H. A. Rowland—Diamagnetie Attachment to the Lantern 359 
ment. The force acting on this particle to cause it to go in any 
given direction will be equal to the product of the magnetic 
moment into the rate of variation of R in that direction,* 
and hence is xvR qB in the direction of x The total force 
acting on the body in the Paey of x is therefore 
Xe lf ff nev Ee) dsp 
and the other components of = tsi are 
os ff xa tnt dady dz 
and % = Mf eS Re) dedyde, 
Let, now, the axis of z be 0? the axis of z in the line 
of the magnetic poles of the magnet, and y at right angles to 
both. Then the moment Hf the forces acting on the body to 
turn it about the axis of 21 
= d aR ) 
sae 4 AS Olea 
where the integration extends throughout the volume of the 
body. 
d(R?*) ) 
a ae x | dedydz, 
td the body is suspended so as to turn freely about py axis 
of 2 it will vibrate shonis the position for which M is a mini- 
mum or else will remain at rest at that point. The nah of 
single oscillations made when the angular elongation $ is very 
ma es. 
= oT ’ 
in which M and $ must be eae simultaneously, and I is 
the moment of inertia of the body. 
= isin Shh «( lf. eg 
w let us suppose that a whole apparatus changes size, 
the setae between the parts remaining constant, so that the 
apparatus becomes m times as great as before. Then a, y, a 
dy, and dz will increase m times and I, m* times. To deter- 
a sk 
mine the changes in — we make use of the the- 
orem of Sir Wm. Thom son, sae ‘similar bars of different di- 
mensions, similarly rolled, with lengths of wire proportional to the 
squares of their linear exons and carrying equal currents, 
cause equal forces at points similarly situated with reference to them.” 
* Thomson, Reprint of Papers, Art. 679, Prob. vii. 
