594 MAGNETIC FIELD. 



The plane of the agates being supposed horizontal, the condition 

 of equilibrium is 



(14) pd cos (I' - y) = FM X sin (I a - I' + /?). 



When the needle is inverted, the angles /3 and y change their 

 sign ; the new inclination I" observed gives 



(15) pd cos (I" + y) = FM X sin (I. - I" - ft). 



Adding these two equations member to member, calling I x half 

 the sum and / half the difference of the observed angles I' and I", 

 we get 



(i 6) jtf cosI 1 -FM 1 sinp.-IJ 



If the angles I' and I" 'differ very little from each other, by i 

 at the maximum, it follows, as we shall see from the difference of 



-H 



Fig. 243. 



the equations (14) and (15), that the angle y - ft of the direction 

 of the centre of gravity with the magnetic axis is very small. The 

 ratio of the cosines which comes into the second member of the 

 equation (16) does not appreciably differ from unity, and we may 

 write 



(17) pd cos I L = FM l sin (I a - Ij). 



The needle having received a magnetic moment M 2 in the 

 opposite direction but little different from the first, the centre of 

 gravity is below the axis, and the inclination I 2 , given by the mean 

 of the observations on turning, is greater than I a , which leads to 

 the equation 



(18) pd cos I 2 = FM 2 sin (I 2 - I tt ). 



