562 Proceedings of Royal Society of Edinburgh. 
Deep Water Ship-Waves.* (Continued from Proc. R.S.E., 
June 20th, 1904.) By Lord Kelvin. 
(MS. received January 23, 1905. Read same date.) 
§§ 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 vertical 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 present 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 
sensibly from what it would be if the water, being incompressible, 
were infinitely deep. This condition is practically fulfilled in 
water of finite depth if the distance between every crest (point 
of maximum elevation), and neighbouring crest on either side, is 
more than two or three times its distance from the bottom. 
§ 34. By “ ship-waves ” I mean any waves produced in open 
sea or in a canal by a moving generator ; and for simplicity I 
suppose the motion of the generator to be rectilineal and uniform. 
* The sectional and equational numbers are reckoned consecutively from 
two previous papers “ On deep-water two-dimensional waves produced by 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 deepwater,’’ §§ 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 1839 ; the case in which the wave length is very long in com- 
parison 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. 
