the Eartlis Magnetic Field. 83 



The value of co s a s is about four times the corresponding 

 value for the earth's surface, so that H s would be about 

 5 electromagnetic units, an amount far too small to detect by 

 the Zeeman effect. The field produced by the sun at the 

 earth would be negligibly small. 



The term cr l cannot contain a part of appreciable im-* 

 portance, involving a higher power of / than the first, for if 

 it involved the second power for instance, it is easy to see 

 that H would be proportional to o) 4 a 3 , in which case H TO would 

 amount to 2*4 electromagnetic units, a quantity far too large 

 to have escaped detection. 



Considering the term <r 2 , we cannot at once predict its 

 absence from the fact that the earth's translatory motion 

 must give rise to no appreciable field; for even if terms of 

 this type did exist, the earth's translatory motion would 

 presumably not result in a magnetic field, since any ten- 

 dency to produce a current along the line of motion of the 

 earth would simply result in an electrostatic displacement 

 parallel thereto, such as to balance that tendency. A similar 

 remark applies to any terms involving the radial acceleration 

 of the earth towards the sun, which terms but for this cause 

 would be of considerable importance, since the radial acee-* 

 leration in question amounts to about 0*2 of the acceleration 

 of a point on the earth's surface towards its centre, 



If we accept the principle of relativity, we must conclude 

 that in uniform translatory motion there is no electrostatic 

 distribution of the kind above mentioned, and consequently 

 no tendency to produce a current along the line of motion, 

 On this basis the term cr% must be discarded, 



With regard to the terms of the type cr 3 , it is easy to see 

 that the expressions to which such terms lead, as far as their 

 dependence on &> and a are concerned, only differ, in general 

 form, from those resulting from terms of the type g x in that 

 they contain additional powers of coa. The value of coa for 

 the sun is not sufficiently different from the corresponding 

 quantity for the earth to provide us with any information 

 further than that provided in the case of terms of the type 

 a x . Again, the presence of additional positive powers of coa 

 only reduces the magnitude of the field which we might 

 expect to obtain in a laboratory experiment on the rotation 

 of a small sphere, so that we must be prepared to admit the 

 presence of terms of the type <r z . 



Considering terms of the type <r 4 , which correspond to a 

 constant current density of the form cr = F(o)) where F(a>) 

 is some function of ca, we find, on working out the field at 

 the equator of a rotating sphere (see appendix, Problem 3) 



Q2 



