﻿56 
  

  

  Prof. 
  T. 
  R. 
  Lyle 
  on 
  the 
  Theory 
  of 
  

  

  12. 
  The 
  torque 
  exerted 
  at 
  any 
  instant 
  in 
  driving 
  the 
  

   alternator 
  is 
  

  

  -.Tf- 
  

  

  d 
  

  

  {7ncos 
  0)^} 
  = 
  mx^&m 
  cot 
  

  

  (see 
  § 
  4) 
  

  

  d{a}t) 
  

  

  IT 
  

  

  on 
  

  

  Taking 
  the 
  mean 
  value 
  of 
  this 
  product 
  we 
  find 
  that 
  the 
  mean 
  

   driving 
  torque 
  T 
  is 
  given 
  by 
  

  

  T 
  = 
  

  

  m 
  

  

  {SaQai 
  + 
  Saiag-f 
  Sa2a3 
  4-Sa3a4 
  4-&c.}, 
  

  

  which 
  result, 
  combined 
  with 
  the 
  last 
  one 
  obtained 
  in 
  § 
  11, 
  

   gives 
  the 
  power 
  equation 
  

  

  g)T 
  = 
  ES+H| 
  

  

  as 
  it 
  ought. 
  

  

  13. 
  The 
  solution 
  obtained 
  can 
  be 
  represented 
  geometrically 
  

   in 
  an 
  interesting 
  way 
  as 
  follows 
  : 
  — 
  

  

  Take 
  two 
  lines 
  OX, 
  OY, 
  fig. 
  2, 
  at 
  right 
  angles. 
  Measure 
  

  

  Fig. 
  2. 
  

  

  off 
  from 
  OY 
  in 
  the 
  positive 
  direction 
  the 
  angles 
  YOl 
  = 
  bi, 
  

   I02 
  = 
  ft, 
  203=b3, 
  304 
  = 
  /54, 
  &c., 
  where 
  bi, 
  A, 
  bg, 
  ft, 
  &c., 
  

   are 
  the 
  angles 
  determined 
  in 
  § 
  8. 
  

  

  