310 CONSTITUTION OF MAGNETS. 



A line of induction is a line to which the force of induction is 

 tangential at every point ; a tube of induction is a channel bounded 

 laterally by lines of induction ; lastly, flow of induction across an 

 element of surface is the product of the surface of the element by 

 the perpendicular component of induction. Since induction satis- 

 fies Laplace's equation for all internal and external points, it follows 

 that the flow of induction is a constant quantity throughout the 

 whole extent of a tube of induction. 



325. DIFFERENT KINDS OF MAGNETS. We may divide mag- 

 nets into distinct categories, according to the manner in which the 

 intensity of magnetisation varies. 



326. MAGNETIC SOLENOIDS. A simple solenoid is a magnet in 

 the form of a filament with an infinitely small constant section, at 

 each point of which the intensity of magnetisation is itself constant 

 and tangential to the direction of the filament. 



The magnetic density is zero throughout the whole mass of the 

 filament and on its lateral surface (310) ; at the ends only are two 

 equal and opposite magnetic masses ; if I is the strength of mag- 

 netisation and a the section of the filament, the absolute value of 

 these two masses is 



This product a\ maybe called the magnetic power vt the solenoid. 



If, while the section of the filament, and the intensity of the 

 magnetisation are variable, the product a\ remains constant, the 

 system will still form a simple magnetic solenoid. 



A simple solenoid acts on all external points as would a magnet 

 whose poles were exactly at the ends. 



The potential at a point P (Fig. 74), at a distance r z from the 

 positive pole A 2 , and at a distance r from the magnetic pole A 15 is 

 thus expressed, 



