the Earth's Magnetic Field. 93 



of rotation, we have a basis for the existence of a magnetic 

 field. 



According to the view suggested by Sir J. J. Thomson, we 

 may look upon the combination of the two atoms A and B 

 as resulting from the gain by A of an electron which B has 

 lost. Any tendency oi: the molecules to set themselves with 

 their axes perpendicular to the axes of rotation would result 

 in a polarized state of the kind contemplated. The rotation 

 of the sphere would then give rise to a magnetic field. 



In order to estimate the order of magnitude of an effect 

 of this kind necessary to account for the earth's field, let us 

 calculate the radial separation* of the elements of a doublet, 

 which is necessary in order to account for the field, assuming 

 that each atom of the rotating sphere takes part. If the 

 radial separation comes out as only a fraction of the diameter 

 of an atom, the meaning will of course be, that it is only 

 necessary for the axes of the doublets to turn on the average 

 through a small angle in favour of the radial direction. To 

 save complication of the expressions, we shall deal with the 

 case of a sphere composed of one elementary substance. 



If h is the radial doublet separation referred to, n the 

 number of molecules per c.c, and e the electronic charge, 

 the magnetic field at the surface and at the equator is 

 H = l*75 nelicoa (see appendix, Problem 4). The field which 

 would act on a compass-needle moving with the earth is 

 found as in the case of the uniformly charged sphere, and is 



Hi = 1*75 nehcoa — 47r<waF, 



where F is the electric polarization at the equator, and is 

 given by 47rF = 2*2 irneh (see appendix, Problem 5). Thus 

 the counteracting field brought about by the motion of the 

 needle is again the main factor in the expression, as in the 

 case of the last problem. Taking the case of a silver sphere, 

 containing 0'8 X 10 23 molecules per c.c, we find that, in order 

 to account for a field equal to that of the earth, we must 

 have h equal to 2 x 10~ 8 cm. Now this is just of the order 

 of the diameter of an atom, which means that it would be 

 necessary for all the doublets to point with their axes com- 

 pletely perpendicular to the axis of rotation. It may be 

 mentioned that the order of magnitude of the quantity h is not 

 materially altered if we take a copper sphere, for example. 

 The fact that h comes out of the order of the diameter of 



* By the radial direction we here mean the direction perpendicular to 

 the axis of rotation. 



