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MR. C. T. R. WILSON: INVESTIGATIONS ON LIGHTNING DISCHARGES 
charge per unit volume and d is the vertical thickness. On this will be superimposed 
the electric force due to the upper charge of the cloud and that due to the induced 
charge on the ground ; the first of these will increase the electric force at the upper 
surface and diminish that at the lower surface, while the second will increase the 
electric force at the lower and diminish that at the upper surface of the charged layer. 
If we assume the electric force below the lower charge to be greater than above it— 
as may easily be the case if the vertical thickness of the cloud (of cumulo-nimbus type) 
is great in comparison with the height of the lower charge—its magnitude will be 
between 2 irpd and 4-rrpd. A flash will occur when the vertical electric force reaches 
the sparking limit, i.e., about 100 in electrostatic measure. If we assume the boundary 
of the lower charge to be a circle of radius r, and the quantity discharged to be 
20 coulombs = 6x I0 10 E.S.U., r is between 350 metres and 500 metres, these being 
the limits obtained by putting F 0 = 2irpd and F 0 = 47 rpd respectively. 
It has thus far been assumed that the horizontal dimensions of the charged portions 
of the cloud are less than the distance apart of their centres, and that the greater 
part of the whole upper or lower charge of the cloud is neutralised by each 
discharge. Let us now suppose that there has been a uniform stratiform distribution 
of charges over a wide area. Take as an example the cases in which the upper 
and lower charges of the cloud are equal, the other extreme case in which one 
of the charges is very small compared with the other is not essentially different—the 
charge on the ground taking the place of the second cloud-charge. There will be a 
discharge when 4?nr = F 0 , cr being the total charge in a vertical column of unit area 
extending throughout the whole thickness of either charged portion of the cloud. If 
20 coulombs are discharged in a lightning flash, and the whole thickness of a limited 
area of the charged portion of the cloud is discharged by the flash, the area A, 
discharged is such that AF 0 /47r = 20 x 3 x 10 9 ; if the area discharged be assumed 
circular, and F 0 be taken as 100, the radius of the area discharged must be approxi¬ 
mately 500 metres. 
XI. Maximum Potential Attained before the Passage of a Lightning Flash. 
The potential at the surface of the sphere, considered in Section X., will immediately 
before discharge be approximately Q/R = F 0 R ; other terms being relatively small 
may be neglected in estimating the order of magnitude of the potential. The 
potential at the centre of the sphere will exceed that at the boundary, the excess 
lying between zero and F 0 R—these being the values in the limiting cases (l) in 
which the radial electric force within the sphere is zero, the charge being confined to 
the boundary, and (2) in which the radial electric force within the sphere reaches 
everywhere the sparking limit. (The case of uniform distribution of the charge 
within the sphere is intermediate, the excess being ^Q/R). The potential at the 
centre thus lies between Q/R = F 0 R = \/QF 0 and twice this value, 
