328 CARNEGIE INSTITUTION OF WASHINGTON. 



The atmospheric potential gradient, and a theory as to the cause of its connection with other 

 phenomena in atmospheric electricity, together with certain conclusions as to the 

 expression for the electric force between two parallel charged plates. W. F. G. Swann. 

 Terr. Mag., vol. 18, pp. 163-184 (1913). 



The paper comprises a mathematical discussion of the electrical conditions 

 which would be expected to prevail in the atmosphere, starting with the 

 assumption of a potential which increases with the height above the ground 

 and utilizing the theory of conduction of electricity in gases. It was under- 

 taken ^\^th the object of determining how far the main features shown by the 

 atmospheric-electric elements are the logical outcome of the mere existence of 

 a potential gradient in a conducting atmosphere. It is shown that this 

 requires : 



(1) That the ratio of the number of positive ions per cubic centimeter at 



the Earth's surface, to the number of negative ions, shall be greater 

 than unity, a similar result holding for the corresponding dis- 

 sipation coefficient. 



(2) That the above ratio shall increase with the potential gradient. 



(3) That neither ?ii, the number of positive ions per cubic centimeter, nor 



n^, the number of negative ions per cubic centimeter at the Earth's 

 surface, are the same thing as the numbers which, if the atmos- 

 pheric field were absent, would exist in order to result in a balance 

 between recombination and formation. According to the theory, 

 both 7ii and n^, near the Earth's surface, should be less than at 

 points high up. 



(4) That the atmospheric potential gradient in a homogeneous atmos- 



phere shall decrease with the height in the neighborhood of the 

 Earth's surface. 



(5) That there should be an apparent, but not necessarily true, increase 



of the rate of ionization with the height. 



Various other minor speculations and conclusions are also involved. 



All of the above conclusions are in harmony with experiment. The calcu- 

 lated quantities are of the same order of magnitude as those found experi- 

 mentally. This is as much as can be expected in view of the fact that the 

 calculation is restricted to a case where the specific velocities of the positive 

 and negative ions are equal, and the rate of formation of ions is independent 

 of the height. As examples of the kind of variations of the elements pre- 

 scribed by the theory, the following may be cited: Suppose that the rate of 

 formation of ions is 11 ions per cubic centimeter per second, the specific 

 velocity of each kind of ion 1.6 cm. per second per volt per second, and that the 

 potential gradient, some considerable distance above the ground, is 100 volts 

 per meter. If A^ is the number of positive or negative ions per cubic centimeter 

 and X the conductivity far above the ground, the value of the conductivity at 

 a height 3.5 meters above the ground should be X/1.6, the number of positive 

 ions being 0.85 N and the number of negative ions 0.40 A''. The potential 

 gradient at the Earth's surface would be 2.76 times the value at a great altitude. 

 Rapid variation of the potential gradient should, however, be confined to the 

 lower altitudes, and at an altitude of 10.4 meters the potential gradient 

 should only differ by 1 per cent from its value at infinite altitude when the 

 latter value is 100 volts per meter. In a case where the value of the potential 

 gradient at infinite altitude is 250 volts per meter, the value at an altitude of 

 26 meters would still only be 1 per cent different from the minimum value. 

 The continual decrease of the potential gradient with altitude up to high 

 altitudes is thus not continued in the present simple form of the theory which 

 assumes the rate of production of ions and specific velocities independent of 

 the altitude. 



