If  one  junction  of  the  thermoelement  AB  is  kept  at  the  con-
stant temperature  tv  while  the  temperature  t  of  the  other  junc-
tion, at  first  equal  to  tv  is  gradually  increased,  ht^ab  w^  increase
from  zero,  its  value  when  t  =  tv  until  t  =  ty  when  it  has  the  value
Va^oft  =  area  A\Af\Ar  If  t  is  increased  beyond  /3,  to  t'  for
instance,  the  e.m.f.  will  diminish,  since


—  Aff^A^A^A^  (2)

tPab  being  negative  between  /  =  /3  and  t  =  tr  When  area  (2)
becomes  equal  in  magnitude  to  area  (i),  t^ab  is  zero,  and  t'  is
a  temperature  of  inversion  for  A  and  B  with  respect  to  tr  As  /
is  still  further  increased,  the  e.m.f.  increases  negatively  until  /=/7,
beyond  which  it  increases  algebraically,  or  decreases  negatively,
with  another  inversion  at^8'(area  BJA^A^B^'  =  ar^A^^A^A^),
until  /  =  /9.  Beyond  this  temperature  tlfl?ab  increases  negatively,
inverting  again  at  BIV  and  thereafter  remaining  negative.
260          ELEMENTS    OF    ELECTROMAGNETIC    THEORY.
When  ^  =  tz  and  /=  /7,  the  Peltier  e.m.f.s  at  both  junctions
are  zero,  no  heat  being  there  absorbed  or  evolved,  and  t^ ab  =

A  =  (negative)  area  Af^A^  (i)  =   ^(S^-S^dt.     The

Jts


Temperature  in  Degrees  Centigrade
Fig.  83.
THERMAL   AND    VOLTAIC    E.M.F.S.  261

e.m.f.  is  negative,  or  the  current  flows  (if  the  circuit  is  closed)
from  B  to  A  across  the  hot  junction  at  temperature  tr

When  t,  =  /7  and  t  =  tv  tlt^ab  =  tltTab  =  area  A^BJ'A^  (2),
and  is  positive,  or  directed  from  A  to  B  across  the  hot  junction.
