THE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



APRIL 1855. 



XXXVI. Elementary Demonstrations of Propositions in the 

 Theory of Magnetic Force. By Professor W. Thomson*. 



Def. 1. f I MIE lines of force due to any magnet or electro- 

 -i- magnet, or combination of magnets of any kind, 

 are the lines that would be traced by placing the centre of gra- 

 vity of a very small steel needle, perfectly free to turn about this 

 point, in any position in their neighbourhood, and then carrying 

 it always in the direction pointed by the magnetic axis of the 

 needle. 



Remark. Except in the cases of symmetrical magnets, the 

 lines of force will generally be lines of double curvature, and no 

 set of them will lie in one plane. 



Def. 2. The lines of component force in any plane are the 

 lines traced by placing the centre of gravity of a steel needle 

 anywhere in this plane, and carrying it always in this plane in 

 the nearest direction to that pointed by its magnetic axis ; that 

 is, the direction of the orthogonal projection of the magnetic 

 axis on the plane ; or the direction that the steel needle would 

 point with its magnetic axis if placed with it in the plane, and 

 free to turn about an axis through its centre of gravity perpen- 

 dicular to the plane. 



Prop. I. If the line of component magnetic force thrpugh any 

 point in a plane be curved at this point, the forcj will vary in a 

 line perpendicular to the line of force in its plane, increasing in 

 the direction towards the centre of curvature. 



Let EABF be a line of component force in the plane of the 

 diagram, and let GCDH be another near it, each and all between 



* Communicated by the Author. 



Phil. Mag, S. 4. Vol. 0. No. 59. April 1855. R 



