the Earth's Magnetic Field. 95 



4 a 3 . 

 due to the sphere H= - 7r- 3 jnm sin (see appendix, 



Problem G). The field is thus independent of the size of 

 the sphere, depending only on the angular velocity, so that 

 by rotating spheres in the laboratory we could obtain fields 

 enormously greater than that of the earth. 



j may be a function of the velocity, and of the acceleration 

 of the element of matter to which it refers, but no terms 

 involving the velocity only can be of importance, as the 

 effect resulting from the translatory motion of the earth, 

 would, owing to the obliquity of the ecliptic, result in a large 

 diurnal variation. Again, it is easy to see that terms in the 

 expression of j proportional to the radial acceleration / 

 would make the field at the surface come out proportional 

 to (D 2 a, which would again result in a field readily detectable 

 on a small sphere rotating in the laboratory, so that it would 

 seem that there are very great difficulties in imagining the 

 directive orientation of the molecular magnets to arise as a 

 direct result of the earth's rotation, and any other explanation 

 of the orientation is virtually equivalent to an assumption of 

 permanent magnetization. 



In conclusion, it may be remarked that the difficulties 

 attending the explanation of the earth's field as arising from 

 currents brought about by its rotation are decidedly less than 

 those attending the explanation of the effect as due to the 

 other causes we have discussed; and though want of coinci- 

 dence of the geographical and magnetic axes is not involved 

 as an obvious necessity, the difficulties in this respect seem 

 less insurmountable than in the case of the rotation of the 

 charged spheres. If, for instance, in the complete elucidation 

 of the causes of these currents, it were found that the effect 

 of the earth's orbital motion, and of its radial motion towards 

 the sun, were to cause the currents of which we have spoken 

 to circulate, not about the geographical axis, but rather about 

 an axis which rotates about the geographical axis with a 

 period of one day, we should have an explanation of the 

 want of coincidence between the two axes, consistent with 

 the permanent position of the magnetic axis with respect to 

 the earth as a whole. A slight difference in the periods, 

 amounting to a loss of one complete revolution in 400 years, 

 would explain the secular variation, and smaller terms in the 

 expression of the difference of periods would result in the 

 annual variation, &c. 



