for  the  Determination  of  Resonance-Curve*.  671 
j  /        j/\ 
curves  should  now  be  redrawn,  taking  the  ratio  yfor  -,. -,  J 
as  ordinate,  and  the  ratio  —  as  abscissa. 
We  are  now  in  the  position  to  determine  the  decrements 
for  the  two  circuits.  Take  out  from  the  curve  corresponding- 
values  of  -T-  and  1 ,  taking  the  mean  for  the  two  sides 
r  ni  n 
of  the  curve  and  noting  that  —  lies  between  0*95  and  1'05, 
or  that  (l—  —  )  is  not  greater  than  0*05. 
Then,  using  Bjerknes'  formula 
obtain  a  series  of  values  for  (o\  +  S2). 
Let  the  mean  value  of  (pl  +  82)  =  X. 
In  like  manner,  if  B2  is  the  logarithmic  decrement  of  the 
auxiliary  resistance,  obtain  a  series  of  values  for  B1-\-B2  +  B2' 
by  taking  out  from  the  second  curve  corresponding  values 
of  (-j-,)  and  I  1 —  |  and  applying  Bjerknes'  formula. 
Let  the  mean  value  of  (8{  -+-  B2  +  B2')  =  X'. 
On  writing  out  D Hide's  formula  for  the  two  cases  we  get : 
when  the  ammeter  only  is  in  circuit 
T2_y2C1C2  TrSl^2 
8     BM^  +  Bs)' 
and  when  the  auxiliary  resistance  is  inserted 
8     B,{B2  +  B2'){Bl  +  B2  +  6^)' 
Hence  we  have  the  relation 
Jr*«  A  +  **)  =  Jr'\B2  +  B2')  (B,  +  *2  +  V ) , 
or  j;282X  =  Jr'2{B2  +  82')X'. 
Hence  8jX' 
(i/x-x' 
The  value  of  B2   may  either  be  taken  as  equal   to  (X'  — X) 
or  may  be  calculated  from  its  resistance  and  the  frequency 
