90 Dr. W. F. G. Swann ow 



out that it is not my intention here to either affirm, or deny, 

 their existence, but merely to show that the chances are in 

 favour of it, and that if they do exist, there is evidence to 



show that they are likely to be of an order Mich as lo account 

 for the earth's field, and, secondly, that there can be but 

 little weight in an argument which denies their existence 

 simply on the ground that the necessity for it is not appa- 

 rently contained in any of those more or less crude forms of 

 dynamical laws by means of which we at present attempt to 

 correlate the electronic motions with the motions of matter 

 in bulk. 



The case of the rotation of a charged earth. 



In considering the question of the rotation of a charged 

 earth, we are at once confronted with the difficulty of 

 explaining the absence of an enormous electrostatic held 

 associated with it, and again, in the case of a conducting 

 earth, we could not have the volume elements charged, the 

 charge would come to the surface. We shall not at once 

 discard the hypothesis for these reasons however, since, as 

 we shall see, the difficulties are not insurmountable. 



We shall consider the problem of a rotating earth, charged 

 with a constant volume density p, the charge being fixed in 

 the volume elements. The problem is one where the current 

 density is proportional to the distance from the axis of rota- 

 tion, and by a method of procedure exactly similar to that 



adopted for this case, we obtain yirpwa 2 for the held H on 



the equator. This is the field which would be observed by a 

 stationary observer, or rather by an observer participating in 

 the translatory motion of the earth but not in its rotation. 

 The field which would influence a compass-needle fixed on 

 the surface of the rotating earth may be deduced from the 

 following considerations*. 



The tield inside the test magnet may be looked, upon :is 

 consisting of two parts, the fi<-ld II referred !o above, and 

 the held 11' (\\w to the motion of the induced charge on the 

 surface <>i the compass-needle. The electric polarization F 

 ai the earth's surface is practically uniform over the compass- 

 needle, so that the charge on the Surface o\ the needle would 



■ 1 1 in.i\ in. remarked that the translatory motion of the earth would 

 rive ri-.' i<> a tield ; this part of the Held, however, could uol he detected 

 h\ .in observer on the earth, for exactly the same reasou that the 

 magnetic tield dae i" a charged Bpbere for example, moving through 

 space in company with an observer, La incapable of detection by the 

 . b ei vei, 



