1904 - 5 .] Lord Kelvin on Deep Sea Ship-Waves. 1067 
§ 76. Fig. 28 is designed on the same plan as fig. 27 but with 
eleven half-wave-lengths as the distance between the two forcives 
instead of one half- wave-length. Like fig. 27, it is symmetrical on 
the two sides of the middle of the diagram ; hut, instead of being 
waveless, as is fig. 27, it shows four and a half waves, all very 
approximately sinusoidal, with two depressional halves of waves at 
their two ends, and elevations coming asymptotically to zero 
beyond the two ends of the diagram. The curve represented by 
fig. 26 is very accurately the right-hand extreme of fig. 28 : and the 
same figure, turned right to left, is the left-hand extreme of fig. 28. 
If we commence with the water wholly at rest, and start the 
forcives at the proper speed, with force gradually (or somewhat 
suddenly) increasing up to the prescribed amount, the motion 
produced will be that represented by fig. 28, with, superimposed 
upon it, a disturbance quickly disappearing in ever lengthening 
waves of diminishing amplitude, travelling away in both directions 
from our field. If now, with the regular regime represented by 
fig. 28, we suddenly cease to apply the forcives, we have left a 
free procession of four and a half very approximately sinusoidal 
waves, between a front and a rear deviating from sinusoidality as 
shown in the diagram. From the instant of being left free, the 
front of this procession and its rear will rapidly become modified ; 
while for three periods the central part of the procession will have 
travelled three wave-lengths, with very little deviation from sinu- 
soidality. But, after four or five periods from the instant of being 
left free, the whole procession will have got into confusion. After 
twenty or thirty or forty periods, the water will be sensibly 
quiescent, not only through the whole space where the procession 
was, but through the whole space over which it would have travelled 
if its front and rear had been kept guarded by the continued action 
of the two travelling forcives. At no time after the cessation of 
the forcives can we reasonably or conveniently assign a “ group 
velocity ” to the group or procession of waves with which we are 
concerned. A prevalent idea is, I believe, that such a group of 
deep sea waves could be regarded as travelling with half the 
“ wave-velocity ” of waves of the length given in the original 
group. In § 30 above, reasons are given for accepting the theory 
of “ group velocity ” only in the case of mutually supporting 
