THE 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OP SCIENCE, 



[SIXTH SERIES. 



JUNE 1905. 



LXXI. Deep Water Ship-Waves*. (Continued 

 Mag., October 1904.) By Lord Kelvin. 



§§ 32-64. Canal Ship- Waves. 



§ 32. To avoid the somewhat cumbrous title " Two- 

 dimensional," I now use the designation " Canal f Waves" 

 to denote waves in a canal with horizontal bottom and ver- 

 tical sides, which, if not two-dimensional in their source, 

 become more and more approximately two-dimensional at 

 greater and greater distances from the source. In the pre- 

 sent communication the source is such as to render the 

 motion two-dimensional throughout ; the two dimensions 

 being respectively perpendicular to the bottom, and parallel 

 to the length of the canal : the canal being straight. 



§ 33. The word " deep " in the present communication and 

 its two predecessors (§§ 1-31) is used for brevity to mean 

 infinitely deep ; or so deep that the motion does not differ 



* From the Proceedings of the Royal Society of Edinburgh for 

 January 23, 1905. Communicated by the Author. 



The sectional and equational numbers are reckoned consecutively 

 from two previous papers " On Deep-water Two-dimensional Waves 

 produced bv any given Initiating Disturbance,'' §§ 1-10, Proc. Roy. Soc. 

 Edin., February 1st, 1904, and Phil. Mag., June 1904 ; and " On Front 

 and Rear of a Free Procession of Waves in Deep Water," §§ 11-31, 

 Proc. Roy. Soc. Edin., June 20th, 1904, and Phil. Mag., October 1904. 



f This designation does not include an interesting class of canal waves 

 of which the dynamical theory was first given by Kelland in the Trans. 

 Roy. Soc. Edin. for 18.39 ; the case in which the wave-length is very 

 long in comparison with the depth and breadth of the canal, and the 

 transverse section is of any shape other than rectangular with horizontal 

 bottom and vertical sides. 



Phil. Mag. S. <j. Vol. 9. No. 54. June 1905. 3 C 



