On the Horizontal Electric Current deduced from the Earth's Magnetic Force. (The First Paper)

Abstract

A. Schmidt, L. A. Bauer and others have pointed out that the small fraction of the earth's magnetic force is due to the electric current flowing in the magnetic field. From our observations of the magnetic force on the earth's surface, the vertical current is able to be calculated. In his treatments L. A. Bauer showed the existence of the vertical current of the order of 10^-2amp/km² over the whole earth. The direction of the current, however, changes itself at about latitudes 45°N and S. This fact necessarily leads us to the conclusion that the vertically upward currents at the polar caps and the vertically downward currents at the equatorial regions must close their circuits as was schematically indicated in the work of H. Hertz.
Then the horizontal electric current should exist in the atmosphere and this current, too, will be calculated from the earth's magnetic force so far as the variation of the magnetic force with height is known to us.
Unfortunately the magnetic observations in the free atmosphere were very scanty in number without giving us any expressions of the changes of magnetic forces with height. Recent investigations on the propagation of electric waves afford us the knowledge of the magnetic state at the ionosphere. From the experiments done by Appleton and Builder, we see that the magnetic force H in the atmosphere is expressed by to a first approximation, where H₀ is the magnetic force on the earth's surface, h, the altitude in the atmosphere, small compared with the mean radius R of the earth. If this formula holds approximately good, the horizontal electric current is easily calculated by the next formulae.
(density of eastwardly directed current)
(density of southwardly directed current)
If the magnetic forces and the length are given in C. G. S. units, the densities of current are expressed in amp/cm²-unit when multiplied by 10. In these expressions, _??_₀ and _??_₀ are the mean values of X, the north component of the magnetic force, and Y, the east component, at the earth's surface between two consecutive points, In the present paper the author calculated these mean values by the graphical method without serious error. Z_o is the vertical component of the magnetic force. The meanings of other letters will be easily understood from Fig. 2 and 3 and the process of deduction of the above expressions was described in pages 5-7.
It is worthy to note that the current is calculated from the magnetic forces on the earth's surface so far as h is small compared with R. This fact seems to us that the electric current thus calculated flows horizontally at every altitude on the earth, but this will be due to the above assumption of the variation of the magnetic force with height. This point will be discussed in the next paper.
In this paper the present author calculated the horizontal current from the data of the magnetic forces given in a paper of A. Schmidt. The calculated values at various places over the globe were tabulated in Tables 1 and 2. Table 1 (p. 8) shows the eastwardly and southwardly directed mean currents, Whence we can conclude that the horizontal currents do not converge to nor diverge from certain points, showing the absences of the sink-and source-like points over the globe. Table 2. (p. 8) gives the values and direc_??_ions of currents at every points and a chart showing the distribution of the current was printed in page 9 (Fig. 4.)
The distribution of current resembles, to a high degree, to the general circulation of the earth's atmosphere, but the magnitude of the electric current can not be explained from the ordinary ion current in the atmosphere. In the average state, the electric current flows westward at the equatorial region, rather a little north, while eastward at the higher latitudes. (Fig. 5 p. 10)