400 Prof. Schuster : Possible Effects of Solar Magnetization 



difficulty in calculating the effects of eccentricity, and I shall 

 do so for the more important terms, neglecting those which 

 depend on the small angle between the solar equator and the 

 ecliptic. 



The previous equations are all strictly correct, if we sub- 

 stitute for nt the angle between the radius-vector drawn to 

 winter solstice and that joining at any time the centres of 

 earth and sun. If we take as reference-line the radius-vector 

 drawn to perihelion, and X be the angular distance between 

 the winter solstice and perihelion, we may write (0— X) every- 

 where for nt. The magnetic force acting in the direction of 

 the earth's axis from South to North becomes 



sin 7 sin e r ,_, „ N , _ , , a/i _ .,-. cos 7 cose 

 — ^ — [cos (fct — /3) + 3 cos (ret— 20 + 2X— /3)] -3 . 



The effects of eccentricity (e) to its first power are obtained 

 by writing 



r = a(l— e cosnt), 

 6=nt + 2esin nt, 



where a is the mean distance of the earth from the sun. 



Taking the last of the three terms of which the force is 

 composed, it is seen that the eccentricity introduces an annual 

 period ; for, retaining only first powers of e, 



cos 7 cos e cos 7 cos e . ., 



$ = ~z (l + 3«cosn*). 



Similarly, for the first term, 



cos(^-/3) = eo S ^-/3) {1 + 3ecosnt) 

 r 3 a° v 7 



cos (ret — 8) , 3e r ,. . _. tl , „._ 



= a 3 + ^- 8 [cos((* + *)*-£) + cos ((tc-n)t-/3)]; 



and writing f=2X — ft in the second term, 

 cos (rct-26 + %) 



= T cos { (ret + J) - 2 (nt + 2e sin nt) \ 



= ^r[cos ((K-2n)t + £) + ±e sin nt sin ((rc-2?i)t + £)] 



= a 3 ^ o K^^ 2? 0^ + ?) + ir[7cos((/c^377.)^r)-cos((«-^ + f)]|:. 



