Vibrations  of  Conducting  Surfaces  of  Revolution.        703 
accurate,  and  were  there  no  phase  change.  On  account 
of  the  phase  change  as  determined  from  the  cadmium  obser- 
vations, the  fractional  parts  should  be  those  entered  in  the 
7th  column.  The  differences  are  trifling,  except  in  the 
cases  of  5016  and  4713.  The  proportional  corrections  by 
which  the  Vs  of  column  5  are  to  be  increased  are  set  out  in 
column  8  expressed  in  million ths  ;  but  of  course  an  accuracy 
of  4  or  5  millionths  is  hardly  to  be  expected  in  results  from 
a  single  set  of  observations  with  the  1  mm.  gauge. 
In  the  observations  (Table  II.)  with  the  5  mm.  gauge  the 
comparisons  were  with  the  cadmium  green,  for  which  P  is 
assumed  to  be  18753,9">,  corresponding  to  14814"00  for 
cadmium  red.  The  numbers  given  embody  the  results  of 
three  days'  observations,  but  they  do  not  include  the  wave- 
lengths 4713,  4472.  The  procedure  is  the  same  as  for 
Table  I.  If  the  observations  with  the  5  mm.  gauge  stood 
alone,  we  should  be  in  doubt  whether  P  for  5016  should  be 
19016*95,  or  19015-95.  The  results  with  the  1  mm.  gauge 
show  that  the  latter  alternative  must  be  chosen.  Except  in 
this  respect,  the  5  mm.  results  are  independent  ;  and  they 
are  of  course  to  be  preferred  as  presumably  more  accurate. 
The  final  numbers  for  helium  are  therefore  those  given  in 
column  6  of  Table  II. 
The  only  further  remark  that  I  will  make  is  that  the 
observations  on  the  helium  yellow  (5876)  are  not  improbably 
somewhat  embarrassed  by  a  companion  of  feeble  luminosity 
which  could  not  be  separated.  In  the  5  mm.  apparatus 
the  two  components  would  be  nearly  but  not  quite  in 
coincidence. 
LXIII.  The  Symmetrical  Vibrations  of  Conducting  Surfaces 
of  Revolution.  By  J.  W.  Nicholson,  B.A.,  M.Sc,  Scholar 
of  Trinity  College,  and  Isaac  Newton  Student  in  the  Uni- 
versity of  Cambridge*. 
IN  a  previous  paper  f,  the  author  investigated  the  possible 
electrical  periods  of  the  space  between  two  perfectly 
conducting  elliptic  cylinders  belonging  to  a  confocal  system. 
The  vibrations  of  symmetrical  type  were  alone  considered. 
The  object  of  the  present  paper  is  to  obtain  a  list  of  the 
simpler  surfaces  of  revolution,  including  cylinders  as  a 
particular  case,  whose  vibrations  admit  readily  of  analytical 
treatment,  and  to  examine  certain  important  cases  in  detail. 
*  Communicated  by  the  Author, 
f  Phil.  Mag.  Aug. '1905. 
