Current and on the Origin of Atmospheric Electricity. 379 



It may be desirable in the first place to make more clear the 

 argument against the sufficiency of the condensation theory when 

 conduction in the upper atmosphere is ignored. 



Let us assume the total positive charge in the atmosphere over 

 an area at a distance from the disturbed region where precipitation 

 is going on to be equal in amount to the negative charge on the 

 ground in that area. Let us suppose also that the rate of dissipa- 

 tion of the charge on the earth's surface is one per cent, per minute, 

 a somewhat low estimate. Then this is also the positive charge 

 lost per minute by the air overlying this area. Thus the total 

 charge in the atmosphere overlying each square metre of the 

 ground, and therefore also the corresponding charge on the ground, 

 will diminish with increasing distance from the disturbed region 

 at a rate which will be greater the smaller the horizontal convec- 

 tion current. It would be impossible to explain the strong electric 

 fields which may persist in calm weather at great distances from 

 any disturbed regions ; for even if the air took only an hour to 

 travel from the region of precipitation it would have lost about 

 half of its charge. In the calm regions the lower layers, which 

 carry nearly the whole positive charge, have a negligible horizontal 

 motion. A quite impossible velocity would have then to be 

 assigned to the upper layers (which carry only a very small 

 fraction of the total charge) if the convection current carried by 

 them is to make good the loss of the lower layers in each region 

 over which they pass. 



The only way in which the condensation theory can be made 

 tu explain the maintenance of the electrical field in fine weather 

 areas at distance from the regions where precipitation is going on, 

 is to suppose that the current in the atmosphere from the wet to 

 the dry regions is one of conduction in the upper atmosphere. 

 The question to be considered is, then, what grounds have we for 

 supposing that the upper atmosphere has sufficient conducting 

 power? 



At a height of about 18 kilometres the pressure will only be 

 about one-tenth of that near the ground; at twice this height it 

 will only be about one-hundredth of an atmosphere. Over this 

 range of pressures the mobility of the ions is inversely proportional 

 to the pressure. Over the same range the coefficient of recombi- 

 nation, a, is approximately proportional to the pressure (Langevin, 

 C. R. 137, p. 177, 1903). Let us suppose that the atmosphere 

 at different heights is exposed to ionising radiation of the same 

 intensity; the rate of production of ions per c.c, q, will be 

 proportional to the pressure. When a steady state is reached 



<l = an? or n = \/ - , n being the number of ions of each sign per 

 c.c. Now according to the assumptions made both q and a are 



