216 MAGNETISM 



field, and if the magnet is turned round so that its axis is perpen- 

 dicular to the lines of force, the couple acting on it is MH. 



Though we thus imagine two "centres of polarity/' it is to be 

 remembered that a distribution of matter, or of electricity, or of 

 magnetism, cannot be replaced by a concentration at a single point 

 in calculating the field which is produced. 



Comparison of moments. We may compare the moments 

 of two magnets of small dimensions to a first approximation by 

 using the value for the field at a distance d from the cent. IT along 

 the axis, 



2 ml 2 M 



For this purpose we may bring up the two magnets, one east and 

 the other west of a suspended needle, and placed so that they tend 

 to deflect the needle in opposite directions ; then adjusting them a! 



distances d l and d 2 so that the needle is not deflect. 



?-$ 



- 



Or we may use each in succession to deflect the needle at the same 

 distance. If the deflections be 1 and 2 rcsp,-cti\ely. the earth's 

 horizontal intensity l>eing H, 



tan t 



tan f = 





Some consequences of the inverse square law. 

 Application of Gauss's theorem. Flux of force. As all 

 experiments go to show that the intensity at any point <>t I 

 magnetic field in air or in any other non-magnetic medium may 

 be regarded as due to each element of polarity (hn acting according 

 to the law rfw/;- 2 . we may apply (iaiiss\ theorem (p. JW) ' 

 magnetic system. If we define the flux of force through an 

 element of surface dS as NJS, where N is the component of the 

 intensity perpendicular to r/S, the theorem tells us that the total 

 flux offeree through any closed surface, which is entirely in air or 

 other non magnetic medium, is /ero. For the total polarity within 

 the surface, even if it encloses magnets, is /ero. 



