570-573] Isotropic Conductor 497 



in which the line-integral is taken round the closed path, and the surface- 

 integral is taken over any area bounded by this closed path. We proceed as 

 in 533, and find that equation (525) is equivalent to the system of equa- 

 tions 



Idh\_ dft_d 

 C dt) dx dy ' 



These are the equations which must replace equations (473) (475) in 

 the most general case of current-flow. 



572. In addition we have the system of equations already obtained in 

 529, namely 



da dZ 87 

 etc 



dt dy dz ' 



in which all the quantities are expressed in electromagnetic units. If the 

 electric forces X, Y, Z are expressed in electrostatic units, we must replace 

 the right hand of this equation by 



'dZ dY' 



and the system of equations becomes 



-It^f-S (529) ' 



1 db = SX _ <)Z_ 

 C at dz dx 



_ldc_dY _dX 



Cdt'dx dy" 



The set of six equations, (526) to (531), form the most general system of 

 equations of the electromagnetic field. In these equations u, v, w, a, b, c, 

 a, ft, 7 are expressed in electromagnetic units, while /, g, h, X, 7, Z are 

 expressed in electrostatic units. 



EQUATIONS FOR AN ISOTROPIC CONDUCTOR. 

 573. In an isotropic medium we may put (cf. 128) 



4?r df _ K dX 



~c di~"c~di' e 



The values of u, v, w are also given in terms of X, 7, Z by Ohm's Law. The 

 electric forces, measured in electromagnetic units (the components of force 



J. 32 



