Prof.  M.  B.  Pell  on  the  Constitution  of  Matter.         167 
When  £=0  let  z=a.  ~  =0,  where  T  is  small.     For  a  first 
at  n  , 
approximation  we  have 
z  —  a  cos  mt. 
By  the  usual  method  of  successive  approximations,  z  may  be 
developed  in  terms  of  y.     The  process  requires  some  care,  but 
involves  no  particular  difficulty ;  so  that  it  will  be  sufficient  to 
give  the  result,  which,  to  the  degree  of  approximation  required 
for  the  present  purpose,  is 
z  =  a  [A  cos  cmt  +  Bp  +  C  cos  2cmt  +  D/)2  cos  Scmt] , 
where 
a 
4 
c  being  a  factor  nearly  equal  to  unity,  which,  as  in  the  lunar 
theory,  it  is  necessary  to  introduce.  In  conducting  the  approxi- 
mations, the  condition  z=a  when  £  =  0is  preserved  throughout. 
The  last  term  is  not  made  use  of  in  the  final  application  of  the 
result,  but  is  required  in  the  course  of  the  approximations. 
The  temperature  may  be  assumed  to  be  proportional  to  the 
average  vis  viva,  or  to 
27T 
Jo     W 
2 
dt 
2tt  2 
cm 
which,  neglecting  higher  powers  of/?, 
mViY 
(A2  +  VC2), 
<•-*+» 
