378 ' ELECTROSTATICS AND MAGNETISM. [PT. II. CH. IX. 



within the hollow is to oppose the external field. We have for 

 the whole potential in the cavity, by (2), (5), and (15) 



The absolute value of the coefficient of any T n is less, the 

 smaller the ratio b/a, that is, the thicker the walls of the cylinder. 

 By making the walls thick enough, we can make the coefficient 

 approach as nearly as we please the value 1 l/M 2 . Now this 

 is smaller, the greater the ratio //^i- For //. 2 /A&i infinite the 

 internal field would be reduced to zero, as in the case of the 

 sphere. 



This principle was used by Lord Kelvin in his marine galvano- 

 meter, in which a thick cylinder of iron shields the galvanometer 

 from the influence of external magnetic fields. Such an arrange- 

 ment is now nearly always necessary to protect magnetic instru- 

 ments from the field of electric railroads (in America). 



In case the external field is uniform, the internal field is also. 

 We then have, if F is the strength of the external field, 



(17) 



In this case if /^//AI = 1000, and if the thickness of the cylinder 

 is only one-tenth of its outer diameter, the field within is reduced 

 to two per cent, of the value outside. The effectiveness of the 

 shielding is thus plainly shown. 



The total field is shown for this case in Fig. 78, for which 



This represents approximately the distribution of the lines of 

 force in a ring-armature of a dynamo. 



198. Magnetization of Hollow Sphere. The case of the 

 sphere may be treated in precisely the same manner as the case of 



