ON PHYSICAL LINES OF FORCE. 459 



We have now to interpret the meaning of each term of this expression. 



We suppose a, /8, y to be the components of the force which would act 

 upon that end of a unit magnetic bar which points to the north. 



fi represents the magnetic inductive capacity of the medium at any point 

 referred to air as a standard, /xa, fj.j3, p.y represent the quantity of magnetic 

 induction through unit of area perpendicular to the three axes of x, y z 

 respectively. 



The total amount of magnetic induction through a closed surface surrounding 

 the pole of a magnet, depends entirely on the strength of that pole ; so that 

 if dxdydz be an element, then 



(-T-/ta + -i-/iij6 + -T- py } dxdydz=kirm dxdydz ............ (6), 



-i- -T- 



which represents the total amount of magnetic induction outwards through the 

 surface of the element dxdydz, represents the amount of "imaginary magnetic 

 matter" within the element, of the kind which points north. 



The first term, of the value of X, therefore, 



d d d 



-J- PP + 'I' 

 dy r dz 



may be written 



am .......................................... (8), 



where a is the intensity of the magnetic force, and m is the amount of mag- 

 netic matter pointing north in unit of volume. 



The physical interpretation of this term is, that the force urging a north pole 

 in the positive direction of x is the product of the intensity of the magnetic 

 force resolved in that direction, and the strength of the north pole of the magnet. 



Let the parallel lines from left to right in fig. 1 represent a field of mag- 

 netic force such as that of the earth, sn being the direction from south to north. 

 The vortices, according to our hypothesis, will be in the direction shewn by the 

 arrows in fig. 3, that is, in a plane perpendicular to the lines of force, and 

 revolving in the direction of the hands of a watch when observed from s 

 looking towards n. The parts of the vortices above the plane of the paper 

 will be moving towards e, and the parts below that plane towards w. 



582 



