170         Prof.  M.  B.  Pell  on  the  Constitution  of  Matter. 
This  is  what  might  be  inferred  from  the  above  considerations ; 
for  — i —  is  the  average  mass  of  an  atom  of  the  compound, 
,  pM  +  gM,      .  -  ,  . 
and — — L  s  the  average  heat  per  atom  to  produce  a  rise  of 
1°  from  the  absolute  zero,  and  therefore  equal  to  k. 
This  subject  is  very  fully  treated  in  a  valuable  memoir  by 
Kopp  in  the  Philosophical  Transactions.  He  points  out  that 
the  circumstance  that  /c  is  nearly  the  same  for  most  simple  solids, 
does  not  indicate  necessarily  that  they  are  really  simple,  but  that 
they  are  of  the  same  order  of  composition.  There  is  some  diffi- 
culty in  the  theory,  however ;  for  Kopp  remarks  that  the  known 
change  of  specific  heat  with  change  of  temperature  is  not  suffi- 
cient to  account  for  the  observed  differences  in  the  values  of  /e, 
even  for  those  substances  which  nearly  satisfy  the  law.  This 
difficulty  disappears,  I  think,  when  we  observe  that  the  quantity 
estimated  and  recorded  as  the  atomic  heat  is 
M<t(1  +  €t), 
and  although  e  is  very  small  it  is  different  for  different  sub- 
stances, and  t  being  the  absolute  temperature  is  considerable. 
If  we  had  the  means  of  reducing  the  observations  with  certainty 
to  the  absolute  zero,  it  is  probable  that  the  discrepancies  would 
disappear. 
The  most  general  case  which  I  have  yet  attempted  to  investi- 
gate in  connexion  with  the  motion  of  atoms,  is  that  of  n  atoms  in 
a  straight  line.  This  is  far,  of  course,  from  being  an  arrange- 
ment which  the  atoms  of  a  molecule  would  really  assume  and 
maintain :  but  it  is  a  theoretically  possible  combination ;  and 
having  some  generality,  its  consideration  may  enable  us  to  form 
by  analogy  an  idea  of  the  nature  of  molecular  arrangements,  and 
lead  the  way  to  something  better. 
.  I  undertook  the  investigation  originally  for  the  purpose  of  de- 
termining the  laws  of  expansion  and  change  of  specific  heat,  but 
I  have  been  led  to  conclusions  having  reference  to  phenomena 
of  far  greater  interest  and  importance. 
The  law  of  force  which  I  have  assumed  affords  a  reasonable 
general  explanation  of  some  of  the  phenomena  relating  to  gases 
and  vapours,  such  as  the  change  of  specific  heat  with  change  of 
temperature,  and  condensation  at  the  dew-point.  It  points  also 
to  an  essential  distinction  between  gases  and  vapours  in  the 
nature  of  the  encounters  between  the  molecules.  I  must,  how- 
ever, defer  the  consideration  of  these  and  many  other  questions 
to  some  future  occasion,  briefly  stating  the  principle  upon  which 
the  change  of  specific  heat,  of  which  the  absorption  of  heat  in 
liquefaction  and  in  vaporization  are  particular  cases,  seems  to 
