5(>6 Prof. Morton on the Propagation of Polyphase 

 if n is odd it is 



n — \ ir \ —2 cos q* 





If n = 2 we have the two-wire case and ?;.= !; In general, 

 the distance of the equivalent pair of wires is tjX the diameter of 

 the circumscribing circle. 



5, The following table gives the values of rj for the different 

 modes, from n = 2 to n=12 : — 



n = 

 q=\ 



2 



3 



4 



5 



6 



7 



8 

 3-48 



9 



5 08 



10 



7-50 



11 



11-2 



12 



1-00 



0-866 



100 



1-28 



1-73 



243 



16-9 



2 







0-500 



0-437 



0-433 



0-457 



0-500 



0-561 



0-640 



0-741 



0-866 



3 











0333 



0-299 



0-288 



0-289 



0-298 



0-313 



0-333 



4 















0-250 



0-228 



0-218 



0-215 



0-217 



5 



















0-200 



0-186 



0-177 



G 























0-167 



In fig. 1 these values of rj are plotted against the number 

 of wires. Points which correspond to modes of the same 

 order are joined by a curve — of course the intermediate 

 points on these curves have no physical meaning. 



6. Inspection of the diagram or of the table brings out the 

 following points. The values for the first mode, or that in 

 which there is the smallest phase-difference between consecu- 

 tive wires, become rapidly much greater than the values for 

 the other modes. We shall see that this means a smaller 

 value for the attenuation-constant of the waves* 



The new mode which makes its appearance at each even 

 value of n corresponds to phase-difference it between successive 

 wires. This case was worked out in the former paper, and 



has 7]— k. The same value of tj reappears when the number 



of wires is doubled — the magnitude, for intermediate numbers, 

 first decreasing and then increasing. The physical reason for 

 this repetition of the same speed and attenuation is obvious. 

 With the doubled number of wires the corresponding mode 



IT 



has phase -difference ^ , and the arrangement admits of being 



broken up into halves. Each half has phase-difference tt and, 

 from symmetry, they have no inductive influence on each other. 

 It is only when n is a multiple of 4 that this division into 

 independent half-systems is possible. 



