Practical  Method  of  Harmonic  Analysis.  29 
Subtracting  now  the  ordinates  of  Cn  so  obtained  from  the 
corresponding  y  ordinates,  we  obtain  a  new  set  of  ?m  e.s. 
ordinates  which  are  those  of  the  original  half- wave  with  its 
wth  component  removed. 
5.  In  practice  it  will  generally  be  sufficient  to  determine 
the  1st,  3rd,  5th,  7th,  and  9th  harmonics  (Hx  H3  H5  H7  H9 
say).  This  can  be  done  with  considerable  accuracy  when 
15  e.s.  ordinates  of  the  original  half-wave  are  given. 
Thus  if  these  be 
I/o,  !/i,  Vi, yu, 
corresponding  to  the  angular  abscissae 
Xq,     Xi,     X2, #14, 
where 
Xi—XQ-=X2  —  Xi= =#14  —  ^13  =  ^/15, 
and  if  zQ}  t\,  z2,  z3,  z±  be  5  e.s.  ordinates  of  the  half-wave  of 
C3,  then 
3^0=^0— ys+ yio =  —  3%= 3^io, 
3~i=yi  — y&+yn=  —  3r6  =  3-lb 
3^4=^/4—^/9+yu=  —3% =3~u, 
and  if  u0,  ul}  u2  be  3  e.s.  ordinates  of  the  half -wave  of  C5,  then 
^-Vo—y^+y^—y^  +2/12=—  5w3=5w6=-5«9  =5m12, 
5u2=y2—y5-\.  y8—yn+yu=  —  5w5  =  5w8=—  5un  =  5uu, 
the  figures  subscribed  to  each  ordinate  indicating  the  abscissa 
to  which  it  corresponds. 
Now  the  full  wave 
C1=H1+H3+H5  +  H7  +  H9+  &c, 
and  C3=  II3  +  H9  +  H15, 
C5=         HB  +  Hi« 
so  that  if  Hi5  be  neglected,  and  the  sums  of  the  corresponding 
ordinates  of  C3  and  C5  be  subtracted  from  those  of  L\,  the 
fifteen  remainders  are  ordinates  of 
HI  +  H7+..., 
i.  e.  of  H1}  if  we  neglect  H7. 
If  H15  cannot  be  neglected  it  can  at  once  be  removed  from 
Cg  before  subtracting   from  Ci,  for   as  it    is    (q,p»)   the  3rd 
