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XLII.   On  Hamilton's  Pri?iciple  and  the  Second  Proposition  of 
the  Mechanical  Theory  of  Heat.     By  C.  Szily*. 
THE  history  of  the  development  of  modern  physics  speaks 
decidedly  in  favour  of  the  view  that  only  those  theories 
which  are  based  on  mechanical  principles  are  capable  of  affording 
a  satisfactory  explanation  of  the  phenomena. 
The  first  proposition  of  the  theory  of  heat  would  certainly  not 
have  spread  so  quickly,  and  in  a  year  or  two  have  penetrated 
every  branch  of  physical  science,  if  it  had  not  been  preceded  by 
an  analogous  proposition,  viz.  that  of  the  equivalence  of  work 
and  vis  viva.  The  perfect  concordance  which  prevails  between 
the  first  proposition  of  the  theory  of  heat  and  a  fundamental 
principle  of  mechanics  secured  to  both  the  possibility  of  quickly 
penetrating  all  branches  of  physics,  although  up  to  the  present 
time  the  mechanical  equivalent  of  light,  of  chemical  affinity,  and 
of  electricity  are  not  yet  known. 
The  second  proposition  of  the  theory  of  heat  is  scarcely  two 
years  more  recent  than  the  first ;  its  bearing  is  already  not  less 
— nay,  when  we  take  into  consideration  the  defective  development 
of  the  other  branches  of  physics,  it  will  perhaps  be  still  greater 
than  that  of  the  first ;  and  yet,  while  the  first  proposition,  one 
might  say,  took  the  whole  domain  of  physical  science  by  storm, 
the  second  has  hitherto  scarcely  been  able  to  extend  beyond 
the  limits  of  the  theory  of  heat. 
Wherein  lies  the  reason  of  this  striking  phenomenon  ?  It 
appears  to  me,  partly  in  this — that  the  second  proposition  of  the 
theory  of  heat  did  not  find  in  mechanics  any  correlative  principle 
so  generally  known  as  the  first  did  in  the  principle  of  the  equi- 
valence of  work  and  vis  viva.  For,  if  we  express  the  second 
proposition  in  words  or  in  mathematical  symbols,  we  can  hardly 
say  that  it  reminds  us  of  any  principle  whatever  in  mechanics. 
Although  the  analogous  proposition  of  mechanics  was  not  re- 
cognized, or  at  least  not  placed  in  apposition  with  that  of  the 
theory  of  heat,  yet  almost  every  one  had  no  doubt  that  there 
must  exist  in  dynamics  a  relation  similar  to  this  second  propo- 
sition ;  for,  if  heat  is  only  a  particular  kind  of  motion,  that  equa- 
tion of  the  theory  of  heat  must  be  contained  in  the  equations 
relative  to  the  most  universal  motion.  The  only  question  was, 
Which  equation  in  dynamics  leads,  in  a  certain  special  case,  to  the 
second  proposition  of  the  theory  of  heat ?  or,  inversely,  To  which 
equation  in  dynamics  can  the  second  proposition  of  the  theory  of 
heat  be  reduced? 
Communicated  by  the  Author.  From  the  Magyar  Akademia  Ertekesei 
(Proceedings  of  the  Hungarian  Academy  of  Science),  having  been  read 
December  11,  18/1. 
Z2 
