340 CARNEGIE INSTITUTION OF WASHINGTON. 



(3) We may imagine that negative electricity is supplied continuously to the 

 Earth and positive electricity to the atmosphere, the supply taking place, 

 however, over only a limited region at any one time. 



Considering the hypotheses of the first type, it turns out that in view of the 

 fact that the Earth is a comparatively good conductor of electricity, the charge 

 will distribute itself uniformly over the Earth's surface. The known fact that 

 the conductivity continually increases Avith altitude to a high value is all that 

 is necessary to insure that things will arrange themselves so that the positive 

 charge in the atmosphere is equal to the negative charge on the Earth. 



Considering any hypothesis of type 3, it turns out that in regions where the 

 replenishment of charge to the Earth and atmosphere is not taking place, the 

 potential-gradient and Earth-air current-density would, under ordinary con- 

 ditions, quickly fall to an insignificant value. If, however, a very high value 

 is assumed for the conductivity of the upper atmosphere, this difficulty ta 

 some extent vanishes, and the assumption of a replenishment of the charge at 

 one place is sufficient to account for the maintenance of atmospheric-electric 

 phenomena at all places. 



A discussion of several former theories is given; among others, those of 

 Elster and Geitel and of Ebert. In these theories a separation of positive 

 and negative electricity takes place in such a way that negative electricity is 

 left on the Earth and positive is supplied to the atmosphere. The positive 

 charge is carried upwards by the ascending air-currents, and in the steady state;, 

 the convection current so produced must be equal and opposite to the conduc- 

 tion current. Apart from the objections which have been raised by others 

 against the Elster and Geitel theory, it is shown that, owing to the conductivity 

 of the atmosphere, the rising positive electricity would become devoured, as 

 it were, before it had reached any great altitudes, and the net result is that on 

 such a theory the potential-gradient and Earth-air current-density would be 

 expected to diminish to practically a zero value at altitudes of the order of 

 magnitude of 1,000 meters, which is contrary to the results of balloon experi- 

 ments. The objection here cited applies to any form of theory in which the 

 convection current is supposed to balance the conduction current. 



The hypothesis provisionally formulated in part 2 consists in assuming that 

 each cubic centimeter of the atmosphere emits negative corpuscles of a pene- 

 trating power sufficiently great to enable them to travel through considerable 

 thicknesses of the atmosphere. The Earth will absorb the corpuscles which 

 fall upon it, and its potential will rise, in a negative sense, until the negative 

 conduction-current back to the various parts of the atmosphere balances the 

 charging effect due to the expulsion of the corpuscles. The total positive 

 charge in the atmosphere will of necessity be equal to the negative charge on 

 the surface of the Earth. In the steady state the resultant downward cor- 

 puscular current at any altitude will just balance the upward conduction 

 current at that altitude. A general consideration of the order of magnitude 

 of the phenomena concerned shows that it is only necessary to assume an 

 extremely small rate of emission of corpuscles per cubic centimeter, and though 

 the degree of penetration necessary for these corpuscles is greater than any 

 we are familiar with in laboratory experiments, a full consideration of all the 

 circumstances shows that the assumption is not as unreasonable as might at 

 first sight be supposed. 



In the simplest case, where the rate of emission of corpuscles and the average 

 range of a corpuscle are independent of the altitude, the corpuscular current- 

 density and consequently the conduction current-density should decrease to 

 practically a zero value at an altitude comparable with the average range of a 

 corpuscle. In the more general case where the rate of corpuscular emission. 



