on Periodic Variations of Terrestrial Magnetism, 397 



along P will be 



F lC osPT + F 2 cosPN. 



If M M 7 is the equator corresponding to the pole P, and a 

 great circle be described through E P, the point of intersection 

 H between this circle and M M/ will be that point which has 

 a right ascension of 90°. The components of magnetic force 

 along H will be 



Fj sin PT cos TPH + F 2 sin PN cos NPH. 



Similarly, the components of force in the direction of a point 

 of right ascension 180° are 



F x sin PT sin TPH - F 2 sin PN sin NPH. 



At the winter solstice the pole P will be on the great 

 circle E T, so that if time is measured from that epoch, the 

 angle PET will be nt. Calling e the inclination of the ecliptic 

 to the equator represented, in the figure by E P, the above 

 components of force, with the help of easy reductions in the 

 spherical triangles N P E and EPT, become 



sin e (F x cos nt + F 2 sin nt) along P, 

 cos e (Fj. cos nt + F 2 sin nt) along H (R.A. = 90°), 

 (Fi sin nt— F 2 cos nt) along W (R.A.= 180°). 



Substituting for F : and F 2 their values, the magnetic com- 

 ponents finally become 



^x[cos (tct — /3)+3cos({tc — 2n)t— £)] along OP, 



COS £ 



-2^[cos(*<-/8)+3cos((«— 2*)*— £)] along OH (R.A. = 90°), 



-^[sin(*«-/8)-3sin((*-2n)*-iS)] along OH' (R.A. = 180°), 



It is thus seen that there are two periods having for time 

 %7r/fc and 2tt/k — 2n respectively; the first of these periods is 

 the sidereal time of solar revolution, the second has an am- 

 plitude three times as large, and is longer than 2tt/(k— n), the 

 period of synodical revolution. The latter is completely 

 absent. If we take the synodic revolutions to be 27 days, 

 the periods introduced have a time of 25*14 and of 29*15 

 days. 



2. We may now treat the problem in its most general 

 Phil. Mag. S. 5. Vol. 46. No. 281. Oct. 1898. 2 F 



