412 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XI. 



sphere, where they vanish, over the small sphere about P, where 

 we have as in 83, on making R decrease indefinitely, 



1 

 r n 

 and over the two sides of the diaphragm, where we have 



Since, however, dfl/dn is continuous, the first terms in the two 

 integrals cancel each other, the normals n^ and n 2 being in opposite 

 directions, and since 



dni dn. 2 



this becomes 



and finally 



(3) 



Since f^ H 2 = J we have 



so that the action of the current is the same as that of a magnetic 

 double-layer or shell of strength 



(5) d> = ^ = <k^ 



47T 4-7T 



This result was given by Ampere, by different reasoning. Experi- 

 ment shows that the magnetic forces are proportional to the 

 strength of the current, so that if A be a factor of propor- 

 tionality, 



r 



(6) Q P = AI - 



J J 0Hl 



