54 ON MAGNETISM. 



presses on a suspended needle whose axis makes the 

 angle 6 with the Local Magnetic Meridian, is EB sin 6 : 

 and if M be the moment of inertia of the needle, the 

 equation which determines its angular motion will be 



72/1 77' 73 



-T72 = yp sin 6. If 6 be very small, or if proper cor- 



CLt Jj-L 



rections be applied to the observed time of vibration (as 

 for an ordinary pendulum) so as to reduce the time of 

 vibration to what it would have been if the arc of vibra- 

 tion had been indefinitely small, we may use the equa- 



tion -j 2 = -- iTf 6 : of which the solution is 

 at M. 



and the time T of a complete double vibration is 



/ M 

 2-7T./ - . This is a single equation containing two 



unknown quantities E and B, and neither of them can 

 be determined from it. 



If we repeat the experiment at a different time at 

 the same station, or at any time at another station, 

 where it may be presumed that the Earth's magnet- 



/ M 

 power is different, we shall have T' = 2?r /-rrp* which 



still gives no information. And if there is suspicion 

 that the magnet-power B may have changed, there is 

 no hope of arriving at any conclusion. 



There is, however, one way of using the vibrating 

 needle, from which an imperfect result may be obtained. 

 If the vibrations be taken at a standard place, (as 



