AYRTOX AND PEEEY'S THEOEY OF THE EAETH'S MAGNETISM 181 



In this uniform field in the interior of the sphere, let a smaller 

 sphere of radius a! be situated; the potential of its induced magnetiza- 

 tion will he 



^ 1 ./' C08<? 



Hence the expression for the potential for the space between the two 

 spheres will be 



and outside the electrified sphere it will be 



i *ww r\ I Q 



w \ fi + 2/ r 2 



Let us now take the most favorable case for the production of mag- 

 netism that we can conceive, making a! = a and fj. = ; we then have 



-, 



n r 2 



which is the potential of an elementary magnet of magnetic moment 



^Va\ 

 n 



But Gauss * has estimated the magnetic moment of the earth to be 



3-3092a 3 . 

 on the millimetre rag. second system. Hence we have 



V= 3-3092 

 w 



for the potential in electrostatic units on the mm. mg. second system. 

 In electromagnetic units it is thus 



V, = 3-3092 ; 

 w 



and hence in volts it is this quantity divided by 10 11 . 



As the earth makes one revolution in 23 56' 4", or in 86164 seconds, 

 we have 



2* 



"86164' 

 and 



n = 299,000,000,000 * millims. per second. 



8 Taylor's Sclent. Mem., vol. ii, p. 225. 



3 From a preliminary calculation of a new determination made with the greatest 

 care, and having a probable error of 1 in 1300. 



