308 Prof. W. B. Morton on the 



To obtain numerical values it is necessary to assume a 



particular value of - . I have taken this as 100, and have 



calculated arg. m by aid of Aldis's tables. The result is 

 shown in the curve marked (ot-0) on fig. 1. The addition 

 o£ the two curves obtained gives the a-curve, showing the 

 phase-difference between R and Z. 



To form an idea of the position on this diagram of actual 

 experimental cases, we may take those given in Sommerfeld's 

 paper as extreme cases in opposite directions. His first case, 

 typical of skin-conduction and very small attenuation, is that 

 of copper wire of 4 mm. diameter with frequency of 10 9 

 alternations per sec. This gives 135 S as the value of 



2a\/ l J L Tr P an( j so li es f ar ou t to the right, where a and j3 

 V p 



are both practically 45°. 



His other extreme case is that of platinum wire of 



0*004 mm. diameter and a frequency of 3 x ]0 8 . This gives 



0'256 for the determining constant ; a comes on the inner 



side of the minimum position for a. 



The quantity (a — /3)=arg. m=tan —1 — is, for small 



values at least, proportional to the attenuation with given 

 wave-length. It runs down to zero with increasing develop- 

 ment of surface- conduction, towards the right in the diagram. 

 Looking now at the state of things just inside the wire we 

 have of course the same phase-difference as before between 

 H and Z. For R the advance of phase on Z is from 

 equations (5) 







7T 



= ~2 +arg * 



m— arg. 



# 2 + arg. 



Ji 



Jo' 







3tt 



. m— arg 



Ji 









7T 









or 



the 



radial electric force 



inside is 



90°°behind that outside. 



§4. Directions of the Lines of Force and of Energy-flow 

 at the Surface of the Wires. 



It is easy to see that when Z and R have opposite signs 

 the lines of force are tilted backwards ; when H Z are oppo- 

 site the energy-flow is outward ; and when H^R are opposite 

 the flow is backward. Taking, then, a half wave-length 



