Prof.  M.  B.  Pell  on  the  Constitution  of  Matter.         169 
?-??('-*+»r) 
=  eT(l  +  ejT), 
which  is  in  accordance  with  the  known  laws  of  expansion,  e  and 
eL  beiDg  constants. 
Suppose  a  solid  body  consisting  of  n  equal  atoms,  and  let  xyz 
represent  a  very  small  displacement  of  an  atom.  There  will  be 
3n  linear  differential  equations  for  the  determination  of  such 
quantities  as  xyz ;  and  it  may  be  shown  that 
#  =  2tfcos  (fAt  +  l),     2/  =  26cos  (fit  +  l),     z=2<c  cos  {[it  +  l), 
where  /x  and  /  have  Sn  different  values  which  are  the  same  for 
all  quantities,  such  as  xyz.  The  displacement  being  small,  and 
no  change  in  the  constitution  of  the  body  beiug  supposed  to  take 
place,  terms  involving  et  or  e~*  cannot,  from  the  nature  of  the 
case,  occur.     The  whole  heat  for  this  atom  is  proportional  to 
IV,  ,"2 
2/*V8  +  &*  +  c«); 
and  the  heat  developed  as  temperature  is  proportional  to  one  half 
the  non-periodic  terms  in 
l)V(S)s+(IT=iv(^^^. 
fdx 
It  follows,  therefore,  that  for  every  atom,  at  very  small  tem- 
peratures, one  half  the  heat  is  developed  as  temperature  and  the 
remainder  is  latent.  If,  then,  there  be  two  bodies  the  masses  of 
whose  atoms  are  M  and  M,  respectively,  at  the  same  small  tem- 
perature the  whole  heat  per  atom  will  be  the  same  for  both ;  and 
if  a  and  cr,  be  their  specific  heats  at  the  absolute  zero  of  tempe- 
rature, we  have 
Mo-=M,o-1, 
which  accords  with  what  is  called  the  constancy  of  the  atomic 
heat  of  simple  substances  in  the  solid  state.  For  such  substances 
we  should  have  Mo-  =  tc,- where  k  is  constant.  If  it  were  possible 
for  two  atoms  M  and  Mx  to  become  united  into  a  single  atom, 
and  s  were  the  absolute  specific  heat  of  the  compound,  we  should 
have  (M +M])s  =  /c.  But  when  two  equivalents  are  chemically 
combined,  it  is  found  that  (M  +  M1)s  =  2/c;  and  if  there  be  p  of 
one  and  q  of  the  other, 
{pM  +  q1>ll)s={p  +  q)K. 
