by  a  Break  in  an  Overhead  Wire  carried  on  Poles.       637 
from  the  next  anchor-pole.     Call  the  deflexions  on  one  side 
of  the  break  x1  ....  xn,  and  on  the  other  y1  . . . .  ym,  Xn  ym  being 
on  the  two  sides  of  the  break,  and  x's  and  ?/'s  being  measured 
away  from  the  break  on  both   sides.     Let  s  represent  the 
„       . .       number  of  wires  remaining 
traction -, — — ^ ^. 
number  originally  on 
The  equations  giving  the  («  — 1)  ratios  o£  #'s  and  (m  —  1) 
ratios    of    ?/'s    are    the    same    as    those    already    got.     The 
connecting  equations  which  determine  the  actual  magnitudes 
are 
{a  —  1  +  s)  xn  -  xn  _  i  +  sym  =  b  (1 .  -  s) 
=  (a—  1  +  s)ym—ym_1  +  sxn. 
The  quantities  a  and  b  have  their  former  meanings,  T  and  w 
which  occur  in  them   referring  to  the  whole  set  of  wires  and 
not  to  a  single  wire. 
We  have     ,       _, .  ,       ., 
{a—l)xn-xn_1={a-\)ym-ym^1. 
So  that  the  ratios  of  the  deflexions  on  the  opposite   sides  of 
the  gap  are  independent  of  the  number  of  wires  broken. 
If  the  break  is  sufficiently  distant  from  both  ends  of  the 
row  so  that  we  may  use  the  limiting  value  for  — 3-  and  - — — >. 
we  get  *»  y™ 
26(1-*) 
xn  — ym  —         -      -     -       /— - —  • 
a  —  l  +  ^s  +  ^a*  —  ^ 
Coming  now  to  the  application  of  our  results  to  the  actual 
case  referred  to,  we  have  the  following  data  from  which  to 
calculate  the  constants  a  and  b. 
Number  of  wires  6. 
Tension  of  each  wire  1000  lbs. 
Weight  of  each  wire  *42  lb.  per  foot. 
Distance  between  consecutive  poles  100  yards. 
A  test  of  the  stiffness  of  a  pole  showed  that  a  deflexion  of 
3  ins.  was  caused  by  a  force  of  800  lbs.  applied  to  the  top  in 
a  horizontal  direction. 
From  these  values  we  calculate 
a=2-21, 
6=0-40, 
the  units  being  lbs.  and  feet. 
The  following  table  gives  the  calculated  deflexions  in  £eet 
