82 Dr. W. F. G .Swann on 



which these restrictions impose, in view o£ the great dif- 

 ferences in the temperature of the bodies dealt with, hut Lhey 



nevertheless serve ;is a useful guide in the formation of a 

 theory. It may here he mentioned, that if the sun has a 

 magnetic field, a knowledge of the magnitude of that field at 

 its surface would he most helpful in the formation of a theory, 

 as it would, when considered in conjunction with the earth's 

 field, to a large extent decide how the field due to a rotating 

 sphere varies with its dimensions and its angular velocity. 



Considering the first theory, which attempts to account for 

 the magnetic field as due to the existence of an ordinary 

 cm-rent brought ahout by the rotation, we have to realize 

 that the motion of any particle of the earth may be looked 

 upon as consisting of a linear velocity, compounded with an 

 acceleration directed towards the earth's centre, and it is in 

 terms of these quantities that the current density must be 

 expressed. The spacial derivatives of these vectors may also 

 be involved, if the current is to he looked upon as in any 

 way dependent on the relative velocities of the different part-. 

 The current density may be written in the form 



cr = cr l + cr 2 + °3 + °"4i 



where <j] represents all terms involving the acceleration only, 

 Co represents all terms involving the velocity only, «r 3 re- 

 presents terms involving products of powers of the accelera- 

 tion and of the velocity, and c 4 represents terms involving 

 only the single spacial derivative &>, i. e. the angular velocity. 



It is interesting to consider the currents represented In- 

 each of these terms, and to see how far we can, from general 

 principles, restrict them. 



Consider the contribution of the first term, and to fix our 



ideas, let us take the case where cr x is proportional to the 



centripetal acceleration f. This case is worked out in the 



4 

 appendix (Problem 2), and gives — 7royrV : for the hori- 



zontal magnetic field II at the equator of a sphereof radius a, 

 a t) being the current density one centimetre from the axis of 

 rotation, for unit angular velocity. 



Lei suffix m refer to a sphere of 10 cm. radius, rotating 

 L0 times per second, suffix e to the earth, and s to the sun. 



Then taking a, = 6 X 10 s cm., H,=0 B 3 O.G.S. unit, we have 



^H.=0-6xlO-*O.G.S. unit. 

 <• 



o l»e readily detected in a laboratory 







II -- 



■"hi — 



1 



a value 



too small 



experim 



ent 





