370-373] Steady Currents in continuous Media 331 



It is clear that at every point on the surface of a tube of flow, the current 

 is tangential to the surface. Thus no current crosses the boundary of a tube 

 of flow, from which it follows that the aggregate current flowing across all 

 cross-sections of a tube of flow will be the same. 



The amount of this current will be called the strength of the tube. 



Thus if C is the current at any point of a tube of flow, and if o> is the 

 cross-section of the tube at that point, then Ceo is constant throughout the 

 length of the tube, and is equal to the strength of the tube. 



There is an obvious analogy between tubes of flow in current electricity and tubes 

 of force in statical electricity, the current C corresponding to the polarisation P. 

 In current electricity, C<o is constant and equal to the strength of the tube of flow, 

 while in statical electricity Pa> is constant, and equal to the strength of the tube of force 

 ( 129). 



Specific Resistance. 



372. The specific resistance of a substance is defined to be the resistance 

 of a cube of unit edge of the substance, the current entering by a perfectly 

 conducting electrode which extends over the whole of one face, and leaving 

 by a similar electrode on the opposite face. 



The specific resistances of some substances of which conductors and insulators are 

 frequently made, are given in the following table. The units are the centimetre and 

 the ohm. 



Silver I'GlxK)- 6 . 



Copper 1-64 x 10 ~ 6 . 



Iron (soft) 9-83x10 ~ 6 . 



(hard) 9-06x10-6. 



Mercury 96'15xlO~ 6 . 



Dilute sulphuric acid (^ acid at 22 C.) 3'3. 

 (J acid at 22 C.) 1'6. 

 Glass (at 200 C.) 2'27 x 10 7 . 



(at 400 C.) 7-35 x 10 4 . 



Guttapercha, about 3 x 10 14 . 



If T is the specific resistance of any substance, the resistance of a wire of 

 length I and cross-section s will clearly be . 



Ohm's Law. 



373. In a conductor in which a current is flowing, different points will, 

 in general, be at different potentials. Thus there will be a system of equi- 

 potentials and of lines of force inside a conductor similar to those in an 

 electrostatic field. It is found, as an experimental fact, that in a homo- 

 geneous conductor, the lines of flow coincide with the lines of force or, in 

 other words, the electricity at every point moves in the direction of the 

 forces acting on it. 



