on Periodic Variations of Terrestrial Magnetism. 401 



Collecting terms, it is found that those involving the first 

 powers of ' e are 



3ecos7Cose esiii7sine r . . _ . ,. s /Q ... 



1 cos nt-\ -p-3 [4 sin X sin ((fc — n)t — (/3 — \)) 



+ 3 cos ((K + n)t—P) +-21 cos ((/c-3n)t- J)]. 



If the magnetic axis of the sun nearly coincides with his 

 axis of rotation, the first term is the only important one. If, 

 on the other hand, the sun were transversely magnetized, the 

 most important period introduced by the eccentricity would 

 have a time 27r//c—Sn, or of about 31*7 days. The amplitude 

 of the synodic period having a time 2tt/(k — n) is quite insig- 

 nificant, for X = 5° 28 / and £=^ ! q, so that esin A, is less than 

 gj : this is only about the thousandth part of the amplitude 

 of the leading period produced by the rotation of a trans- 

 versely magnetized sun ; and it may therefore well be said 

 that the synodic period is practically absent. 



4. It remains to discuss the effects of those magnetic forces 

 which act in the equator along directions which are fixed in 

 space, and which now must be referred to axes fixed in the 

 earth. If the force is constant as in the simple case discussed 

 by Lord Kelvin, a periodicity with a time equal to the sidereal 

 day will result; if the forces themselves are variable, other 

 periodicities will be produced. 



If pt represents stellar time, the hour-angle of a star having 

 right ascension a will be pt — a ; unit-force directed to a star of 

 zero declination and right ascension a may be decomposed 

 into three components which, if u denotes the colatitude, are 



sin u cos (pt — a) acting vertically upwards, 



cos u cos (pt — a) acting towards the North, and 



sin (pt — a) acting towards the East. 



We obtain the solution of our problem by making a equal 

 to 90° or 180° respectively, and multiplying each compo- 

 nent by the intensity of the forces which have been found to 

 act towards points of the sky having these right ascensions. 

 Neglecting the inclination of the solar axis and the eccentricity 

 of the earth's orbit, it is found that all terms are of the form 

 cos Kt cos pt or cos (tc — 2nt) cospt. The periodic times are 

 therefore 2irjp + k, 2irjp — /c, 2ir/p — ic + 2n, 27r/p + K—2n. It 

 will be remembered that 2irjp represents the sidereal day, 

 27r//; the sidereal revolution of the sun, and 27r/^ the year. 

 These four periods measured in solar davs have a time of 

 23 h l-3 m , 24 h 55-4 m , 24 h 46«9 m , and 23 h 8 r 6 m . These varia- 

 tions are characterized by the fact that the amplitude of the 



