the tension of overhead wires supported by equidistant j)oles. 209 



The complicated form of the solution of the differential 

 equation renders it less convenient than the simple function 



V = ^\ — 2x 



for estimating the degree of convergence, although the former 

 is valid over a greater range and gives a closer approximation. 



Concluding Remarks. 



In the foregoing investigation we have treated the problem as 

 a statical one in which an equilibrium condition has been attained. 



The extent to which this supposition is permissible will depend 

 upon the circumstances of the break, and the rate at which energy- 

 is dissipated in the system. If the wire is suddenly cut the nearest 

 pole will initially be subject to a force equal to T, but this force 

 will quickly diminish before it has produced much effect in bending 

 the pole. 



In any case the dynamical problem appears too complicated to 

 lead to trustworthy results even if the purely mathematical diffi- 

 culties should be overcome. 



Another important point is the actual number of poles which 

 must be passed over, counting from the break, before the statical 

 tension T^ may be practically regarded as equal to T,^ or T. 



It is clear that this depends almost entirely on the value of K, 

 and n will be very large if K is nearly equal to unity. 



Q 



We may estimate the size of n by considering that -^ must be 



negligible in comparison with unity. If quantities less than e be 

 regarded as negligible then we must have 



That is n> 



It may perhaps be 

 value of Ti is given by 



C_ 

 log C — log e 



Jln< 



\og K 

 It may perhaps be worthy of note that a superior limit to the 



X f xY / xy 



T,<T^\-^-a,[j^j-a.,y-^j 



where 



2 



4f V7 l^rr^ 



x = - J Wi-v 



7(\/l-7 + l| 



