4 ASHWORTII, Moment , in, I Energy of a Vibrating Magnet. 



Assigning to « a series of values from o' to i8o the 

 relative mean values of the energy may be computed, as 

 in column (3) of the subjoined table, where the maximum 

 is put equal to 100. 



Comparing the numbers in columns (2) and (3) it is 

 seen that the mean magnetic moment decreases more and 

 more as the mean energy increases and that the mean 

 magnetic moment vanishes a little before the energy of 

 vibration has reached its maximum. At the maximum 

 the magnetic moment has a mean value in the opposite 

 sense to that of the controlling field and exhibits the 

 diamagnetic character. 



When the vibrations pass into rotations the dia- 

 magnetic character will still be in evidence. 



II. Field Due to an Oscillating Magnet. 



Suppose the field controlling the magnet is not 

 constant but is set up by a similar neighbouring vibrating 

 magnet. If the two magnets vibrate freely in the same 

 period and in such a way that the controlling field is 

 proportional to cos 0, where Q is the common angle of 

 deflection from the axis of alignment, then the equation 

 of motion is, 



md 



.^ +7i'sin9cos0 = O (6) 



'^^ = A'*(sinV(-sin=mi 

 dt ^ ' 



a being the extreme angle. 



Hence substituting for 7" and <r// in equation (i), and 

 inserting a constant c we have 



e'M' = { /"__--^!L_ r' f"(sin\t - snYd)icos6d6. 

 {J {sin" a - sm^ dji ) J ^ ' 



