On the Dimensions of the Magnetic Pole. 395 



portion of the body of an inhabitant of the most distant 

 member of the universe. But whichever way we consider the 

 subject in the light of the facts which we have stated, it is full 

 of unusual difficulty, and is singularly devoid of accurate 

 experimental data. 



XLIII. On the Dimensions of the Magnetic Pole 

 in Electrostatic Measure. 



To the Editors of the Philosophical Magazine and Journal. 

 GrENTLEMEN, 



I HA YE had the honour of reading a letter upon the di- 

 mensions of the magnetic pole in electrostatic measure 

 which Dr. Lodge addresses to you this month. His sugges- 

 tion seems to me to reconcile the views of Prof. Clausius and 

 Mr. J. J. Thomson on this subject. A model of the maguetic 

 system must be made in a substance of the same magnetic 

 permeability as the medium that is to surround the current- 

 system, and must be substituted in the place of the magnets, 

 before any comparison can be effected. The two systems, 

 cm-rent- and magnetic, will then be always equivalent if once 

 equivalent. 



Dr. Lodge treats this as a suggestion ; but I think it is 

 almost susceptible of demonstration. According to Weber's 

 law. a current flowing in a closed circuit can be replaced by a 

 simple magnetic shell of which the edge coincides with the 

 circuit. The shell maybe as thin as we please; but its strength 

 must have a definite value. This law we only know to be true 

 for air. Consider any equipotential surface of the positive 

 magnetism on one face of the shell, at a distance from it infi- 

 nitely smaller than the thickness of the shell. It passes through 

 the substance of the shell, issuing at the edges, and covers the 

 positive face. Similarly such an equipotential surface of the 

 negative magnetism on the other face passes through the 

 substance without cutting the former surface, and covers the 

 negative face. 



If on each of these surfaces toe spread a surface-magnetism 

 of which the density is the quotient of the magnetic force by 4-7T, 

 then for all points outside the pair of surfaces and the shell ice 

 may replace the latter, and therefore its equivalent current- 

 system, by the magnetic coats upon the equipotential surfaces. 



Now consider any diaphragm, S, completely enclosing these 

 surfaces and the shell. If instead of air we substitute a me- 

 dium of magnetic permeability /j, throughout space outside S, 

 a surface-density cr is developed upon S. But the equipoten- 

 tial surfaces and the coats of magnetism thereon are not 

 affected bv this development ; for thev relate onlv to the en- 

 2D2 



