84 Dr. W. F. G. Swarm on 



that H is proportional to aF(co). Thns, even considering a 

 case where only the first power of w is involved, the field is 

 proportional to wa, and according to this a sphere of 10 cm. 

 radius rotating 10 times per second should give rise to a 

 field at its surface amounting to one-seventieth of the earth's 

 field, a quantity far too large to have escaped detection. 

 We are thus restricted to terms of the forms a ] and cr 3 in 

 the expression for o\ A term of the type o-j, proportional to 

 the radial acceleration /', gives rise, as we have seen, to a 



4 

 field at the equator given by 11= --Tra^rco-. The current 



density a^aco 2 , which must exist on the equator at the surface, 

 in order to account for the earth's field, thus amounts to 

 7 X 10 _1 ° electromagnetic unit. 



It is easy to see that a term of the type a ?> , proportional 

 to the product of the velocity and of the radial acceleration, 

 would require a current density on the equator of the same 

 order of magnitude. 



Although 7 x 10~ 10 C.G.s. unit is a current of an order 

 readily detectable by a galvanometer, we could not of course 

 detect the earth current in question in this way, for a very 

 little consideration will show that, even if the current exi-ted 

 in the earth's crust, we could not control the direction of its 

 flow so as to make it curl round the coils of a galvanometer. 



At first sight the permanent existence of such currents 

 would seem at variance with reason, in view of the apparent 

 necessity for the rapid conversion of their energy into heat 

 owing to friction; but in examining the question it is neces- 

 sary to take a closer view of the matter than one involving 

 considerations of resistance, viscosity, &c, and to look upon 

 the permanent existence of these currents, if they do exist, 

 as one of the necessary conditions for that fine-grained dyna- 

 mical equilibrium of matter, the elucidation o^ which mast 

 necessarily involve the explanation of viscosity and resistance 

 themselves in its scope. When this attitude is adopted, the 

 hypothesis for the existence of such currents falls well within 

 the range of possibility. 



There are two obvious ways in which we may imagine 

 Such a current to come about. Suppose that we admit that, 

 in ordinary matter, corpuscles do occasionally leave the 

 atoms and join those corpuscles which exist between them, 

 the balance being kept up hv a re-absorption into the atoms 



of similar corpuscles ; then, if the rotation results in a very 



slight wani or symmetry, lore and aft. in tin 1 rate of expul- 

 sion of these elect i ons, it" we have, lor example, an increase 

 in I he rate of expulsion to the fore, and a corresponding 



