40 Report 8. A. A. Advan'.cemknt of Sciknce. 



strenijtli uf the oun-ent imiltij'lied by tlie solid angle subtended l)y the 

 circuit in which it tlows. 



Tt then follows, by consideriiiu the changes of magnetic potential 

 along any closed path, that 



the first circuital relation of electrodynamics. 



At tliis point it is convenient — still considering non-magnetic 

 media — to calculate the field in t!ie iiiteiior of a solenoid, either 

 infinitely long or finite, and, if desired, to calculate the forces and 

 couples exerted on circuits — plain or solenoidal -when place<l in a 

 magnetic field 



It may then be pointed out that, on the view that magnets area 

 collection of molecular circuits, the same formulae are applicable to 

 them, and the usual deductions as to magnetic moments, the (4auss 

 positions, ikc, can be made. 



This, however, leads to the ijuestion of 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 constaJit, and is called the 

 )nagnetic induction; while the term "field"' is usually restricted to 

 that part of the total effect which is not due to currents in the 

 immediate neighbourhood of the point considered. The usual proce- 

 dure 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 veiy commonly unintelligible to students. Ft is 

 also (juite unnecessary, as may be seen from the following : — 



To determine the magnetic induction in the interior of a inagnet. 

 Let the magnet be of 1 sfjuare 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 \' be the angle between the 

 a.xis of one of tliese circuits and the axis of the magnet. Then tlie 

 mo)nent of this circuit, resohed in the length of the magnet, is ; A cos ■)(^ 

 (which ma}' be positive or negative), and the intensity of magnetisation 

 of the bar (or magnetic moment pei* c.c.) is mi Acvw^ = 1. 



Now consider a straight line diawn at random down the length 

 of the magnet. This will cut ihrough som(^ of the moU^cnlar circuits, 

 and the numbei- of those cut will bear to the total the ratio of the 

 projected area of a circuit A ros -^ to the area of tlie bar, oi- unity. 

 Tlie number cut is therefore m A cv.s-^. Hence, iiy the first circuital 

 relation the aveiage change of magnetic potential per unit length is 



4 TT I "i A cos ])( = 4 TT I . 



'J1iis is in addition to any rate of change of magnetic potential 

 due to outside causes, say H. Henc«' we have, for the magnetic 

 induction (per sijuare cm.) as defined above — 



B = H + 1 TT L 



'I'he sanie argument, apjilied to a })ar of finit(» length, gives, in the 



