for  the  Determination  of  Resonance- Curves.  G69 
an  oscillation  per  semiperiod  is  here  defined  to  be  the  Naperian 
logarithm  o£  the  ratio  of  two  successive  maximum  oscillations 
in  opposite  directions.  In  this  connexion  it  is  to  be  noted 
that  most  German  physicists  have  defined  the  decrement  as 
the  logarithm  o£  the  ratio  of  two  successive  maximum 
oscillations  in  the  same  direction. 
The  problem  of  the  oscillation  transformer  has  been 
attacked  more  particularly  by  Oberbeck,  Bjerknes,  Drude 
and  Wien ;  and  Bjerknes  and  Drude  haire  given  solutions  for 
obtaining  the  decrements,  and  although  the  proof  is  very 
long  the  final  equations  are  simple  and  easily  interpreted. 
For  the  complete  proof  we  must  refer  to  the  original  papers  *; 
the  essential  parts,  however,  have  been  translated  into 
English  nomenclature  by  Dr.  Fleming,  and  are  given  in  his 
book  on  "  The  Principles  of  Electric  Wave  Telegraphy "" 
(Longmans,  Green  &  Co.).  In  this  note  we  can  do  little 
more  than  state  the  final  result  of  their  work.  We  shall  use 
the  following  symbols  : — 
Sx  =  logarithmic  decrement  per  semi-period  of  the  oscillation 
in  the  condenser  circuit. 
82  =  logarithmic  decrement  per  semi-period  in  the  secondary 
circuit  inductively  coupled  with  the  primary. 
?ii  =  frequency  of  oscillation  in  condenser  circuit. 
n2  =  frequency  in  secondary  circuit. 
J  =  value    of    R.M.S.    current   in    the    secondary    circuit 
corresponding  with  the  frequency  n2. 
Jr= maximum  value  of  R.M.S.  current  in  secondary  circuit, 
i.  e.  the  "  resonance  current." 
Then  Bjerknes  shows  that  the  following  equation  holds;: 
7i181  +  n282  =  7r(n1  —  n2)  —    '        -  ; 
or,  if  w2  is  nearly  equal  to  ?ih  that  is  the  secondary  is  very 
nearly  resonant  to  the  primary,  this  becomes 
g1  +  g2  =  7r(l      M         *_... 
1       «iVJ2-J2 
Writing 
this  becomes 
(£)*• 
;,=tt.v\  /■  ■' 
!iH=wVr-; 
*  V.  Bjerknes:  Annalen  der  Physik,  vol.  lv.  (1895)  p.  121 ;  and 
vol.  xliv.  (1891)  p.  74.  P.  Drude  :  Annalen  der  Physik,  vol.  xiii.  (1904) 
p.  512. 
