408 Induced Magnetism [CH. xn 



very small, shewing that the magnetisation had previously been nearly at 

 the point of saturation. 



Now if, as Weber supposed, the molecules of iron were already magnets 

 before being deposited on the silver wire, then any magnetic force sufficient 

 to arrange them in order on the wire ought to have produced a filament in 

 a state of magnetic saturation, while if, as Poisson supposed, the magnetism 

 in the molecules was merely induced by the external magnetic field, then 

 the magnetisation of the filament ought to have been proportional to the 

 original field, and ought to have disappeared when the field was destroyed. 

 Thus, as between these two hypotheses, the experiments decide conclusively 

 for the former. 



478. Weber's theory is illustrated by the following analysis. 



Consider a molecule which, in the normal state of the matter, has 

 its axis in the direction OP, and let 

 the field of force from the neigh- 

 bouring molecules be a field of in- 

 tensity D, the direction of the lines 

 of force being of course parallel to 

 OP. Now let an external field of 

 intensity H be applied, its direction 

 being a direction OA making an 

 angle a with OP. The total field 

 acting on the molecule is now com- 

 pounded of D along OP and // 

 along OA. FIG. 115. 



In fig. 115, let SO, OP represent H and D in magnitude and direction, 

 then SP will represent the resultant field, so that the new direction of the 

 axis of the molecule will be SP. Suppose that there are n molecules per 

 unit volume, each of moment m. Originally, when the axes of the molecules 

 were scattered indifferently in all directions, the number for which the 

 angle a had a value between a and a. + da. was ^n sin ada. These molecules 

 now have their axes pointing in the direction SP, and therefore making an 

 angle PSA (= 6, say) with the direction of the external magnetic field. 

 The aggregate moment of all these molecules resolved in the direction of OA 

 is accordingly 



\mn sin a cos 0da, 



and on integration the aggregate moment of all the molecules per unit 

 volume, which is the same as the intensity of the induced magnetisation /, 

 is given by 



r<t=ir 



I \mn sin a cos 6 da. (409). 



J a = 



