﻿1874.] 
  On 
  Polishing 
  the 
  Specula 
  of 
  Reflecting 
  Telescopes. 
  121 
  

  

  and 
  computing 
  the 
  integral 
  as 
  extended 
  over 
  an 
  area 
  bounded 
  by 
  the 
  four 
  

   straight 
  lines 
  thus 
  represented, 
  we 
  have 
  

  

  V2 
  

  

  After 
  I 
  had 
  discovered 
  this 
  formula, 
  I 
  found 
  that 
  it 
  had 
  been 
  already 
  

   given 
  in 
  a 
  memoir 
  by 
  Dr. 
  Winckler 
  in 
  the 
  Vienna 
  Transactions 
  for 
  

   1862. 
  This 
  memoir 
  treats 
  of 
  the 
  transformation 
  of 
  double 
  integrals 
  

   between 
  fixed 
  limits, 
  and 
  seems 
  to 
  me 
  one 
  of 
  great 
  interest 
  and 
  import- 
  

   ance. 
  My 
  present 
  object 
  is 
  to 
  give 
  two 
  formulae 
  for 
  the 
  multiplication 
  

   of 
  definite 
  integrals 
  which 
  will 
  not 
  be 
  found 
  in 
  Dr. 
  Winckler's 
  paper. 
  

  

  1 
  \ 
  2 
  \ 
  z+ 
  *° 
  2 
  X 
  

  

  Also 
  

  

  

  

  The 
  use 
  of 
  these 
  formulae 
  is 
  easily 
  seen. 
  

  

  December 
  17 
  ' 
  , 
  1874. 
  

  

  JOSEPH 
  D 
  ALTON 
  HOOKER, 
  C.B., 
  President, 
  in 
  the 
  Chair. 
  

  

  The 
  Presents 
  received 
  were 
  laid 
  on 
  the 
  table, 
  and 
  thanks 
  ordered 
  for 
  

   them. 
  

  

  The 
  following 
  Papers 
  and 
  Communications 
  were 
  read 
  : 
  — 
  

  

  I. 
  " 
  On 
  Polishing 
  the 
  Specula 
  of 
  Reflecting 
  Telescopes/' 
  By 
  W. 
  

   Lassell, 
  F.R.S., 
  V.P.R.A.S. 
  Received 
  November 
  11, 
  1874; 
  

  

  (Abstract.) 
  

  

  The 
  object 
  of 
  this 
  paper 
  is 
  to 
  describe 
  a 
  method 
  of 
  giving 
  a 
  high 
  lustre 
  

   and 
  true 
  parabolic 
  curve 
  with 
  ease 
  and 
  certainty, 
  by 
  appropriate 
  ma- 
  

   chinery, 
  to 
  the 
  surfaces 
  of 
  the 
  specula 
  of 
  large 
  reflecting 
  telescopes. 
  

  

  