734 Lord Kelvin on 



sensibly from what it would be if the water, being incom- 

 pressible, 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 less 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 recti- 

 lineal and uniform. The generator may be a ship floating 

 on the water, or a submarine ship or a fish moving at uniform 

 speed below the surface ; or, as suggested by tiayleigh, an 

 electrified body moving above the surface. For canal ship- 

 waves, if the motion of the water close to the source is to be 

 two-dimensional, the ship or submarine must be a pontoon 

 having its sides (or a submerged bar having its ends) plane 

 and fitting to the sides of the canal, w r ith freedom to move 

 horizontally. The submerged surface must be cylindric with 

 generating lines perpendicular to the sides. 



§ 35. The case of a circular cylindric bar of diameter small 

 compared with its depth below the surface, moving horizon- 

 tally at a constant speed, is a mathematical problem which 

 presents interesting difficulties, worthy of serious work for 

 anyone who may care to undertake it. The case of a floating 

 pontoon is much more difficult, because of the discontinuity 

 between free surface of water and water-surface pressed by a 

 rigid body of given shape, displacing the water. 



§ 36. Choosing a much easier problem than either of those, 

 I take as wave generator a forcive* consisting of a given 

 continuous distribution of pressure at the surface, travelling 

 over the surface at a given speed. To understand the rela- 

 tion of this to the pontoon problem, imagine the rigid surface 

 of the pontoon to become flexible ; and imagine applied to it, 

 a given distribution II of pressure, everywhere perpendicular 

 to it. Take 0, any point at a distance h above the undis- 

 turbed water-level, draw X parallel to the length of the 

 canal and Z vertically downwards. Let f, f be the dis- 

 placement-components of any particle of the water whose 

 undisturbed position is (x, z). We suppose the disturbance 

 infinitesimal ; by which we mean that the change of distance 

 between any two particles of water is infinitely small in com- 

 parison with their undisturbed distance ; and that the line 



* " Forcive " is a very useful word introduced, after careful consultation 

 with literary authorities, by my brother the late Prof. James Thomson, 

 to denote any system of force. 



