296 Mr. G. J. Stoney on the Magnetic Effect of the Sun 



MM' 

 2— prg-, and arises when cos« = l and cos«' = 0*; that is, when 



the magnetic axis of the distant magnet is pointed towards the 

 needle, and at the same time the needle stands in a perpendi- 

 cular direction. 



Now if H signify the horizontal, and T the total intensity of 

 the earth's magnetism at any station expressed in Gauss's abso- 

 lute units, M'Hsin/* and M'Tsintf will be the moments by 

 which the earth tends to restore the declination and dipping 

 needles respectively, when displaced from their positions of rest 

 through the angles h and t. If we suppose then that the moon 

 is brought successively into the positions in which it will most 

 deviate the two needles, we find that 



MM' 



M'H sin h — 2— ™r is the condition of rest for the declination 

 D 3 



needle, and 



2MM' 

 M'Tsm?= -p. - 3 is the condition of rest for the dipping 



needle. 

 Hence the greatest deviations which the moon can produce on 

 the declination and dipping needles respectively will be 

 2M 2M 



D 3 H' ' - D 3r r 

 writing the small angles h and t instead of their sines. 



In order to arrive at numerical values, it will be necessary to 

 remember that the magnetic moment M, or 



v /{(j , ^ W ) 2 +(j^) 2 +(J , ^m) 2 }, 



is independent of the position of the origin of coordinates. In 

 fact the moment referring to a new origin abc is 



s/{^{x-a)dmf + ^{y-b)dmf+^{z-c)dmf}, 

 which = M, since, from the fundamental property of magnetism, 

 ylm—§. It is obvious that it is also independent of the di- 

 rection of the coordinate axes. From this we conclude that in 

 magnetic bodies, since they consist of parts throughout each of 



* This may be easily seen by conceiving the force of which the compo- 

 nents are —2 cos a, cos/3, and cosy, applied to the point of which the co- 

 ordinates are cos «', cos j3', cos y'. The radical in the text will then repre- 

 sent the moment of this force round the origin : and bearing in mind that 

 cos a', cos /3', cos y' are coordinates of a point at a unit distance from the 

 origin, and that — 2 cos a, 2cos/3, 2 cosy wonld be components of a force 

 equal to 2, it is obvious that the maximum moment of the given force will 

 amount to 2, and will arise when cos u=\ cos «'=0. 



