of Terre&tr ial Magnetism. 357 



surface, according to a surface harmonic of order i, Y { , the 

 current function will be given by 



. (2i + l)A Y ». 

 the potential just inside the sphere, 



that just outside, 



V=-(i+l)^Y, 



a 



or, if the current-sheet is just outside the earth, therefore 

 (which supposition would, as we have seen, give a good agree- 

 ment for the vertical force), we find 



. = _2i ± l_J_ v> 

 i + 1 4tt 



It follows from this, that the currents flow at right angles to 

 the magnetic force at the point. If, however, the distribution 

 of potential cannot be represented by a single surface har- 

 monic, then, as the coefficient of V differs for harmonics of 

 different orders, the currents need not necessarily be at right 

 angles to the magnetic force. If i is infinitely large, the 

 fraction depending on i is 2 ; if i is 2, the fraction is J ; 

 and it must always lie between those limits if i varies be- 

 tween 2 and infinity. There seems for diurnal variation 

 no term of the first order ; and we may therefore take very 

 approximately the currents to be at right angles to the mag- 

 netic force at any place. In order to obtain the currents in 

 C.G.S. measure from the magnetic force we have to apply a 

 factor, which, as we have seen, is approximately obtained by 

 putting i = 2, and therefore is equal to 5/12 7T. 



In the following table I give the direction and intensity of 

 the currents at Greenwich and Bombay for the local solar 

 hours. The direction of the current is as accurate as the 

 observations will permit ; the intensity is calculated, as ex- 

 plained above, by multiplying the magnetic force by 5/127T, 

 and is therefore approximate only as far as its absolute value 

 is concerned, but the relative value of the numbers ought to 

 be correct. The Greenwich result applies to the year 1882, 

 that for Bombay is founded on the mean values during a 

 succession of years. 



* Maxwell, ' Electricity and Magnetism, vol. ii. p. 281. 



