Ou Rapid Periodic Variations of Terrestrial Magnetisui. 77 



According to our assuiiiptioii, ^ i^^ given ]»y 



If C is small and we neglect the small quantities of the second 

 order against unity, we may put cos ^=^1 and sin d^C cos{pt+<p). 

 Hence 



= ; Y=— ^ ^C coä[pt-\-e) ; Z—— - -— . 



x^ + Jr xr + Jir ' ' x'^ + h' 



Thus, the Y-component onh^ will be sensibly affected while the 

 others remain constant, if i be considered constant. If l be 

 variable and given by 



i = i^-\-i^ cos qt , 



where y'o and ii are constants and /i is small compared with /o, 

 the periodic parts of the three components will be given by 



JX= — pA_cos qt, 

 x^ + h" 



Jr=---^M^cos (pt + f), 

 x- + 7r 



dZ=- ^^^'^ cos qt, 

 X +h- 



neglecting the small quantities of the second order in JF. If 

 p=q, as may be the case when the see-saw motion is the direct 

 cause or result of the fluctuation of the current and moreover if 

 <^=^0, we will have a rotatory motion of the kind desired. 

 Besides, we notice that the sense of rotation is opposite on both 

 sides of the ^5;-plane. The relation of JJC and JY is just the 

 same as in § 22 a), as is evident. JZ must be of the opposite 

 sign on both sides of the current. The results of observations 

 show, however, that the phase relation between JX and JZ is 

 generally the same all through, JZ never being ahead of JJT. 

 Hence the maximum intensity of the current in question can 

 not be running largely in the meridional direction, but 23robably 

 more or less near the equatorial zone, since otherwise we should 

 expect that in some hours JZ may run in advance of JJC. To 

 reconcile the present case with the result shown in Fig. 23, it 

 will be plausible to assume that in passing along the four 



