ELECTROMAGNETIC THEORY OF LINES AND SHIELDS 533 



theory, thereby gaining all the simplicity of the latter combined with 

 all the accuracy of the former. 



Circularly Symmetric Electromagnetic Fields 

 In polar coordinates, Maxwell's equations assume the following 

 form : 



7a^ - ^ = (« + "")^" 

 ^' - ^' = fe + i-)£., 





dE, 



dz 



dE, 



dp dip 



djpE^) _ dEp 



dp d(p 



dp 



= (g + io:e)E^, 



= — ioip-H^, 



(1) 



where E and H are respectively the electromotive and magnetomotive 

 intensities.' 



In general, all six field components depend upon each other. If, 

 however, these quantities are independent of either tp or z, the partial 

 derivatives with respect to the corresponding variable vanish and the 

 original set of equations breaks up into two independent subsets, each 

 involving only three physical quantities. Each of these special fields 

 has important practical applications. 



In the circularly symmetric case, that is, when the quantities are 

 independent of ^, one of the independent subsets is composed of the 

 first and the third equations on the left of (1), together with the second 

 on the right: 



d{pH^) 

 dp 



(g + icc€)pE„ 



dE. dEn 



dH, 

 dz 



= - (g + io:e)Ep, 



(2) 



dp 



dz 



= ioijxH^. 



This circular magnetic field, with its lines of magnetomotive intensity 



^ In this paper we have adopted a unified practical system of units based upon 

 the customary cgs system augmented by adding one typically electric unit. This 

 system has three obvious advantages: first, theoretical results are expressed directly 

 in the units habitually employed in the laboratory; second, the dimensional character 

 and physical significance of such quantities as io>ix and g + io^e are not obscured as 

 in other systems by suppressing dimensions of some electrical unit such as permea- 

 bility or dielectric constant; and third, the form of electromagnetic equations is very 

 simple. In this system of units the electromotive intensity E is measured in 

 volts/cm., the magnetomotive intensity H in amperes/cm., the intrinsic conductance 

 g in mhos/cm., the intrinsic inductance ix in henries/cm., and the intrinsic capacity e 

 in farads/cm. Thus, in empty space /x = 47rl0~^ henries/cm. or approximately 

 0.01257 nh/cm. and e = (l/367r)-10~" farads/cm, or approximately 0.0884 mmf./cm. 



