﻿294 
  Dr. 
  Russell 
  and 
  Mr. 
  Wright 
  : 
  Ihe 
  Wright 
  Electrical 
  

  

  and 
  a 
  coil 
  SB 
  o£ 
  resistance 
  R/10 
  be 
  put 
  in 
  series 
  with 
  it, 
  

   the 
  resistance 
  from 
  N 
  to 
  B 
  will 
  equal 
  (7//k)'R, 
  that 
  is, 
  R/p. 
  

  

  When 
  the 
  resistances 
  are 
  fixed 
  on 
  the 
  device, 
  the 
  resistance 
  

   between 
  N 
  and 
  B 
  is 
  in 
  circuit, 
  and 
  this 
  always 
  equals 
  R/p, 
  

   where 
  p 
  is 
  the 
  reading 
  on 
  the 
  top 
  scale 
  [(a), 
  tig. 
  1]. 
  I£ 
  we 
  

   have 
  n 
  o£ 
  these 
  slide 
  resistances 
  in 
  parallel, 
  and 
  their 
  readings 
  

   are 
  pi, 
  ^93, 
  ... 
  pn, 
  the 
  sum 
  of 
  the 
  currents 
  will 
  be 
  

  

  (E/R)(pi+Jt>2+...+Pn), 
  

  

  where 
  E 
  is 
  the 
  applied 
  potential-difference. 
  

  

  Instead 
  of 
  having 
  the 
  logarithmic 
  scale 
  placed 
  as 
  in 
  (a), 
  

   fig. 
  1, 
  we 
  may 
  reverse 
  it 
  and 
  place 
  it 
  as 
  in 
  (b) 
  . 
  If 
  p' 
  be 
  the 
  

   value 
  of 
  ON 
  read 
  on 
  this 
  scale, 
  we 
  obviously 
  have 
  p' 
  = 
  10/p 
  ; 
  

   and 
  hence 
  the 
  resistance 
  between 
  N 
  and 
  B 
  is 
  {R/10)p\ 
  If 
  

   the 
  n 
  resistances 
  be 
  now 
  connected 
  in 
  series, 
  their 
  combined 
  

   resistance 
  will 
  be 
  

  

  (R/10)(p/+p/ 
  + 
  ...-hp/); 
  

  

  and 
  if 
  E 
  be 
  the 
  applied 
  potential-difference, 
  the 
  current 
  

   flowing 
  through 
  them 
  will 
  be 
  

  

  (10E/R)l{p,'+p,' 
  + 
  ...+pJ). 
  

  

  In 
  some 
  problems 
  it 
  is 
  more 
  convenient 
  to 
  use 
  the 
  scale 
  

   placed 
  as 
  in 
  (a), 
  and 
  in 
  others 
  it 
  is 
  more 
  convenient 
  to 
  use 
  it 
  

   as 
  in 
  (6). 
  In 
  what 
  follows, 
  unless 
  otherwise 
  stated, 
  we 
  shall 
  

   suppose 
  that 
  it 
  is 
  placed 
  as 
  in 
  {a). 
  

  

  TV, 
  Multiplication. 
  The 
  Index 
  Line. 
  

  

  The 
  method 
  of 
  performing 
  multiplication 
  is 
  practically 
  

   identical 
  with 
  that 
  utilised 
  in 
  the 
  ordinary 
  slide-rule, 
  which 
  

   was 
  originally 
  designed 
  by 
  Seth 
  Partridge 
  *. 
  In 
  Partridge's 
  

   instrument 
  two 
  logarithmic 
  scales 
  (fig. 
  2) 
  slide 
  with 
  their 
  edges 
  

  

  Fig. 
  2. 
  

  

  «^»i 
  

  

  P 
  / 
  TQ 
  

  

  in 
  contact. 
  If 
  the 
  reading 
  on 
  the 
  top 
  scale 
  at 
  P 
  equals 
  Xi^. 
  

   and 
  on 
  the 
  lower 
  scale 
  at 
  Q 
  equals 
  a'o, 
  the 
  reading 
  on 
  the 
  top 
  

  

  * 
  ' 
  The 
  Description 
  and 
  Use 
  of 
  an 
  Instrument 
  called 
  the 
  Double 
  Scale 
  

   of 
  Proportion.' 
  London, 
  1671. 
  Near 
  the 
  beginnlEg 
  of 
  the 
  book 
  we 
  

   read: 
  "Here 
  might 
  have 
  been 
  expected 
  a 
  print 
  of 
  the 
  rule, 
  but 
  in 
  

   regard 
  to 
  its 
  sliding 
  it 
  could 
  not 
  well 
  be 
  demonstrated 
  : 
  wherefore 
  

   I 
  thought 
  good 
  to 
  advertise 
  that 
  this 
  Scale 
  and 
  all 
  other 
  Mathematical 
  

   Instruments 
  are 
  accurately 
  made 
  by 
  Mr. 
  Walter 
  Hayes 
  at 
  the 
  Cross- 
  

   Daggers 
  in 
  More-Fields, 
  next 
  door 
  to 
  the 
  Popes-Head-Tavern, 
  London." 
  

   Slide 
  rules, 
  therefore, 
  were 
  for 
  sale 
  in 
  London 
  238 
  years 
  ago. 
  

  

  