Prof.  C.  A.  Young  on  Recurrent  Vision.  343 
whence  it  follows  that 
SE=T .Slog  (if)2. 
Or  if  we  replace  the  symbol  of  variation  by  that  of  differen- 
tiation, and,  instead  of  by  T,  denote  the  mean  value  of  the  vis  viva 
simply  by  T,  then 
~=dhg(iT)* (C) 
Let  us  suppose  this  equation  integrated  for  a  circular  process, 
and  bear  in  mind  that  iT  has  the  same  value  at  the  end  of  the 
process  as  at  its  beginning  ;  then 
Jf =0; (7) 
and  this  is  the  equation  which  Clausius,  in  the  year  1854,  first 
published  as  an  expression  of  the  second  proposition  of  the 
theory  of  heat,  for  conservative  circular  processes. 
When  the  system  is  not  conservative,  and  therefore,  besides 
the  forces  wTith  a  force -function,  either  the  friction  of  solid  bodies, 
or  viscosity  of  fluids,  or  other  such  like  dissipative  forces  operate, 
the  energy  lost  8E,  in  overcoming  the  resistance  must  be  added, 
in  the  last  term  of  equation  (1)  expressing  Hamilton's  principle, 
to  the  variation  of  the  total  energy,  and  therefore  equation  (5) 
is  transformed  into  the  following :- — 
8A=i(8E  +  8R).    c (8) 
Taking  into  account  that  SR  always  denotes  energy  lost,  and 
hence  is  always  positive  in  this  equation,  equation  (7)  changes 
into  the  following  inequality  : — 
f  <0 (9) 
This  is  the  identical  one  advanced  by  Clausius,  in  the  theory 
of  heat,  for  dissipative  circular  processes. 
Hereby  the  second  proposition  of  the  theory  of  heat  is  reduced 
to  a  universal  principle  of  dynamics.  What  in  thermodynamics 
ice  call  the  second  proposition,  is  in  dynamics  no  other  than  Ha- 
mil  ton's  principle,  the  identical  principle  which  has  already  found 
manifold  applications  in  several  branches  of  mathematical  physics. 
XLIII.  Note  on  Recurrent  Vision. 
By  Professor  C.  A.  Young,  of  Dartmouth  College*. 
TN  the  course  of  some  experiments  with  a  new  double-plate 
■*■  Holtz  machine,  belonging  to  the  college,  I  have  come  upon 
a  very  curious  phenomenon,  which  I  do  not  remember  ever  to 
*  Communicated  bv  the  Author  from  the  American  Journal  of  Science 
and  Art  for  Aprill-; 
J 
