DlAMAGNETIC CONSTANTS OF BlSMUTH AND CALC-SPAR 185 



EXPLORATION OF FIELD 



The first operation to be performed is to find a formula to express 

 the force of the field at any point, and an experimental means of deter- 

 mining it in absolute measure. The magnet used was one on the 

 method of Euhmkorff, and hence the field was nearly symmetrical 

 around the axis of the two branches, and also with respect to a plane 

 perpendicular to the axis at a point midway between its poles. Should 

 any want of symmetry exist by accident, it will be nearly neutralized 

 in its effect on the final result, seeing that the diamagnetic bar hangs 

 symmetrically. 



The proper expansion of the magnetic potential for this case is 

 therefore a series of zonal spherical harmonics, including only the un- 

 even powers. Hence, if V is the potential, 



V=A l Q t r + A HI Q til i+A w QS + etc., . . . . (1) 



where r is the distance from the centre of symmetry, Q t , Q tit , etc., 

 are the spherical harmonics with respect to the angle between r and 

 the axis, and A t , A ltl , A v , etc., are constants to be found by experi- 

 ment. The only method known of measuring a strong magnetic field 

 with accuracy is by means of induced currents, and in this case I have 

 used a modification of the method of the proof plane as I have described 

 it in this Journal, III, vol. x, p. 14. In the method there described the 

 coil was to be drawn rapidly away from the given point: in the present 

 case the coil was moved along the axis, thus measuring the difference 

 of the field at several points; on then placing it at the centre and 

 drawing it away, the field was measured at that point. The field at 

 the other points "along this axis could then be found by adding the 

 measured difference to this quantity. This method is far more accu- 

 rate than the direct measurement at the different points. 



When a wire is moved in a magnetic field the current induced in it 

 is equal to the change of its potential energy, supposing it to transmit 

 a unit current, divided by the resistance of the circuit. The potential 

 energy of a wire in a magnetic field is (Maxwell's Elec., Art. 410), 



P=I(n- + m:V- + nV 



J \ dx dy dz 



which is simply the surface integral of V over any surface whose edge 

 is in the wire. 



In the present case, take the axis of x in the direction of the axis of 

 the poles and the surface, S, parallel to the plane YZ, and let p be the 



