of Elect vie Oscillations along Parallel Wires. G13 



§ 8. Three Wires in Isosceles Triangle. 

 Use 1 for the vertex wire, 2, 3 for the base wires. Let the 

 base wires have the same radius and material, then B 12 = B 13 , 

 A 2 = A 3 ,/ 2 =/ 3 . The determinant equation becomes 



A & 



B12, 



Bl2, 



B ]2 , B 12 , 

 A — -^ B 



"R A — /2 



•D23? ^2 "oj 



= 0. 



(22) 



Subtracting the third column from the second we see that 



f 

 A<> — B 9 ,— - 2 , is a factor 



/ 



Using this root of the equation, 

 b 



f =A 3 -B 23 =log 



(23; 



•here b is the length of the base. Putting in the value for 



- in the equations 



we get at once 



D x =(), D s =-D 8 (24) 



Therefore we have got the case in which the base wires 

 are carrying equal and opposite currents, and the vertex wire 

 is quite free from current. The equation for c 2 is the same 

 as if there were no third wire. The remaining two roots of 

 the cubic in c 2 correspond to the cases where the base wires 

 are similar, and either opposite or similar to the vertex wire. 

 The equation for these arrangements is intractable. 



We infer from the above that when two wires are con- 

 veying electric oscillations, a third wire equidistant from them 

 plays a passive part. It follows at once that if we have two 

 pairs of wires at the corners of a, rhombus there will be no 

 mutual influence between the pairs. For example, telephone- 

 messages sent along the pair at the ends of one diagonal of the 

 rhombus will not be overheard along the other pair. 



When the triangle is equilateral we can have currents, 

 whose algebraic sum is zero, divided among the wires in any 

 manner. 



§ 9. Four Wires in Rectangular Arrangement. 



In this case we can split up the determinant into four 

 factors corresponding to the four ways of grouping the wires. 



