230  Royal  Society : — 
at  about  the  commencement  of  the  rapid  ascent  from  the  liquid 
state  is  to  be  ascribed  to  a  trace  of  air  unavoidably  present  in  the 
carbonic  acid — and  that  if  the  carbonic  acid  had  been  absolutely  pure, 
the  ascent  from  the  liquid  to  the  gaseous  state  would  doubtless  have 
been  quite  abrupt,  and  would  have  shown  itself  in  his  diagram  by  a 
vertical  straight  line,  when  we  regard  the  coordinate  axes  for  pres- 
sures and  volumes  as  being  horizontal  and  vertical  respectively. 
Now  in  the  diagram  here  submitted  the  continuous  curves  (that  is  to 
say,  those  which  are  not  dotted)  are  obtained  from  Dr.  Andrews's 
diagram,  with  the  slight  alteration  of  substituting,  in  accordance 
with  the  explanations  just  given,  an  abrupt  meeting  instead  of  the 
curved  transition  between  the  curve  for  the  liquid  state  and  the 
upright  line  which  shows  the  boiling  stage.  Looking  to  either  of 
the  given  curves  which  pass  through  boiling,  and,  for  instance, 
selecting  the  curve  for  13°*1,  we  perceive,  from  what  has  been  said 
as  to  the  conditions  to  which  boiling  by  bumping  is  due,  that  for 
the  temperature  pertaining  to  this  curve  the  liquid  state  does  not 
necessarily  end  at  the  boiling  pressure  for  this  temperature,  and 
that  thus  in  the  diagram  the  curve  showing  volumes  for  the  liquid 
state  must  not  cease  at  the  foot  of  the  upright  line  which  marks 
the   boiling  stage  of  pressure,   but  must  extend  continuously,  for 
