VI        .  ::Aj. 
the 
LONDON,  EDINBURGH,  and  DUBLIN 
PHILOSOPHICAL    MAGAZINE 
AND 
JOURNAL    OF    SCIENCE. 
[SIXTH  SERIES.] 
v  
A  JANUARY   1906. 
I.  Deep  Sea  Ship-  Waves  *.     (Continued  from  Phil.  Mar/., 
June  1905.)     By  Lord  Kelvin. 
§  65.  T)  EFERRING  to  §  63,  we  must,  for  the  present,  as 
Jl\j  time  presses,  leave  detailed  interpretation  of  the 
curves  of  fig.  17  :  merely  remarking  that,  according  to  §  44, 
if  8  =  0,  (which  means  that  J  is  an  integer),  the  disturbance,  d, 
is  infinitely  great ;  of  which  the  dynamical  meaning  is  clear  in 
(70)  of  §  39. 
§  66.  Let  us  now  find  the  depression  of  the  water  at 
distance  x  from  the  origin,  when  the  disturbance  is  due  to  a 
single  forcive,  expressed  by  the  formula  f 
/■A2 
n0'')=^_^ (95), 
2  +  /> 
travelling  uniformly  with  any   velocity   v.     If  this   Borcive 
were  applied  steadily  to  the  surface  of  water  at  rest  it  would 
produce  a  steady  depression    —  II  (.»•),   as  we  are  taking  the 
density  of  the  water,  unity.     Thus  the  forcive  II(.i')  would 
shape  the  water  to  an  infinitely  long  trough,  of  cross-section 
shown  in  fig.  25,  representing  z=zkb2/(x2  +  b2)  on  the  seale  of 
/~10  cms.  and  6  =  1  cm. 
If* 
Taking  -  \    dxoi  (95)  we  find  Uu\-\xjb) .  bL     Hence  the 
*  Communicated  by  the  Author;  having  been  read  before  the  ; 
Society  of  Edinburgh,  July  17,  L905. 
t  What  is  denoted  by  x  in  this  and  following  expressions,  is  thi> 
(x—vt)  of  §§S6....40;  the  origin  of  co-ordinates  being  now  fixed 
relatively  to  the  travelling  forcive, 
Phil.  Mag.  S.  (>.  Vol.  1 1    No.  61.  Jan.  1906.  B 
