On Knpid Periodic Variations of Terrestrial Magnetism. 



57 



wlience 



From tlie first set of the fundamental equations results 



^. 



i-r + iß) Jnt-(^ + h)=- ,,, 



sm ax, 



an 



[Ill 



Taking tlie real parts and putting 5;=0, we obtain at last 

 (©z/)a=o==cos nt sill ax. 



.(6) 



/Ä \ iry « sin nt 



an 



•(7) 



Similarly in tlie case of progressive waves, we ma}^ proceed by 

 assuming 



(^^^ = J.'^'±ccv)i-i?±fi)= ^Q^ 



and obtain 



JX= — 1 ycos{nt ± ax) + ßsiii(nt±ax) \ , 



fjin \ ) 



AZ=^ cos(;i^±aa;), 



where the values of ß and /' are the same as above (5). 

 Putting 



ß=.Aco^ (p, ^=^siii if, 



or 



.(9) 



(7) becomes 



AX: 



dZ= 



[xn 

 a 





siu(;iiî + ^)siii ax,\ 

 sin nt cos ax. 



.(10) 



.(70 



un 



