G14 Prof. W. B. Morton on some Cases of Propagation 



We may indicate these arrangements by the notation (1234), 

 (12) (34), (13) (24), (14) (23), numbers enclosed in one 

 bracket indicating similar wires which are opposite to the 

 wires in the other bracket. The wires in this and the re- 

 maining cases are identical in size and material. All the A's 

 and fs are equal, and B 13 = B 34> B 13 = B 24 , B 14 =B 23 . The 

 determinant is 



A- 



/ 



B 



12j 



B12, 

 B13, 

 Bl45 



A- 



/ 



14; 



B 

 B 13 , 



Bl3; 



B K , 



A- 

 Bio 



/ 



Bl4, 



B 13 , 

 B 12 , 



A-/ 



(25) 



= (a-^+b 1s +b 1i +b 11 )(a-^+b„-b 1 ,-b m ) 



x(A-^-B 12 + B 13 - 



/ 



B w )(a-£-B 1s ,-B 1s +B^ 



Taking the factors in turn, and finding the corresponding 

 ratios for the D's, we find r — 



Di= D 2 = T) 3 = D 4 grouping (1234) 7 

 D 1= D 2 =-D 3 --D 4 ' „ (12) (31) 



IV=-D 2 = D 3 =-D 4 „ (13) (24), 



D 1= _D 2 =-D 3 = D 4 , ,, (14) (23). 



For the first case, where the wires are similar, we get an 

 equation which can bi reduced to SommerfekPs x log x type, 

 viz.-: — 



/ 



= loff. 



16 



(26) 



The other cases give simple equations of the two-wire type, 



e. g. for (12) (34):- 



/ i h 3 b 14 



— =lo°" . 



c' 2 & a b 12 



(27) 



Thus Avhen the oscillations are propagated along four wires 

 in ,rectangular arrangement, two wires serving as returns to the 

 other two, the speed and tJie attenuation are the same as if we 



had two wires at distance — -, ; i. e^ the rectangle behceen 



