From a harmonic analysis of the earth's magnetic field, Gauss concluded that part was of external and part of internal origin. Analyses by A. D. and later by L. A. lead the authors to the conclusion that part of the field was of a form which could not be attributed to any distribution of magnetiza tion inside or outside of the earth. In the technical mode of expression this part is one which is not derivable from a potential, and is of a type requiring for its explanation in terms of classical electrodynamics the existence of electric currents flowing through the atmosphere in the regions where the magnetic observations are made. Bauer concludes that about 94 per cent of the earth's magnetic intensity is attributable to a potential arising from internal sources, about 3 per cent to a potential arising from external sources, and about 3 per cent is of non-potential origin.
The values of the average vertical current densities necessary to produce the non-potential part are given in Table I. for various The average value of the vertical current density taken regard less of sign is about i o,000 times the average atmospheric-electric current density (see ELECTRICITY : Atmospheric), so that if the former represents a reality the currents associated with it must be of a type produced, for example, by the influx or efflux of charged particles of high speed which derive their velocity from sources other than the atmospheric potential gradient.
According to the conclusions of Sir F. Dyson, and H. the non-potential part of the earth's magnetic field is not indicated with any certainty, although there is some evidence for it. Again, even as regards the part of the field depending upon a potential, different analyses have given different results depending or the data used. Thus the analyses made by Schmidt') on the basis of the data available in 1898 limits the surface field which can be of external origin to less than one per cent of the total; and the chief part of it is a uniform field of intensity 3 X gauss.
The variable part of the earth's magnetic field corresponding to the diurnal variation has its main origin outside of the earth, and, according to S. about 28 per cent of it owes its origin to sources inside the earth.
Gauss laid down the fundamental principle for the analysis of the earth's magnetic field corresponding to a case where the field If we should work out the magnetic potential due to a distribu tion of doublets inside and outside of the sphere of radius r, we should obtain an expression of the type of (r), and the part of (I) involving the and the /r,In would depend entirely on the dou blets outside the sphere of radius r, while the part involving and would depend entirely on the doublets inside that sphere. For this reason, in the empirical analyses of the earth's field, we regard the part depending upon the an and the as due to external causes and the part depending upon gIin and as due to internal causes.
The determination of the Gaussian constants from the experi mental data is by no means as simple a matter as it might seem; and slight errors in the data are apt to cause large errors in the constants, particularly in those of high order.
Magnitudes of the Magnetic Elements over the Earth's Surface.—The elements which enter into the discussion of terres trial magnetism data are : The Declination, D, the angle made with the geographic merid ian by the vertical plane containing a freely suspended compass needle.
The Dip, or Inclination, I, the angle made with the horizontal by a freely suspended compass needle.
The Horizontal Intensity, H, the Vertical Intensity V, and the Total Intensity, R of the field.
Between the four quantities I, H, V and R there exist the relations so that a determination of any two of them serves to yield the others.
Table II. gives, according to a compilation made in a list of values of the magnetic elements as recorded at various observa tories throughout the world.
It is customary to represent the characteristics of the earth's magnetic field by means of charts, in which on a map of the world are drawn the lines of equal Declination, or Isogonics, the lines of equal Inclination, or Isoclinics, and the lines of equal Horizontal Intensity, or Isodynamics; figs. r, 2 and 5, represent a set of such lines based on the British Admiralty Charts for 1922.
The variations of a regular nature comprise a Secular Varia tion, and a periodic variation comprising a part, the Diurnal Variation, based upon a fundamental period of a day, and a part, the Annual Variation, based upon the fundamental period of a year. It is probable that the periodicities of all the members of the solar system reflect themselves upon the periodicity of the magnetic elements although, in general, to an immeasurably small degree, except in the case of the moon, where the effect is well marked. Data for the discussion of the Secular Variation in declination extend back to about 1540, but naturally with relia bility decreasing with the remoteness of the epoch. For the Dip the data are fewer, and there are no absolute intensity measure ments prior to 1830. The general orders of magnitude involved will be gathered from the facts that, at London, the Declination was I I° E. in 1580. It reached its extreme westerly value at 24° W. in 181o, and since then it has been changing towards the east until in 1925 it reached the value 13° W. A value of 71° so' was recorded for the Dip in London in 1576, a value of 74° 30' in 1700, and the present value is about 67°.