Theory of Terrestrial Magnetism. 407 



Now Gauss gives for the magnetic moment of the earth, 



3-3092 n 3 , 



in millimetre-milligramme-second units, and where n is the 

 number of centimetres in the earth's radius. Consequently, 

 since the dimensions of a magnetic moment are 



the earth's magnetic moment becomes 



•00033092 n~t^, 



the units being the earth's radius, gramme, second. 



Assuming Biot's distribution of magnetic force over the 

 surface of the earth, which is also what our theory has led us 

 to, we then get from Gauss's expression for the moment the 

 result that the magnetic potential on the earth is 



0-33092 cos 6n-%, 

 or 



0*00001311 gos0 nearly; 



so that roughly we have, for a point on the earth's surface, 



^p<nt'= 0*00001311. 



But 2tt 



24x60x60' 

 .*. the density 



cr = 0*0107 unit of electricity, 



or the total charge 



= 4ttx 0-0107, 



the fundamental units of space, mass, time being the radius of 

 the earth, the gramme, and the second. But the dimensions 

 of cr are M* L*; so that, in order to express a in C.G.S. units, 

 we must multiply by Vn ; therefore the total charge 



=4. x o-oio7 ^zmmm c . a s. u„i ts 



a ~rwvtn7 /2,000,000,006 1A7 . , -, 

 = 47r x 0-0107 a / _i 2 1 x 10 7 microfarads. 



V 7T 



To get an idea of the electromotive force required to pro- 

 duce this charge, let us imagine one pole of a Daniell's battery 

 connected with the earth and the other with all bodies in space. 

 Then, since the capacity of the earth is 630 microfarads, this 

 charge will be produced for each cell so employed ; so that, if 



