, No. 100. April 1909. 2 U 



