TO THE THEORY OF MAGNETISM. Ill 



of which the general integral is 



where /3 2 = ^ 7f > -^ an ^ ^ being two arbitrary constants. 



OOCL JL 



JV fff 



Determining these by the conditions = ^ -r -X"'" and 



-r X" we ultimately obtain 



3gf ( efto-e-P* \ 



- VP)| f 



But the density of the fluid at the surface of the wire, which 

 would produce the same effect as the magnetized wire itself, is 



- 

 dw 



~dd> I d z X 

 = ^L = _ _ a __ very nearly, 

 dr 2 dx* 



and therefore the total quantity in an infinitely thin section 

 whose breadth is dx, will be 



s , -, 



Tra -j-g- dx = -j-ff -- c . -fi - zr dx. 

 dx 4(1 ^) e^ A + e-p^ 



As the constant quantity f may represent the coercive force 

 of steel or other similar matter, provided we are allowed to sup- 

 pose this force the same for every particle of the mass, it is clear 

 that when a wire is magnetized to saturation, the effort it makes 

 to return to a natural state must, in every part, be just equal to 

 f\ and therefore, on account of its elongated form, the degree of 

 magnetism retained by it will be equal to that which would be 

 induced in a conducting wire of the same form by the force f, 

 directed along lines parallel to its axis. Hence the preceding 

 formulas are applicable to magnetized steel wires. But it has 

 been shown by M. BIOT (Traitt de Phy. Tome 3, Chap. 6) 

 from COULOMB'S experiments, that the apparent quantity of free 

 fluid in any infinitely thin section is represented by 



This expression agrees precisely with the one before deduced 



