Intelligence  and  Miscellaneous  Articles,  477 
sary  to  produce  the  amount  of  heat  radiated  by  the  sun  into  space 
is  so  remarkably  small,  that  ages  must  elapse  before  the  effect  of  this 
contraction  can  become  visible  to  us  at  our  comparatively  great  dis- 
tance from  the  sun. 
In  order  to  show  that  this  is  the  case,  let  one  foot  and  one  second 
be  taken  as  the  units  of  space  and  time,  and  suppose  that  each  unit 
of  volume  of  the  sun's  mass  contracts  by  the  same  amount  in  the 
same  time,  so  that  if  zQ  be  the  linear  contraction  of  the  sun's  radius 
r0  in  one  second,  and  if  z  be  the  contraction  of  any  other  length  r, 
measured  from  the  centre  and  for  the  same  duration  of  time,  then 
ft  f 
—  =     .     The  effect  of  this  contraction  may  thus  be  compared  to  a 
series  of  intermittent  pulsations,  acting  throughout  the  whole  of  the 
mass  and  tending  to  diminish  the  volume.  Let  g0  be  the  force  of 
gravity  at  the  surface  of  the  sun,  and  let  g  be  the  force  of  gravity  at 
any  point  within  the  sun's  mass  considered  homogeneous,  whose 
q         y 
distance  is  r  from  the  centre;  then—  =='—'.     Again,  let  p  be  the 
mean  density  of  the  sun's  mass,  so  that  the  weight  of  any  thin  con- 
centric shell,  whose  radius  is  r  and  thickness  £r,  will  be  4irgpr2cr ; 
and  since  every  unit  of  mass  in  this  shell  falls  through  z  feet  to- 
wards the  centre  in  a  second  of  time,  4irgpzrlr  will  be  the  kinetic 
enersrv  generated  and  destroyed  every  second  by  this  shell  alone ; 
fr° 
and  therefore  I     4*gzrdr  will  be  the  whole  kinetic  energy  destroyed 
•^  o 
every  second  of  time ;  and  we  proceed  to  find  the  corresponding 
amount  of  heat  evolved. 
Now 
1     4-gpzr-dr=  —~-\     rdr=z 
«-  o  °      «-  o 
and  this  is  the  kinetic  energy   destroyed  by  the  fall  of  a  weight 
i*Wo3  through  a  height  of  z0  feet,   or  by  the  fall  of  a  weight 
A-T(J  jW\  through  a  height  of  1390  feet ;  but  the  fall  of  one  pound 
5x1  a  90 
avoirdupois  through  a  height  of  1390  feet  generates  sufficient  heat 
to  raise  one  pound  of  water  through  1°  Centigrade,  or  it  generates 
4/rcr  oz  v 
one  thermal  unit ;  hence  by  expressing  g^iaon   m  foot-pounds  we 
shall  get  the  number  of  thermal  units  generated  every  second  of 
time.  Now  (j  p  is  the  weight  of  a  cubic  foot  of  the  sun's  mass  at 
the  surface,  and  since 
g    =27'20  times  the  force  of  terrestrial  gravity,  and 
p     =1*43  times  the  density  of  water,  therefore 
g  n=z27"20  x  1*43  times  the  weight  of  a  cubic  foot  of  water  at  the 
surface  of  the  earth.     But  a  cubic  foot  of  water  weighs  G2'5  pounds, 
so  that  ^,o  =  2431  pounds. 
^.  r  3  X  2431 
Therefore       ,      . aQn      ,  when  both  r   and  za  arc  expressed  in 
0  X  I'jJ'J 
*g^oro  ; 
