Manchester Memoirs, Vol. Ivii. (19 13), No. 4. 



IV. Note on the Mean Magnetic Moment and Mean 

 Energy of a Vibrating Magnet. 



By J. R. ASHWOKTH, D.Sc. 



( Comminiicatcd by Mr. R. L. lay/or, KC.S., F.I.C.) 



( Read December loth, igi3. Received for Publication January 21st, igi^. ) 



I. Uniform Magnetic Field. 



Let a magnet, the inoment of which is /x, vibrate in a 

 given plane in a constant field without friction. The 

 component of the magnetic moment in the direction of 

 the field is /mcosO, when it is deflected through an angle 6, 

 and the mean magnetic moment M in this direction over 

 a period of time T is 



]ficosOd/ (i) 



if' 



The equation of motion 



+ A"sine = (2^ 



at' ^ ' 



hence 



do 

 dt 



2 A * I sm- - - sin--| 

 a being the extreme deflection. 



Substituting for T and dt in (ij and inserting a 

 constant c we have the equation 



1^^ 2A v/s„-,2. _ g,j^-_\ J 2A i-( Sin -- - Sin --j 



February 2Sth, i(^ij. 



