on Periodic Variations of Terrestrial Magnetism. 309 



o acting towards an ideal star of zero declination 



and right ascension 90°. 



(b) A fixed sphere of magnetic moment sin 7 sin cos fct, 

 the axis of magnetization being OE. This produces an effect 

 similar to (a), the forces parallel and at right angles to the 

 earth's axis being 



sin 7 sin 8 cos e cos Kt/r* and sin 7 sin 8 sin e cos /ct/r z . 



The periodicity introduced is that of the sidereal revolution. 



(c) A sphere of magnetic moment sin 7 magnetized at right 

 angles to E, the sphere rotating round E with angular 

 velocity k. 



The effect of such a sphere has been deduced in § 1 ; the 

 final equations there obtained are based on the assumption of 

 unit magnetic moment, and should therefore be multiplied by 

 sin y. 



(d) A fixed sphere magnetized along A, with moment 

 sin 8 cos 7. This sphere will produce a magnetic force which 

 always acts parallel to the ecliptic. If y^jn represents the 

 time when the earth crosses the line A; the force resolved 

 along and at right angles to the radius-vector will be 



2cos(w*- x ) and sin(ng-x) . 



r 3 c ?' 3 



Resolving along the earth's axis and at right angles to it, wo 



oO DO/ 



obtain the following components : — 



sin 8 cos 7 sin e r fa ± x , -, , ,, ,,, 

 ^~y L cos (^~%) + " cos X\ a ^ on g the earth s axis ; 



sin 8 cos 7 cos e ^ ( 2n t- x ) + 3 cos ^ towards H (R.A. = 90°); 



Sm I? 8 7 [ gin (^-x) + 3 sin X\ towards H' (R.A. = 180°). 



The periodicity introduced here is a semiannual one, but 



the amplitude is small in the case of the sun, the value of 

 sin 8 being *12. 



(e) A fixed sphere magnetized along A with moment 



2 sin 2 gj sin 7 cos Kt. The result of this may be written down 



from the previous one; but as the effect depends on sin 2 8, it 

 may be considered wholly negligible in the case of the sun. 



3. It has so far been assumed that the earth's path round the 

 sun is a circle described with uniform velocity; but there is no 



2F2 



