54*      Royal  Society : — Mr,  G.  Gore  on  the  Thermo-electric 
factory.  The  different  solutions  do  not  require  any  analytical 
processes  different  from  those  employed  in  the  investigations 
above  referred  to. 
I  partly  dissent  from  the  solution  of  Problem  (I.)  by  polar 
coordinates,  as  given  by  Mr.  Todhunter  in  pp.  68-70  of  his 
'  History/  on  the  ground  that  the  process  of  integrating  with 
.respect  to  6  from  0  to  2tt  depends  on  assuming  the  position  of 
the  pole  to  be  within  the  closed  curve,  whereas  it  is  a  general 
rule  that  the  nature  of  a  curve  which  is  required  to  fulfil  the 
condition  of  a  maximum  or  minimum  admits  of  being  deter- 
mined independently  of  the  arbitrary  position  of  the  origin  of 
coordinates.  This  might  be  done  in  the  present  instance  by 
•adopting  the  principles  expressed  by  the  two  Lemmas  I  have 
announced  in  the  Philosophical  Magazine  for  July,  p.  28. 
The  method  of  integration  by  the  intervention  of  an  evolute, 
employed  in  the  solutions  of  the  second  and  third  problems  dis- 
cussed in  the  July  Number,  is  so  entirely  new  that  I  might  have 
anticipated  that  its  application  in  the  Calculus  of  Variations 
would  be  called  in  question.  I  shall  be  glad  to  give  attention 
to  any  arguments  Mr.  Todhunter  may  bring  against  the  results 
to  which  the  method  has  conducted  in  those  instances.  Although 
the  two  problems  have  hitherto  received  only  discontinuous  so- 
lutions, I  venture  to  assert  that,  whether  or  not  I  have  been  suc- 
cessful, they  must  also  admit  of  continuous  solutions  such  as 
those  which  I  profess  to  have  obtained.  It  might  be  worth 
while  to  compare  the  content  of  a  maximum  solid  given  by  the 
discontinuous  solution  with  that  of  the  solid  deducible  from  the 
same  data  by  the  new  method,  for  the  purpose  of  determining 
which  is  the  greater ;  but  at  present  I  have  not  leisure  for  the 
requisite  numerical  calculation. 
Cambridge,  December  8,  1871. 
VIII.  Proceedings  of  Learned  Societies. 
ROYAL  SOCIETY. 
[Continued  from  vol.  xlii.  p.  385.] 
February  23,  1871. — William  Spottiswoode,  M.A.,  Treasurer  and 
Vice-President,  in  the  Chair. 
HPHE  following  communication  was  read : — 
**■      "On  the  Thermo-electric  Action  of  Metals  and  Liquids."     By 
George  Gore,  F.R.S. 
It  is  well  known  that  the  degree  of  rapidity  with  which  a  metal 
immersed  in  an  acid,  alkaline,  or  saline  liquid  is  corroded  varies 
considerably  with  the  temperature,  and  that  the  speed  of  corrosion 
usually  increases  with  the  heat ;  also  a  few  experiments  have  been 
published  (Gmelin's  'Handbook  of  Chemistry,'  vol.  i.  p.  3/5)  show- 
