Influence of Masses of Iron, (^c. 447 



trifled bodies upon conductors ; which was first given by M. 

 Poisson, in tlie Memoirs of the Institute for 1811, and employed 

 by him to determine the development of the electric fluids in 

 spheres that mutually act on each other; an investigation to 

 which, 1 believe, it has been heretofore entirely restricted. 



Confining ourselves in this place to magnetic forces, the law 

 which 1 have here alluded to may be briefly deduced as follows : 



Conceive every particle of the given mass of iron, as contain- 

 ing equal quantities of the magnetic fluids ; it is then manifest 

 that they will, by their mutual actions, neutralize each other; and 

 the magnetism, thus reduced to a latent state, will be incapable 

 of producing any external effect by which its presence might be 

 detected. 



But on the approach of a magnet, this.state of equilibrium is 

 immediately disturbed ; the different fluids are repulsed or at- 

 tracted according as the predominant pole is of the same or a 

 contrary denomination ; the liberated fluids in their turn cause 

 a further displacement ; and a series of these successive actions 

 will go on until the developed magnetism is so distributed that 

 its action upon any particle is equal, and opposite, to that of the 

 disturbing magnet. 



In the case we are considering, the disturbing force is the la- 

 tent magnetism of the earth; which, from the distance of its 

 poles, may be considered as acting in parallel lines, and with equal 

 forces on all the particles of the mass : hence the condition which 

 we have deduced for the equilibrium of the fluids may be enun- 

 ciated as follows : 



If the latent magiietism of a mass of iron he developed ly the 

 action of the earth, it will recede to the iurfacc, and will there 

 form a very thin shell, whose nature is such, that its action in a 

 given direction is always equal to a certain constant quantity. 



To determine from this law the thickness of the shell at any 

 required point, is, in most instances, a problem that seems nearly 

 to surpass the powers of analysis : when however tlie given soHd 

 is a sphere, a case which is immediately connected with our pre- 

 sent inquiry, the solution may readily be obtained as follows : 



Let A N B S (fig. 6) be the given si)herc, of which the centre 

 is in O ; through O draw N S in the direction of the dijj, and 

 conceive an equal sphere A N'BS' to have its centre at O'j 

 wiiich is in the line N S, and at an infinitely little distance 

 from O. 



^'^%n the force with whicli any particle p, which is common 

 to the two sjiheres, is urged towards O, by the attraction of the 

 sphere A N B S, will vary as p O ; and towards O', by the at- 

 traction of A N' B S', will vary as p O'. Resolve this last force 

 into the two p i, i 0', at right angles to each other, and con- 

 ceive 



