672         Mr.  G.  B.  Dyke  on  the  Use  of  the  Cymometer 
and  inductance  of  the  circuit,  for  we  have 
RxlO9 
8.'= 
^iLj 
where  R= resistance  of  auxiliary  wire  in  ohms, 
Lx=: inductance  of    cymometer    in    resonance    position 
in  cms. 
n1  —  resonance  frequency. 
And    as    S2/   is    known    from    either    of    these    equations, 
82  becomes  known,  and  8X  =  X— S2  ; 
therefore  Sx  is  known. 
Hence  the  decrements  of  the  two  circuits  are  determined. 
The  resistance  of  the  primary  spark  can  be  deduced  from 
the  value  of  8-|  in  the  following-  manner. 
Let  R'=high  frequency  resistance    of  the    wire   of   the 
primary  circuit  in  ohms. 
?'  =  resistance  of  spark  in  ohms. 
L  =  inductance  of  primary  circuit  in  cms. 
7ix = resonance  frequency. 
Then  we  know 
,   _(R'+r)109 
K  +r  =  — 
4:?l1L81 
101 
The  following  numerical  example  of  the  deduction  of  the 
decrements  from  the  resonance  curves  may  be  useful  as 
illustrating  the  method  of  arranging  the  work.  The  primary 
oscillation  circuit  consisted  of  a  rectangle  of  wire  (diameter 
"162  cm.)  inductance  =5000  cms.,  a  condenser  of  capacity  = 
5560  micro-microfarads,  and  a  2  mm.  spark-gap  between 
1*25  inch  iron  balls.  The  oscillations  were  excited  by  a  high 
tension  transformer.  The  cymometer  was  set  up  parallel  to 
one  side  of  the  rectangular  inductance  and  about  6  inches 
away  from  it. 
We  will  suppose  that  the  resonance  curves  have  been 
drawn  as  described  above,  and  the  result  to  be  as  shown  in 
fig.  2  (a  and  (3),  where  the  full-line  curve  shows  the  result 
obtained  with  the  ammeter  (resistance  3*5  ot)  only  in  circuit, 
and  the  dotted  curve  the  result  with  the  extra  resistance 
(7*2  -or)  also  connected. 
