1936 Volume 14 Issue 7 Pages 338-347
From the observations of the potential gradients in the atmosphere we see that there exist the positively charged space charges and their quantities diminish with height very rapidly. The seasonal variation of the space charge near the earth's surface was treated by K. Kähler and others. According to the existence of the space charge in the atmosphere there should flow the ion currents of conduction and convection natures; the former its produced by the potential gradient and the conductivity of the air, while the latter is due to the flow of the net quantity of the space charge by the wind. The formula showing these relations is given by where i is the current; λ, the conductivity; _??_, the wind velocity; _??_, the potential; p, the space charge and these two quantities are related by the Poisson's formula: In this paper the present author considered, first of all, the variation of the space charge with season and height using many observed data by various authors: where a and b are given by (4) and T indicate_??_ the air temperature, being assumed to be expressed by a series of spherical harmonics of various orders as is given by (6). (p. 340) Then the Poisson's equation is easily solved as was given by (8). Now we a_??_sume that the negative charge is distributing on the earth's surface and the same quantity of the positive charge is wholly contained in the earth's atmosphere and hence at some altitude from the earth's surface the potential should be zero. This assumption is expressed by (9) if R1 indicates the height of the zero potential. This height is assumed to be the upper boundary of the troposphere. Thus we have the complete solution of the Poisson's equation as (10) and (11). Whence we can express the ion current by the expressions (12). In this paper the conductivity of the atmosphere was assumed as (13) and the thickness of the atmosphere was considered to be very small as compared with the radius of the earth.
By the above assumptions and the next algebraic relations: if kn=A1K+A2k(k-1)…+Ank(k-1)…(k-n+1), we can solve the ion current at various cases after the elaborate calculations as (18) for the case when the atmosphere is at rest (21) for the case when the temperature is expressed by (22) for the case when the temperature is expressed by By the above expressions for the ion currents we can theoretically deduce the genraal feature of the current as follows using the numerical values of the air temperature on the earth's surface.
(1) Ion current due to the convection process; this is expressed by the components (24) indicating that:
(a) The horizontal componeat of the current is very small as compared with the vertical component and the same result is deduced as to the potential gradient.
(b) The vertical component is generally of the same order of magnitude coinciding with the observations and this is the greastest at the polar regions and the smallest at the equatorial belts so far as we consider the values of the same altitude concerns, or in other words, it is the greatest in winter, while the smallest in summer in the northern hemisphere and in the southern hemisphere the feature is reversed. The same conclusion is deduced as to the potential gradient also.
(c) The ion current of horizontal direction is zero at the earth's surface and the upper boundary of the atmosphere and maximum in the intermittent altitude. This flows to the thermal equator from the polar regions and its intensity is the greatest in the middle latitudes of both hemispheres.
(2) Ion current due to the conduction process; this is expressed by the components (27) indicating that: