The  arbitrations  which  I  have  juft  exemplified  are
thole  of  particular  reference  to  London,  and  I  (hall
difpenfe  with  giving  inllances  adapted  to  other  places
which  are  not  now  of  great  importance  in  exchange
Operations.  It  mav  be  obfcrved,  however,  that,  not-
withflanding  fuch  limitation  of  the  work  to  the  moft
eflTenlial  arbitrations,  the  general  rules  which  I  have
developed,  and  the  line  which  I  have  traced,  will  afford
fufficient  means  for  the  folution  of  every  fimilar  cafe;
and  it  cannot  fail  of  occurring,  to  thofe  who  know  the
fufceptibility  of  this  branch  of  calculations  to  combi-
nations almoft  infinite,  that  it  would  be  abfolutely  im-
poffible,  even  in  an  extenfive  treatife,  to  point  out  all
the  cafes  which  are  feafible.
It  will  have  been  obferved,  by  the  preceding  arbitra-
tions, that  the  only  variable  numbers  in  the  ftatement
of  the  quellions  are  thofe  of  the  two  courfes  of  ex-
change;  whence,  in  order  to  fimplify  the  calculations,
I  have  given  the  fixed  numbers  refulting  from  the  fup-
prelhon,  multiplication,  or  divifion  of  the  invariable
numbers  in  each  equation.
Arbitrations  are  neverthelefs  fufceplible  of  greater
fimplification,  by  the  ufe  of  logarithms.
It  is  not  my  intention,  at  this  moment,  to  fpeak  of
the  nature  and  properties  of  logarithms,  being  a  lub-
je61;  of  which  I  have  treated  in  the  obfervalions  pre-
ceding the  table  with  which  I  have  clofed  my  work ;
but,  in  order  that  the  reader  may  judge  with  precifion
of  the  application  of  logarithms  to  arbitrations  of  ex-
change, and  of  the  means  which  they  afford  of  fim-
plifying  them,  Ifliall  proceed  to  perform,  by  logarithm;?,
the  fame  operations  which  I  have  already  efl'edled  by


OF    ARBITRATIONS    OF    EXCHANGE.  319

the  common  rules  of  arithmetic,  whence  it  will  be
eafy  to  compare  the  two  methods.
