1904-5.] Lord Kelvin on Deep Water Ship- Waves. 581 
under the covers, and under the free portions of the surface. The 
pressure II constituting the given forcive, and represented by the 
F curve in each case, is now automatically applied by the covers. 
§ 56. Do the same in figs. 18, 19, 20 with reference to the 
isolated forcives which they show. Thus we have three different 
cases in which a single rigid cover, which we may construct as the 
bottom of a floating pontoon, kept moving at a stated velocity rela- 
tively to the still water before it, leaves a train of sinusoidal waves 
in its rear. The D curve represents the bottom of the pontoon in 
each case. The arrow shows the direction of the motion of the 
pontoon. The F curve shows the pressure on the bottom of the 
pontoon. In fig. 20 this pressure is so small at — 2^ that the 
pontoon may be supposed to end there ; and it will leave the 
water with free surface, almost exactly sinusoidal to an indefinite 
distance behind it (infinite distance if the motion has been 
uniform for an infinite time). The F curve shows that in fig. 19 
the water wants guidance as far hack as - 3 q, and in fig. 18 as far 
back as — 8 q to keep it sinusoidal when left free ; q being in each 
case the quarter wave-length. 
§§ 57-60. Shapes for Waveless Pontoons , and their Forcives. 
§ 57. Taking any case such as those represented in figs. 18, 19, 
20 ; we see obviously that if any two equal and similar forcives 
are applied, with a distance IrA between corresponding points, and 
if the forcive thus constituted is caused to travel at speed equal to 
\/pA/27r, being, according to (77) above, the velocity of free waves 
of length A, the water will be left waveless (at rest) behind the 
travelling forcive. 
§ 58. Taking for example the forcives and speeds of figs. 18, 19, 
20, and duplicating each forcive in the manner defined in § 57, we 
find, (by proper additions of two numbers, taken from our tables 
of numbers calculated for figs. 18, 19, 20,) the numbers which give 
the depressions of the water in the three corresponding waveless 
motions. These results are shown graphically in fig. 21, on scales 
arranged for a common velocity. The free wave-length for this 
velocity is shown as 4 q in the diagram. 
§ 59. The three forcives, and the three waveless water-shapes 
