236 MAGNETISM 



may point out what would correspond to a permanent magnet in 

 the fluid illustration. 



A steel magnet in air would correspond to a larger pored 

 legion, and in the pores we should have to imagine small turbines 

 fixed, driving the liquid in a given direction. The turbines would 

 represent the magnetic molecules, and each turbine would have to 

 produce a flow proportional to the strength of the molecular pole. 

 As much fluid would be drawn in at one end of the region as was 

 driven out at the other, and the fluid would circulate back through 

 the surrounding space, the lines of flow rc-pn-s<-nting the lines of 

 force. 



Equations expressing continuity of potential and 

 continuity of induction tubes. We may conveniently term 

 the condition that the difference of potential between two points U 

 the same, whether we pass from one to the other through air or 

 through iron, the condition of continuity of potential, for it implies 

 that the potential is the same at two points quite close together, 

 one in air, the other in iron, and we may put the condition into the 

 following form : 



I^et PQ be two neighbouring points on the surface of the iron. 

 Let Hj be the intensity in the air close to PQ and let its din (lion 

 make 0j with the normal to the surface at 1\>. linn II, sin t\ 

 is the component of the intensity parallel to the surface in tin- air. 

 Let H 2 be the intensity in the iron close to PQ and let its 



direction make # 2 with the normal. 

 Then H t sin 6 t is the component of the 

 intensity parallel to the surface in the 

 iron. In order that the difference of 

 Fie. 182. potential between Pand <<) shall be the 



same in air and in iron, these com- 

 ponents must be the same in direction and equal in magnitude. 

 The first condition implies that H l and H t are in one plane with 

 the normal, while the second requires that 



II, sin flj = II 2 sin r 



We may conveniently term the condition that the flux of induction 



across a tube is constant, the condition of continuity of induction 

 tubes, and we may put it in the following form : 



Let Fig. 183 represent the section of a tube of induction enter- 

 ing the iron at PQ by the plane through the normal QM and the 

 line of induction in the air through Q. It passes through the line of 

 induction in the iron also, if we assume that the directions of 

 induction and intensity in the iron coincide, as they do in air. Let 

 #1 2 be the angles which the direction of the induction makes 

 with the normal in the two media. Let QR PS represent cross- 

 sections of the tube in the two media, the breadth of the tube 

 perpendicular to the paper being the same in each. The con- 



