August 25, 1923] 



NA TURE 



297 



Z-series, but may also require consideration in the 

 derivation of the coefficients of the X-series and of 

 the Z-series, M there is a non-potential system N. So 

 tar as the Z-component is concerned, if we do not 

 assume the integral to be zero, a small constant term 

 is added to the Z-series, which slightly improves the 

 mathematical representation. If we have an N- 

 system caused by vertical currents, as already 

 described, then the question arises whether for a 

 limited portion of the earth, for example from 60° N. 

 Lat. to 60° S. Lat., we may legitimately assume that the 

 total amount of electricity leaving the earth equals 

 the total amount entering it in this 

 region ; if not, then Jt^A^ would not be 

 exactly zero. It is of interest to note 

 that Gauss himself intimated, in his 

 celebrated memoir on the " General 

 Theory of the Earth's Magnetism," 

 that the day might come when it 

 could not longer be assumed that 

 the integral of dfi. is zero. Investi- 

 gations in progress will further eluci- 

 date this matter. 



Question {e) {Variations of the 

 Earth's Magnetic Field). — We now 

 come to crucial tests that may be ap- 

 plied to any theory of the cause of 

 the earth's magnetic field. It would 

 seem as though the surest approach 

 to a solution of the two problems, the 

 origin of . the earth's magnetic field 

 and the origin of the earth's electric 

 field, will be by means of the strik- 

 ing variations, geographic, diurnal, 

 annual, sun-spot, and secular, to 

 which they are subject. The two 

 chief sets of variations, which a theory 

 of the earth's magnetic field will have 

 to explain satisfactorily, are : (i) the 

 geographic variations ; (2) the secu- 

 lar variations. 



Fig. I is intended to show how p, 

 the equivalent intensity of magnet- 

 isation or any other corresponding 

 physical quantity, would have to vary 

 from parallel to parallel in order to 

 produce the portion (about 70 per 

 cent.) of the earth's total magnetic 

 field symmetrical about the axis of 

 rotation, as represented by zonal harmonics to the sixth 

 degree inclusive. If this portion of the field were 

 uniform, then p, represented by the radius- vector from 

 O, would be constant ; this case is shown by the outer 

 circle. Were the zonal field symmetrical about the 

 equator, then instead of the outer circle we have an 

 ellipse, which has been drawn for each of the two epochs 

 1 885 and 1922 (indicated by broken curves) ; for this case 

 P for the equator would be about 17 per cent, greater 

 than for the combined parallels 60° N. and S. The 

 heart-shaped full curves represent the actual state 

 of affairs for the field symmetrical about the axis of 

 rotation. Comparing the radii vectores, p, for corre- 

 sponding parallels of latitude, north and south, it is 

 seen that for both curves (1885 and 1922) p is 

 invariably greater for a land-predominating parallel 

 than for an ocean-predominating parallel, and this 

 fact obtains even for the dotted portions of the 

 curves which apply to the polar regions (see con- 

 clusion 3.) It will be noticed that the 1922 heart- 

 shaped curve lies wholly within the 1885 one, just as 

 was the case for the ellipses, and the difference, dp, 

 between the curves represents, proportionately, the 

 shrinkage in the earth's magnetic moment, or in the 

 equivalent intensity of magnetisation, between 1885 

 and 1922. It will be noticed that the shrinkage is 

 greater for the south, or ocean - predominating, 



NO. 2808, VOL. I 12] 



hemisphere, than for the north, or land-predominating, 

 hemisphere. The effect of the distribution of land 

 and water is one calling for careful examination, and 

 its further study may result in material advancement 

 of our knowledge as to the cause or causes of the 

 earth's magnetic field. 



If we wish also to take into account the balance of 

 the earth's magnetic field, about 30 per cent., which 

 is unsymmetrical about the axis of rotation and is 

 represented by the tesseral harmonics, then the pear- 

 shaped solid, obtained by the revolution of the 

 heart-shaped curve about the earth's axis of rotation. 



would have an irregular surface with specially 

 pronounced humps at the magnetic poles. The 

 radius vector to this somewhat irregular pear-shaped 

 solid would serve to represent the volume or surface 

 distribution of the physical quantity entering into, 

 or evoking, the observed magnetic field. It is clear 

 that no approximately homogeneous spherical iron 

 core inside the earth could produce such a magnetic 

 field as that actually observed. 



Now consider the shrinkage in the earth's magnetic 

 moment. The average annual rate of shrinkage was 

 i/iooo part between 1885 and 1922 ; • it was found to 

 be 1/2 1 70 part between 1890 and 1900, and about 

 1/2580 part between 1843 and 1883.' Whether the 

 annual rate of shrinkage varies as greatly from time 

 to time as is apparently indicated by these figures is 

 open to question and subject to further investigation 

 with sufficiently trustworthy magnetic data. The 

 steady diminution in the strength of the earth's 

 magnetic field, averaging during the past 80 years 

 about I /1 500 part annually, presents one of the 

 greatest difficulties in the theory as to the cause 

 of the earth's field, the srfrmounting of which may 

 prove to be the key to the sought-for secret. It 

 should be borne in mind that the annual loss is 



• Terr. Mag. and Aim. Elect., March-June 1923, pp. 15, 22, and 23. 

 ' Terr. Mag. and Attn, Elect., vol. 9 (1904), p. 183. 



