1904 - 5 .] Lord Kelvin on Deep Sea Ship-Waves. 1065 
heaped up in front of the travelling forcive, which is a distribution 
of downward pressure whose middle is at 0. On the left side of 
0, we see the water surface not differing perceptibly from a curve 
of sines beyond half a wave-length rearwards from O. A small 
portion of a wave-length of true curve of sines in the diagram 
shows how little the water’s surface differs from the curve of sines 
at even so small a distance from 0 as a quarter wave-length. 
It must be remembered that in reality the water surface is 
everywhere very nearly level ; and in considering, as we shall have 
to do later, the work done by the forcive, we must interpret 
properly the enormous exaggeration of slopes shown in the 
diagrams. It is interesting to remark that the static depression , 
h , which the forcive if at rest would produce, is about 87 times 
the elevation actually produced above 0 by the forcive, travelling 
at the speed at which free waves, of the wave-length shown in the 
diagrams, travel. It is interesting also to remark that the limita- 
tion to very small slopes is not binding on the static forcive curve. 
Thus for example, a distribution of static pressure, everywhere 
perpendicular to the free surface, producing static depression 
exactly agreeing with fig. 25, would, if caused to travel at a 
spefed for which the free-wave-length is very large in comparison 
with b, produce a disturbance, represented by fig. 26 with waves 
of moderate slopes : and, as said in § 69 above, would produce no 
disturbance at all if the speed of travelling were infinitely great. 
§ 75. Fig. 27 is interesting as showing the waveless disturbance 
produced by two equal and similar forcives with their middles at 
distance equal to half the wave-length. This disturbance is 
essentially symmetrical in front and rear of the middle between 
the two forcives. By dynamical considerations of the equilibrium 
of downward pressures, we see that the area of fig. 27 (portion 
above line of abscissas being reckoned as negative) must be exactly 
equal to 2 A, the sum of the areas of the two forcives, representing 
their integral amount of downward pressure. This area, being 
2 t rbh, with the numerical data of § 73, is numerically JA, ; that is 
to $ay a rectangle whose length is JA., and breadth the unit of our 
vertical scale. Approximate mensuration, with a very rough 
estimate of the area beyond the range of the diagram, continued to 
infinity on the two sides, verifies this conclusion. 
