﻿74 
  Prof. 
  L. 
  E/. 
  Ingersoll 
  on 
  Magnetic 
  

  

  The 
  power 
  supplied 
  by 
  the 
  source 
  is 
  

  

  = 
  ^ 
  . 
  -^ 
  OE' 
  . 
  ai 
  cos 
  aiOE^ 
  

   am 
  . 
  ^ 
  

  

  = 
  -T-SLi/CSm&iKjK, 
  

  

  = 
  -^ 
  X 
  area 
  of 
  triangle 
  aiO/^, 
  

  

  and 
  the 
  power 
  developed 
  by 
  the 
  motor 
  = 
  wT 
  = 
  — 
  ^ 
  x 
  sum 
  

  

  of 
  areas 
  of 
  the 
  triangles 
  ao^ai, 
  aiOag, 
  a20a3, 
  &c., 
  attending 
  

   to 
  signs. 
  

  

  Hence 
  the 
  efficiency 
  is 
  equal 
  to 
  

  

  gQOai 
  -}- 
  ai 
  0«2 
  + 
  ^20^3 
  + 
  &c. 
  

   aiO/c 
  

  

  By 
  rotating 
  the 
  vector 
  from 
  to 
  the 
  middle 
  point 
  o£ 
  

   ^0^2 
  backwards 
  through 
  90° 
  and 
  doubling 
  we 
  obtain 
  OEi, 
  

   which 
  represents 
  in 
  amplitude 
  and 
  phase 
  2/ma) 
  times 
  the 
  

   first 
  harmonic 
  of 
  the 
  total 
  e.m.f. 
  of 
  the 
  motor 
  (see 
  § 
  13). 
  

  

  This 
  vector 
  can 
  now 
  be 
  compared 
  with 
  OE^ 
  which 
  repre- 
  

   sents 
  2lm(ii 
  times 
  the 
  applied 
  e.m.f. 
  

  

  Fig. 
  4 
  easily 
  explains 
  how, 
  by 
  increasing 
  the 
  exciting 
  

   current 
  of 
  an 
  A.C. 
  motor, 
  the 
  phase 
  of 
  the 
  armature 
  current 
  

   is 
  advanced 
  relative 
  to 
  that 
  of 
  the 
  applied 
  e.m.f. 
  

  

  IX. 
  Magnetic 
  Rotation 
  in 
  Iron 
  Catliode 
  Films. 
  By 
  L. 
  R. 
  

   ; 
  Ingersoll, 
  Ph.D., 
  Assistant 
  Professor 
  of 
  Physics, 
  Univer^ 
  

   sity 
  of 
  Wisconsin^, 
  

  

  [Plate 
  I.] 
  

  

  Part 
  I. 
  Tlie 
  Bolometric 
  Method 
  of 
  Measuring 
  Rotations. 
  

  

  Part 
  II. 
  Rotation 
  dispersion 
  Curves 
  for 
  the 
  Faraday 
  and 
  Kerr 
  

  

  Effects 
  in 
  the 
  Infra-red 
  Spectrum. 
  

   Part 
  III. 
  Dependence 
  of 
  the 
  Kerr 
  Rotation 
  on 
  the 
  Refractive 
  Index 
  

  

  of 
  the 
  Overljing 
  Medium. 
  

  

  Introduction. 
  

  

  THE 
  purpose 
  of 
  the 
  present 
  work 
  has 
  been 
  an 
  experimental 
  

   study 
  of 
  certain 
  problems 
  in 
  the 
  magneto-optics 
  of 
  the 
  

   magnetic 
  metals, 
  viz. 
  the 
  Faraday 
  and 
  Kerr 
  effects 
  for 
  a 
  long 
  

   range 
  of 
  spectrum 
  ; 
  the 
  thickness 
  of 
  the 
  surface 
  layer 
  which 
  

  

  * 
  Communicated 
  by 
  the 
  Author. 
  This 
  work 
  has 
  been 
  aided 
  by 
  a 
  

   grant 
  from 
  the 
  Rumford 
  Fund 
  of 
  the 
  American 
  Academy 
  of 
  Arts 
  and 
  

   Sciences, 
  for 
  which 
  the 
  writer 
  wishes 
  to 
  express 
  his 
  appreciation. 
  

  

  