168         Prof.  M.  B.  Pell  on  the  Constitution  of  Matter. 
This  is  proportional  to  r,  the  absolute  temperature;  so  that  we 
may  put 
where  X  is  some  constant.  If  M  be  the  mass  of  an  atom,  H  the 
quantity  of  heat  to  each  atom,  J  the  mechanical  equivalent  of 
heat, 
where  u  is  the  velocity  when  £=0.     It  may  be  easily  shown  that 
W2=m^y(l-2jo  +  ^), 
H-«gK(i-*t¥), 
and  approximately, 
16 
/.  H 
2ig 
-(**&) 
If  s  be  the  specific  heat  at  the  temperature  t,  or  the  quantity 
of  heat  necessary  to  raise  a  unit  of  mass  through  one  degree, 
./H\      mVi^X/.   ,   21Xt\ 
If  cr  be  the  specific  heat  at  the  absolute  zero, 
s=<r(l+^T)  =  a(l  +  eT), 
where 
2Jff<r        _  21Jffcr 
The  expansion  is 
zdt 
..  0 __' 
tor        *"P' 
mc 
and  the  rate  of  expansion 
