TERRESTRIAL MAGNETISM. 189 



the Intensitas Vis Magneticce, S^c, for our positive fundamental 

 unity, that quantity of northern fluid which at the unit of di- 

 stance exercises on an equal quantity of the same fluid a moving 

 force equivalent to what we assume as unity. 



When we speak of the magnetic force which in any point of 

 space is produced by the action of the magnetic fluid elsewhere, 

 we always mean to speak of the moving force which is there ex- 

 ercised on the unity of the positive magnetic fluid ; therefore in 

 this sense the supposed magnetic fluid /x concentrated in a point 



exercises at the distance p the magnetic force —g, of either repul- 



r 



sion or attraction in the direction p, according as fx. is positive 

 or negative. Representing by a, b, c, the co-ordinates of fi in 

 relation to three rectangular axes, and by x, y, and z, the co-or- 

 dinates of the point where the force is exercised, so that 



p= ^{\x-aY + {y-by--^ {^-cY); 

 and resolving the force in parallels to the co-ordinate axes, the 

 components ai-e 



fj'{x-a) fj'jy -b) pA^- c) 

 p^ ' p^ ' p^ ' 

 which, as is easily seen, are equal to the partial differential co- 

 efficients of — — relatively to x, y, and z. 



If besides p., there are also in operation other portions of the 

 magnetic fluids pJ, p.", p."', &c., concentrated in points, of which 

 the distances from the spot where the force is exercised are p', 

 p", p'", &c., then the components of the whole resulting mag- 

 netic force, parallel to the co-ordinate axes, are equal to the 

 partial differential co-efficients of 



relatively to x, y, and z. 



Hence may easily be shown what magnetic force is exercised 

 in each point of space by the earth, however the magnetic fluids 

 may be distributed therein. Imagine the whole volume of the 

 earth, as far as it contains free magnetism (that is to say, sepa- 

 rated magnetic fluids), to be divided into infinitely small ele- 

 ments ; designate generally the quantity of free magnetic fluid 



VOL. II. PART VI. N 



