136 Mr. Satyendra Ray on the 



any how. The thickness decreases from the axis to the rin , 

 and therefore the intensity of magnetization of shell in- 

 creases, becoming infinite at the rim. The line rim prevents 

 inversion of the direction of magnetization of the shell shown 

 in fig. 1, which, it will be noticed, cannot be got rid of by 

 making the shell indefinitely this;. 



As tubes of magnetic induction form closed curves en- 

 circling the current, and as for each tube of induction BxS 

 is constant, from the above mode of choosing the equivalent 

 shell, we get immediately the relation thatJBdS taken over 

 any equipotential surface bounded by the rim is constant. 

 Or, the Total Magnetic Pole on the surface of the equivalent 

 magnetic shell is constant, no matter how we choose the 

 equivalent shell. 



§ 2. Total Magnetic Pole. 



To find this Total Magnetic Pole, icrdS, on the surface of' 

 the Magnetic Shell we shall find that the plane surface through 

 the rim gives us the best equipotential surfaces to choose. 

 One equipotential surface extends from the centre to the 

 rim, the other from the rim to infinity. For the first of 

 these, 



, 1.3...(2n-l) r*"+ l p ,*.*,„ \ 

 2 . 4. . . In a"' 1 ^ 1 J 



(Maxwell, Vol. ii. Art. 695.) 



For the plane of the coil 6= jr , so that all the harmonics 



— 



in the series vanish and Y = 2ttI, a constant. H is therefore 



perpendicular to the plane of the circuit. 



rdd~ nifi'de 



rd/JL I 



Therefore 



2irifdF 1 (0) 1 r 2 dP s (0) t ].3 r 4 dP 6 (6) _ 



a I dp' ~ 2'a*' d/i + 2.4V d/ & °' J 



2iri f , , /1\ 2 3r 2 , /l . 3\ 2 5?- 4 , / ] . 3 . 5V 7^ 6 , *) 

 " V l l + (2J ' aJ + \2 .4/ ^ + (27476) '"* + &C ' J 



