for  the  Determination  of  Resonance- Curves.  675 
According  to  Lord  Rayleigh's  formula 
where    R  =  low    frequency    resistance,    and    d=  diameter    of 
wire  in  cms. 
In  our  case  R,  =  '0386  ohms., 
d='lfi2  cms., 
ii=;95xl06. 
Putting  in  theee  values  we  get 
r=r23w. 
The  above  example  is  chosen  rather  as  as  example  of  the 
ease  and  speed  with  which  reasonably  good  results  can  be 
obtained,  than  as  a  criterion  of  the  accuracy  of  the  method, 
as  all  the  observations  necessary  for  drawing  the  resonance 
curves  were  taken  in  less  than  half  an  hour.  If  more  time 
is  taken  over  the  observations  much  closer  agreement  between 
the  calculated  and  observed  values  of  the  decrements  can  be 
obtained. 
The  example  first  worked  out  is  a  case  of  two  rather  loosely 
coupled  oscillation  circuits,  and  in  this  case  we  have  seen 
that  the  resonance  curve  has  a  single  peak.  If,  however,  the 
coupling  is  at  all  tight,  the  resonance  curve  develops  a  double 
hump,  the  maxima  becoming  more  and  more  separated  as  the 
coupling  becomes  tighter  and  tighter,  until  when  the  coupling- 
is  perfect  (i.  e.  when  the  mutual  inductance  is  the  geometric 
mean  of  the  two  self-inductances),  one  of  the  maxima  has 
gone  off  to  infinity,  and  we  are  again  left  with  a  single- 
hump  resonance  curve. 
Oberbeck  has  developed  the  theory  of  two  coupled  oscil- 
lation circuits,  and  has  given  formulae  by  means  of  which 
the  two  resonance  frequencies  may  be  predetermined.  For 
the  general  solution  we  must  refer  to  the  original  paper*, 
but  in  one  particular  case  the  result  deserves  special  mention 
on  account  of  its  importance  in  wireless  telegraphy.  If  the 
primary  and  secondary  circuits  are  tuned,  that  is,  are  so 
adjusted  that  when  far  apart  they  have  the  same  oscillation 
constant  and  the  same  frequency  n0,  then,  when  put  near 
together  so  that  the  coupling  coefficient  has  a  value  k,  the 
following    very    simple    relations     hold    between    the    two 
*  A.  Oberbeck,  Wied.  Ann.  der  P/n/siA;  1895,  vol.  lv.  p.  623.  See 
also  Dr.  J.  A.  Fleming-,  "Principles  of  Electric  Wave  Telegraphy," 
chap.  iii. 
