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

Abstract

In the first paper, the present author has attacked the same problem using the data given in A. Schmidt's paper, but some important points were remained untouched there. These point are such as those of the assumption of the variation of the magnetic force with height, the error accompanied by the calculation and the recalculation based on the new and precise data of the magnetic force. In this paper these important problems are discussed with an additional notice on the physical interpretation of the current.
(a) In the first paper, the present author adopted the following expression after the wireless research made by Appleton and Builder:
This expression is the same as that which shows the distribution of the magnetic force near the earth's surface when a magnet was placed at the centre of the earth. Then the values of the magnetic force on the earth's surface calculated by the above assumption are considerably different from the observed ones. The expression which characterizes, without serious error, the distribution of the magnetic force on the earth's surface was already given by Gauss and others. This expression may afford us a criterion of the expression used in the first paper.
According to Gauss, the components of the magnetic force are expressed by
If we put r=R+h, we have
The observation shows us that the second term of the right hand side of this expression is of the order of 1/10 or so as compared with the first term. This means that
The expression (1) is able to be used if h/R is of the order of 1/10, namely if we consider h to be of the order of several hundred kilometers.
Therefore the horizontal electric current calculated in the first paper is the average current in the region extending from the earth's surface to the upper atmosphere of several hundred kilometers of height, generally including the ionosphere.
(b) The values of the magnetic force adopted in the first paper were based on those given in A. Schmidt's paper. Therefore the original value may have a considerable error of 100γ or so. Thus the average value _??_₀ or _??_₀ obtained by the graphical method will be accompanied by the error of 500γ or so. Thus the expressions 2α_??_₀+Z_0A-Z_0B and 2 sin θβ_??_₀+Z_0A'-Z_0B', each of them is of the order of 1, 000γ, will have, the error less than 500γ. Therefore
the calculated value of the horizontal electric current may generally lie out of the error.
(c) The above discussions show us that the treatment in the first paper is not meaningless. Hence the author recalculated the horizontal current according to the data given by the magnetic surveying in 1922.
In this paper the average values as to the latitude were calculated with the following result.
The horizontal electric currents flow generally to the direction of the east and west as is tabulated in Table 1 and schematically given in Fig. 2. (pp. 61, 62.)
The comparison of the current calculated from the data given in A. Schmidt's paper with those obtained in 1922 is graphed in Fig. 1, showing that the average features of the current are very similar.
(d) It is concluded that the current is directed to east in the northern part than 30°N and in the region between the equator and 50°S. In the other part of the earth the current flows westwardly. The intensity of the current is of the order of 1amp/km² and it is somewhat great at the polar caps.
As in the upper atmosphere there exist the ionosphere with considerably deep distribution, the current of the same order of the above calculated value will be flowing in the ionosphere.