﻿298 
  Dr. 
  Kussell 
  and 
  Mr. 
  Wright 
  : 
  The 
  Wright 
  Electrical 
  

  

  points 
  are 
  equal, 
  and 
  so 
  the 
  differences 
  of 
  their 
  potentials 
  

   from 
  that 
  at 
  are 
  equal, 
  and 
  thus 
  we 
  find 
  that 
  

  

  Cir-tC2(r/10) 
  + 
  C,(r/100) 
  

  

  = 
  Cr 
  + 
  Ci 
  V 
  + 
  C/Cr/lO) 
  + 
  G/{r 
  /lOO) 
  . 
  

   Hence 
  

  

  c 
  = 
  Ci 
  + 
  cyio 
  + 
  C3/100 
  - 
  (0/ 
  + 
  C2V10 
  + 
  C37100). 
  

  

  Let 
  E 
  be 
  the 
  potential 
  of 
  R, 
  and 
  Vj 
  the 
  potential 
  of 
  P. 
  

   and 
  Qi 
  (fig. 
  6). 
  Then, 
  if 
  V^, 
  V3, 
  Y^', 
  Vs^ 
  be 
  the 
  potentials 
  

   or 
  P2, 
  P3J 
  Q25 
  and 
  Q3, 
  and 
  pi, 
  ^2, 
  Ps; 
  qi, 
  92^ 
  gz, 
  and 
  x 
  be 
  the 
  

   readings 
  on 
  the 
  scales 
  of 
  the 
  slide 
  resistances 
  in 
  the 
  branches 
  

   RPi, 
  RP2, 
  &c., 
  we 
  have 
  

  

  (E-v).^ 
  = 
  (E-yopi+(E-V2)(i?2/io)+ 
  (E-y3)(j93/ioo) 
  

  

  -{(E-VOgi 
  + 
  (E-V/)fe/10) 
  

  

  ,. 
  , 
  +CE-V3')teA00)}; 
  

  

  and 
  thererore 
  

  

  X 
  = 
  ;9i+p2/10+^3/100 
  + 
  A^-(giH-^2A0-f 
  ^3/100 
  + 
  A,), 
  

   where 
  

  

  and 
  

  

  ^p- 
  E-Vi*10"^E-Vi-100' 
  

  

  A 
  -Ji^ll 
  92,Yi^Jl 
  g^ 
  

   ^?- 
  E-Vi 
  '10 
  "^ 
  E-Vi 
  '100' 
  

  

  The 
  readings 
  pi 
  and 
  qi 
  on 
  the 
  scales 
  cannot 
  be 
  less 
  than 
  1, 
  

   and 
  the 
  readings 
  p2, 
  pzi 
  ^'2? 
  and 
  ^3 
  cannot 
  be 
  greater 
  than 
  10. 
  

   Hence, 
  remembering 
  that 
  (Vi 
  — 
  V2)/(E 
  — 
  Yj) 
  cannot 
  be 
  greater 
  

   than 
  (Y-Y3)/(E-Yi), 
  we 
  see 
  that 
  if 
  (Yi-Y3)/(E-Yi) 
  be 
  

   equal 
  to 
  or 
  less 
  than 
  1/53, 
  Ap 
  is 
  not 
  greater 
  than 
  the 
  hundredth 
  

   part 
  of 
  Pj 
  +P2/IO 
  4-i93/100. 
  Similarly, 
  if 
  (Yi- 
  Y30/(E 
  - 
  Yi) 
  

   be 
  equal 
  to 
  or 
  less 
  than 
  1/53, 
  A^ 
  is 
  not 
  greater 
  than 
  the 
  

   hundredth 
  part 
  of 
  q-^ 
  + 
  ^2/!^ 
  + 
  ^'s/lOO. 
  We 
  have 
  therefore 
  to 
  

   arrange 
  the 
  relative 
  values 
  of 
  the 
  resistances 
  of 
  the 
  slides 
  

   and 
  the 
  bridge 
  wire 
  so 
  that 
  this 
  may 
  be 
  true. 
  As 
  we 
  have 
  

   pointed 
  out 
  above, 
  however, 
  the 
  inaccuracy 
  in 
  the 
  value 
  of 
  x 
  

   depends 
  on 
  the 
  relative 
  values 
  of 
  <2? 
  andpi+jc>2/10 
  +^3/100 
  + 
  Ap. 
  

   When 
  these 
  quantities 
  are 
  nearly 
  equal, 
  approximate 
  methods 
  

   of 
  computation 
  fail. 
  

  

  By 
  Ohm's 
  law, 
  we 
  see 
  from 
  fig. 
  6 
  that 
  

  

  ~9 
  ~ 
  Ri 
  ' 
  ^^' 
  

  

  ir 
  

  

  and 
  V.-V3 
  E-Vi 
  E-V^ 
  

  

  100 
  *■ 
  

  

  