Magnetized Non-crystalline Substances. 243 



that it vanishes if P be in a plane through P at right angles 

 to the line of those two directions. Hence it follows that the 

 resultant force upon the small sphere is along that line, in one 

 direction or the other, according as ju, is positive or negative, 

 and accordingly we draw the following conclusions : — 



(1.) A small ferromagnetic sphere, in the neighbourhood of 

 a magnet, will experience a force urging it in that direction in 

 "which the " magnetic force " increases most rapidly. 



(2.) A small diamagnetic sphere, in the neighbourhood of a 

 magnet, will experience a force urging it in that direction in 

 "which the magnetic force decreases most rapidly. 



(3.) The absolute magnitude of the force in any case in which 



the distribution of magnetic force in the neighbourhood of the 



magnet is known, is the value which the expression in § 1 ob- 



R' 2 — R 2 

 tains when we give the value found by means of the 



differential calculus, for a point P at an infinitely small di- 

 stance PP' in the direction of the most rapid variation of the 

 magnetic force from P, the actual position of the ball. 



4. It is deserving of special remark, that the direction of the 

 force experienced by the ball has no relation to the direction 

 of the lines of magnetic force through the position in which it 

 is placed. The mathematical investigation thus affords full 

 confirmation and explanation of the very remarkable observa- 

 tion made by Faraday (§ 2418), that a small sphere or cube 

 of inductively magnetized substance is in some cases '* urged 

 along, and in others obliquely or directly across the lines of 

 magnetic force." It is in fact very easy to imagine, or actu- 

 ally to construct, arrangements in which the resultant force 

 experienced by a ball of soft iron, or of some diamagnetic 

 substance, is perpendicular to the lines of the magnetizing 

 force. For instance, if a ball of soft iron be placed symme- 

 trically with respect to the two poles of a horseshoe magnet, 

 and at some distance from the line joining them, it will be 

 urged towards this line, in a direction perpendicular to it, 

 and consequently perpendicular to the lines of magnetizing 

 force in the space in which it is situated ; and a ball of bis- 

 muth, or of any other diamagnetic substance, similarly situated, 

 would experience a force in the contrary direction. Or again, 

 if a ball of any substance be placed in the neighbourhood of 

 a long straight galvanic wire, it will be urged towards or from 

 the wire (according as the substance is ferromagnetic or dia- 

 magnetic) in a line at right angles to it, and consequently 

 cutting perpendicularly the lines of force, which are circles with 

 their centres in the wire and in planes perpendicular to it. 



5. The preceding conclusions enable us to define clearly the 



R2 



