404  Prof.  Challis  on  the  Hydrodynamical 
dV 
frequently,  by  employing  this  equation  to  eliminate  -t-  from  (a), 
it  will  be  found  that 
a°~dp        «2V2  dD  V2^D  ,  ,M 
The  force  on  the  left-hand  side  of  this  equation,  which  is  entirely 
due  to  the  gradation  of  atomic  density  expressed  by  -=-,  takes 
effect  in  producing  the  streams  I  have  called  secondary ;  and  the 
reasoning  shows  that  the  intensity  of  such  streams  is  indepen- 
dent of  the  direction  of  the  primary  current.  (See  the  Theory 
of  Electricity  in  the  Philosophical  Magazine  for  October  1860, 
art.  18). 
5.  In  the  applications  of  the  above  views  respecting  the  gene- 
ration of  secondary  streams  to  the  Theories  of  Electricity,  Gal- 
vanism, and  Magnetism,  I  have  assumed  (Principles  of  Physics, 
pp.  547  &  548)  that  the  primary  stream,  the  velocity  of  which 
is  V,  might  be  one  which  relatively  passes  through  all  terrestrial 
substances  in  consequence  of  the  earth's  motion  about  the  sun, 
and  that  two  other  primary  streams  would  similarly  be  due  to 
the  earth's  rotation  about  its  axis,  and  the  motion  of  the  solar 
system  in  space.  It  was  also  argued  that  the  resulting  secondary 
stream  would  be  the  sum  of  those  which  the  three  primaries, 
supposed  to  be  steady  motions,  would  produce  separately,  and 
that  it  would  consequently  be  quam  proxime  steady. 
But  it  has  since  appeared  to  me  that  this  argument  cannot  be 
maintained,  and  that  the  generation  of  the  secondary  stream 
must  be  ascribed  to  the  resultant  at  each  instant  of  the  three 
primary  velocities.  Since  there  is  reason  to  conclude  that  the 
motion  of  the  solar  system  is  comparable  with  the  earth's  orbital 
motion,  that  resultant  would  be  subject  to  large  variations,  to 
which  there  is  nothing  corresponding  in  the  observed  intensity 
of  magnetism.  Hence  the  movements  of  the  earth  fail  to  ac- 
count for  the  primary  velocity  of  the  theory. 
6.  The  formula  (b)  shows  that  the  force  which  generates  the 
secondary  streams  varies  as  the  square  of  the  primary  velocity  V, 
since  the  factor-- — -,.,  1  may  be  considered  to  be  constant.  Now, 
(1—  B)dg      J 
since  no  observed  magnetic  variations  are  attributable  to  varia- 
tions of  the  primary  velocity  such  as  those  which  the  composi- 
tion of  the  earth's  velocity  with  that  of  the  solar  system  might 
be  supposed  to  produce,  a  fortiori  the  much  smaller  variations 
of  the  earth's  velocity  in  its  orbit  can  have  no  perceptible  effect. 
This  inference  agrees  with  a  conclusion  drawn  by  the  Astronomer 
Royal  from  discussions  of  the  Greenwich  Magnetical  Observa- 
