904 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1952 



if necessary by making tir and/or \iir complex. In MKS units we have 



t2 = e2rCD , M2 = M2rM« > (81) 



where the electrical constants of vacuum are 



12 



e„ = 8.854 X 10"'' farads •meter~\ 

 /x„ = 1.257 X 10~ henrys • meter" . 



(82) 



It follows that 



•" = <" V«,.. = ^;— = 299.8 ""'^'' ' (83, 



V2 



= Vv^/n2r/e2r = 376.7\/M2r/e2r ohmS, 



where as usual the subscript v refers to vacuum. It is clear that unless 

 we deal with ferromagnetics, the quantities ao and rjo will be of roughly 

 the same order of magnitude as a-„ and tjv ■ From (56) and (69) we have 



K2 = 0-2(1 — 7 /<^2y, 



, o . (84) 



/I 2/ 2x| ^ ^ 



T?2j/ == r?2p = 7?2(1 - 7 /0-2) , 



where since 0-2 and 7 are both of the same order of magnitude as 2-Ki/\v , 

 in general no further approximations can be made. 



In all of what follows we shall assume that the thickness to of each 

 insulating layer is very small compared to the vacuum wavelength at 

 the highest operating frequency ; in practice h will be at most a few mils 

 and Xi, at least a few meters. Then the quantity | ^2^2 |, which is of the 

 order of 2irt2/'Kv , will be so small that to an excellent approximation we 

 may set sh K2/2 = '<2^2 and ch ^2^2 = 1- Using this simplification, together 

 with the fact that 771^ « r]2y for all frequencies which may concei^'ably 

 be of interest, it is not difficult to show from (58) that the matrix ele- 

 ments of the plane double layer reduce to 



a = ch Kiti , 



(S> = V2yK2t2 ch Klf\ + Viy sll K'l^i , 



e = — sh Klh , (^^) 



3D = '?^%h .1^ + ch .1/1 . 



The determinant of the matrix is unity, and from (61) the propagation 

 constant per section is defined by 



