VITRUVIUS.
134
under  fde  of  hebeamn,  i  s  much  as  thei  lengh  waning  fourch  pat:  he  emnainder  s.
given  to  the  lacunaria  and  arce  above  the  beaims.

The  breadch  of  the  als  on  the  right  and  eft,  if  the  lengh  of  the  atiumn  be  som  thit,
toforty  set,  is  made  achid  pat  herof.  I  the  lengh  be  fom  forty  to  fily  ket,  k  i.
dided  into  che  patsand  a  halg,  d'vlich  one  pat  i  gjven  to  the  als;  if  the  lengh  be
fom  fity  to  firy  fet,  he  dle  hare  a  fourth  pat  of  the  lengh;  i  from  firty  to  eighty,  the
lenethis  divided  inte  four  parts  anda  half,  of  vhich  one  part  makes  the  beadch  of  the  ale;
if  tom  eichty  toa  hundred  fet,  the  fith  part  of  thelength  exadly  constitutes  the  breadth
of  the  ala  :  their  lintel  beams  are  placd  so  high  that  the  heights  may  be  equal  to  the
breadths.

(25)  What  is  to  be  understood  by  the  word  reliquum
is  a  little  doubtful:  by  the  sentence  preceding  it  seems
most  naturally  to  point  to  the  remainder  of  the  length  of
the  atrium  when  three  fourths  is  deducted  therefrom;  and
vet  one  fourth  of  the  length  of  the  atrium  seems  to  be
too  great  an  allowance  for  the  lacunariae  and  arcae,  it  by
those  words  the  entablature  be  understood.
The  lacunaria  very  probably  means  the  entablature,

but  the  arcae,  which  in  the  foregoing  chapter  is  mentioned
in  speaking  of  the  gutters,  and  generally  signifies  some
kind  of  fence,  may  very  likely  allude  to  a  plutaeum  or
fence  (like  our  balustrades  or  parapets)  on  the  top  of  the
cornice;  on  this  supposition,  one  fourth  of  the  length
may  be  a  very  reconcileable  proportion.
Galiani  supposes  that  as  Vitruvius  hereafter  prescribes

(as  a  general  rule  for  all  apartments)  that  their  height
should  be  equal  to  half  the  united  sum  of  their  length  and
breadth,  the  word  reliquum  alludes  to  the  remainder  of
that  proportional  height  when  three  fourths  of  the  length
of  the  atrium  is  deducted  therefrom;  but  then  he  has
understood  the  words  lacunariorum  &  arcae  to  mean  the
parts  between  the  tops  of  the  columns,  and  the  ceiling  of
the  alæ  :  which  idea  the  following  note  will  contribute  to
disprove.

(3*)  Vitruvius  does  not  explain  whether  the  breadth
allowed  to  the  alae  is  to  be  given  to  each,  or  divided  between -
  both,  nor  whether  the  alae  were  included  or  excluded -
  from  the  proportional  measure  of  the  atrium
before  assigned.  Both  which,  as  well  as  the  sentence
concerning  the  height  of  the  lintel  beams  of  the  alae,
have  been  differently  understood  by  the  commentators.
Barbaro  and  Palladio  have  believed  that  the  proportion

allowed  to  the  alae  should  be  divided  between  both,  and
that  the  alae  should  be  excluded  from  the  beforementioned
proportion  of  the  atrium.  Perrault  and  Galiani  have
agreed  with  them  in  the  former,  but  differed  in  the  latter
point,  understanding  that  the  alae  are  to  be  included  in
the  proportional  measure  of  the  atrium.  Barbaro  indeed
seems  to  have  been  in  doubt  concerning  the  former  point,
having  made  dotted  lines  to  shew  that  the  whole  measure
allowed  might  be  given  to  the  breadth  of  each  alae.

These  points  will  be  determined  by  the  following  question
concerning  the  height  of  the  lintel  beams.
et  Trabes  earum  liminares  ita  alte  ponantur  ut  altitue -
  dines  latitudinibus  sint  æequales."  *  Their  lintel  beams
e  are  placed  so  high,  that  the  heights  may  be  equal  to  the
«  breadths."  These  words  seem  to  allude  to  the  height  of
the  lintel  beams  of  the  alae,  of  whose  proportions  Vitruvius
is  here  treating,  and  the  breadth  here  mentioned  seems
also  to  mean  the  breadth  of  the  alae  (making,  according
to  his  usual  method,  the  height  and  breadth  equal);  for  in
speaking  of  the  atrium  before,  and  of  the  tablinum  afterwards,

  he  gives  their  respective  heights  at  the  places  where
he  treats  of  their  other  proportions;  and  those  heights  are
proportioned  to  their  own  measures,  either  of  length  or
breadth:  it  therefore  appears  most  probable  that  Vitruvius
follows  the  same  method  in  treating  of  the  alae,  and  that
consequently  the  heights  and  breadths  here  mentioned  allude -
  to  the  alæe  only:  yet  this  has  been  otherwise  understood. -
  Barbaro  and  Palladio  understand  the  height  here
mentioned  to  be  that  of  the  alæe,  but  conceive  the  breadth
to  mean  that  of  the  whole  atrium;  and  to  reconcile  this
with  the  height  before  allowed  to  the  atrium,  they  imagine
the  one  to  mean  the  height  to  the  under  part  of  the  beams
or  entablature,  and  the  other  to  the  upper  part;  although