270 Mr. J. Parker on the Theory of Magnetism and 



If both A and B be liquid or solid, we obtain 



(1 + iirk b )F b cos 6 b = (1 + 4rf )F. cos e a . 

 If A be air or any gas, and p be the mass density at P, 



(l + 49r*,)F,oostf, = (l + 4w*£.)F.cos0.. 



If A be a perfect " vacuum/' we put k a = 0. 



This result, which is even more important in electricity 

 than in magnetism, can be written in a very brief form. For 

 if F an , F bn be the normal components of ~F a and F 6 , and if /m a 



stand for 1 + ^irk a or 1 + ^irk a £- and fi b for 1 + 4tt& 6 , we have 



Po 



^K^^an (8). 



The foregoing is the usual method of stating the result; 

 but if we keep to the convention of supposing every normal 

 to be drawn outwards, we shall have 



Since for many substances k is very small (being less than 

 iocTooo )? ^ follows from the preceding investigation that the 

 abrupt change of the force in crossing the boundary of two 

 soft bodies may generally be neglected. Hence, if a number 

 of soft, feebly magnetic bodies be magnetized by permanent 

 steel magnets, we may suppose, without sensible error, that 

 the force at any point is entirely due to the permanent- 

 magnets; in other words, we may neglect the force due to 

 the magnetization induced in the soft bodies. This may also 

 be shown as follows: — Let B be any soft, feebly magnetic body. 

 Then the force at any point is the resultant of two forces — F b 

 due to B and F a due to the rest of the system. To make a 

 rough comparison between F b and F , we take the point 

 close to the surface of B, in which case it is evident that F b 

 is comparable with 27rl 6 , that is, with 27rk b F, or with the 

 resultant of 2'nk b F b along F b and 27r& & F a along F . Thus F b 

 is comparable with 27r& 6 F a , or if k b = mfi00 , with the 60,000th 

 of F ; and we draw the same conclusion as before. 



a 7 



Let us now suppose that a soft, feebly magnetic body B, 

 which is either a solid or a liquid contained in a bag, is 

 magnetized inductively by a permanent steel magnet situated 



