408 
Mr.  D.  Owen  on  the  Comparison  of  Electric 
length  varying  from  5  to  10  mms.  To  this  wire  was  cemented 
a  quartz  fibre  about  TT-  mm.  in  diameter,  and  about  8  cms. 
long,  the  upper  end  of  the  fibre  being  cemented  to  a  supporting- 
piece  attached  to  one  of  the  plates.  These  needles  were  sup- 
ported in  succession  between  the  plates,  which  were  kept  at 
the  same  distance  apart  and  at  the  same  difference  of  potential 
throughout  the  experiment.  The  time  of  vibration  of  each 
was  thus  determined  : — The  dimensions  and  mass  of  the 
needles  being  known,  the  moments  of  inertia  could  be  calcu- 
lated, and  by  equation  (I)  the  couple  on  each  when  in  a 
specified  field  could  be  determined. 
No  high  degree  of  accuracy  was  to  be  expected  where  the 
moment  of  inertia  of  such  small  needles  was  involved.  The 
results  given  below,  however,  show  sufficiently  the  effect  of 
alteration  of  length  and  of  diameter.  The  frequency  came 
out  less  for  the  brass  than  for  the  aluminium  needles,  just  as 
calculated  from  their  relative  density.  The  values  of  the 
frequency  in  column  4  are  for  needles  of  aluminium. 
Dependence  of  Frequency  on  Dimensions  of  Needle. 
Electric  field  =  100  volts  per  cm. 
Length 
(cms.). 
Diameter 
(cms.) 
wri       ,        ,     "        7      Relative    ,    Relative 
X  Couple      (per  sec.)                 ,         L. 
,  -.                \          tvt               couples,    [frequencies. 
(dyne-cms.)          JN. 
1-526 
1-103 
•510 
•101 
•1025 
•1025 
9-82               -197               100 
4-42               -233                 45 
•643             '275               654 
100 
118 
140 
1-500 
rooo 
•050               -693            -337              70-5               171 
•050               -253             -371              257               178 
These  numbers  show  that  although  the  couple  on  the 
needle  increases  rapidly  with  length  and  slowly  with  diameter, 
yet  the  effect  on  frequency  is  more  than  counterbalanced  by 
the  increase  in  the  moment  of  inertia.  Thus  whilst,  as  the 
first  three  rows  of  numbers  above  show,  the  length  of  needle 
decreased  in  the  proportion  of  about  3"1,  the  couple  decreased 
in  the  proportion  of  about  15  :  1,  whilst  the  frequency  went 
up  in  the  proportion  of  only  1 :  1*4. 
Hence,  while  as  the  needle  gets  smaller  the  disturbing- 
effect  on  the  field  rapidly  diminishes,  its  frequency  of  vibration 
increases,  though  slowly.  This  is  a  favourable  circumstance 
to  be  borne  in  mind  in  experiments  such  as  that  suggested 
above  for  the  determination  of  specific  inductive  capacity. 
