﻿102 
  Prof. 
  Sudhansukumar 
  Banerji 
  on 
  Aerial 
  

  

  3 
  T 
  b 
  3 
  {a 
  2 
  + 
  ab-b 
  2 
  ) 
  2 
  b 
  3 
  (2b 
  2 
  -a 
  2 
  ) 
  2 
  b 
  3 
  (2 
  a 
  2 
  + 
  ab 
  -2b 
  2 
  ) 
  2 
  

  

  + 
  L 
  (a 
  + 
  6) 
  5 
  + 
  (a 
  + 
  26) 
  5 
  (2a 
  + 
  26) 
  5 
  

  

  b 
  3 
  (3b 
  2 
  -2a 
  2 
  ) 
  2 
  -] 
  P 
  8 
  (co8 
  0) 
  

  

  + 
  (2a+36) 
  5 
  "/J 
  r 
  4 
  

  

  3 
  H* 
  b 
  3 
  (a 
  2 
  + 
  ab-b 
  2 
  ) 
  3 
  b 
  3 
  {2b 
  2 
  ~a 
  2 
  ) 
  3 
  6 
  3 
  (2a 
  2 
  + 
  afr-2ft 
  2 
  ) 
  3 
  

   + 
  L 
  (a 
  + 
  b) 
  6 
  + 
  {a 
  + 
  2b) 
  G 
  (2a 
  + 
  2b)« 
  

  

  b 
  3 
  (Zb 
  2 
  -2a 
  2 
  y 
  _ 
  l 
  P 
  4 
  (cosfl) 
  

   + 
  (2a 
  + 
  36) 
  6 
  "J 
  r 
  5 
  

  

  + 
  &c, 
  (7) 
  

  

  and 
  

  

  q./ 
  lafi 
  a? 
  , 
  a 
  3 
  a 
  3 
  

  

  9 
  ~ 
  L 
  (6+a) 
  3i 
  ~(6 
  + 
  2a) 
  3 
  (26+2a) 
  3 
  

  

  + 
  (26 
  + 
  3a) 
  3 
  '"J 
  r 
  2 
  

   a 
  z 
  (V 
  + 
  ab-a 
  2 
  ) 
  , 
  a 
  3 
  (2a 
  2 
  -6 
  2 
  ) 
  a 
  3 
  (26 
  2 
  + 
  a6-2a 
  2 
  ) 
  

  

  + 
  2V 
  

  

  T 
  a 
  3 
  6' 
  + 
  a6 
  

   L 
  fl 
  - 
  — 
  Th 
  + 
  i 
  

  

  (b 
  + 
  a)* 
  ' 
  (6 
  + 
  2a) 
  4 
  (26 
  + 
  2a) 
  4 
  

  

  a 
  3 
  (3a 
  2 
  -26 
  2 
  ) 
  _ 
  i 
  P 
  2 
  (cos 
  (9) 
  

   + 
  (26 
  + 
  3a) 
  4 
  -J 
  r 
  3 
  

  

  + 
  

  

  3 
  r 
  2 
  a 
  3 
  (6 
  2 
  + 
  a6-a 
  2 
  ) 
  2 
  , 
  a 
  3 
  (2a 
  2 
  -6 
  2 
  ) 
  2 
  a 
  3 
  (26 
  2 
  + 
  a6-2a 
  2 
  )' 
  2 
  

   oD 
  I 
  a 
  *"" 
  

  

  (b 
  + 
  a) 
  5 
  ' 
  (6 
  + 
  2a) 
  5 
  (26 
  + 
  2a) 
  5 
  

  

  a 
  3 
  (3a 
  2 
  -26 
  2 
  ) 
  2 
  1 
  P 
  3 
  (cos 
  (9) 
  

   (26 
  + 
  3a) 
  5 
  "'J 
  r 
  4 
  

  

  AA3 
  r 
  *- 
  a 
  8 
  (^ 
  + 
  ^--^ 
  2 
  ) 
  3 
  a 
  3 
  (2a 
  2 
  -6 
  2 
  ) 
  3 
  _ 
  a 
  3 
  (26 
  2 
  + 
  a6--2a 
  2 
  ) 
  3 
  

   + 
  4 
  * 
  L 
  a 
  (6 
  + 
  a) 
  6 
  + 
  (6 
  + 
  2a) 
  6 
  (26 
  + 
  2a) 
  6 
  

  

  a 
  3 
  (3a 
  2 
  -26 
  2 
  ) 
  3 
  "] 
  P 
  4 
  (cos 
  0) 
  

   + 
  (26 
  + 
  3a) 
  6 
  •"J 
  r 
  5 
  

  

  - 
  &c, 
  (8) 
  

  

  the 
  law 
  of 
  formation 
  of 
  the 
  series 
  within 
  the 
  brackets 
  being 
  

   obvious. 
  

  

  Coming 
  now 
  to 
  the 
  present 
  problem 
  of 
  two 
  unequal 
  spheres 
  

   of 
  the 
  same 
  material, 
  let 
  us 
  take 
  

  

  a=2 
  inches 
  and 
  6 
  = 
  1 
  inch. 
  

  

  Since 
  the 
  changes 
  of 
  velocities 
  of 
  the 
  two 
  spheres 
  are 
  in- 
  

   versely 
  proportional 
  to 
  their 
  masses, 
  we 
  must 
  have 
  

  

  U„ 
  = 
  8U_ 
  

  

  