Treatment of Electrodynamics. 279 



are a collection of molecular circuits, the same formulae are 

 applicable to them, and the usual deductious as to magnetic 

 moments, the Grauss positions, <fec, can be made. 



This, however, leads to the question o£ the field in the 

 interior of a magnet. The total field there varies from point 

 to point, very rapidly and irregularly; but the average is 

 constant, and is called the magnetic induction ; while the 

 term " field " is usually restricted to that part of the total 

 effect which is not due to currents in the immediate neigh- 

 bourhood of the point considered. The usual procedure is 

 to elucidate (?) this distinction by considerations about a 

 tube or crevasse in the interior of the iron ; an argument in 

 the highest degree artificial, and very commonly unintelligible 

 to students. It is also quite unnecessary, as may be seen 

 from the following : — 



To determine the magnetic induction in the interior of a 

 magnet. Let the magnet be of 1 square cm. cross-section, and 

 infinitely long. Let there be m circuits per cubic centimetre, 

 each of a small area A with current i circulating in it ; and 

 let x De the angle between the axis of one of these circuits 

 and the axis of the magnet. Then the moment of this circuit, 

 resolved in the length of the magnet, is i A cos x (which may 

 be positive or negative), and the intensity of magnetization of 

 the bar (or magnetic moment per c. c.) is mi A. cos^=L 



N"ow consider a straight line drawn at random down the 

 length of the magnet. This will cut through some of the 

 molecular circuits, and the number of those cut will bear to 

 the total the ratio of the projected area of a circuit A cos% to 

 the area of the bar, or unity. The number cut is therefore 

 mA cos X- Hence, by the first circuital relation the average 

 change of magnetic potential per unit length is 



4z7r i m A cos x — 47rl. 



This is in addition to any rate of change of magnetic 

 potential due to outside causes, say H. Hence we have, for 

 the magnetic induction (per square cm.) as defined above — 



B=H + 4ttI. 



The same argument, applied to a bar of finite length, gives, 

 in the simplest possible manner, the relation between field 

 and induction, in that case, i. e. the " demagnetizing effect of 

 the ends." 



To deal with the induction of currents, we will take, first, 

 an element of a circuit moved at right angles to itself, in a 

 magnetic field. Let the wire —of length dl — lie in the 



U2 



