1903-4.] Lord Kelvin on Two-dimensional Waves. 189 
g = 4, and z= 1, for six values of t ; 5, 1’5, 2, 2*5, and 5 ; and for 
a sufficiently large number of values of x to represent the results 
by the curves shown in figs. 2 and 3. Except for the time t = 5, 
each curve shows sufficiently all the most interesting characteristics 
of the figure of the water at the corresponding time. The curve 
for t = 5 does not perceptibly leave the zero line at distances 
^<L8 ; but if we could see it, it would show us two and a half 
wavelets possessing very interesting characteristics ; shown in 
the table of numbers, § 7 below, by which we see that several 
different curves with scales of ordinates magnified from one to 
one thousand, and to one million, and to ten thousand million, 
would be needed to exhibit them graphically. 
§ 6. Looking to the curves for t = 0 and we see that at 
first the water rises at all distances from the middle of the 
disturbance greater than x— 1*9, and falls at less distances. And 
we see that the middle ( x = 0) remains a crest (or positive maximum) 
till a very short time before t = J, when it begins to be a hollow. 
A crest then comes into existence beside it and begins to travel 
outwards. On the third curve, t = 1 , we see this crest, travelled 
to a distance x = 1 *7, from the middle where it came into being ; 
and on the fourth, fifth, sixth, seventh curves (figs. 1, 2) we 
see it got to distances 2*9, 4‘8, 6 '5, 22, at the times 1J, 2, 2J, 
5. This crest travelling rightwards on our diagrams has its 
anterior slope very gradual down to the undisturbed level at 
x = oo . Its posterior slope is much steeper ; and ends at the bottom 
of the hollow in the middle of the disturbance, at times from t = J 
to t=\\. At some time, which must be very soon after ^=14, 
this hollow begins to travel rightwards from the middle, followed 
by a fresh crest shed off from the middle. At t = 2, the hollow 
has got as far as x — '9 • at t = 2 J, and 5, respectively, it has reached 
x= 1'75, and x = 6‘7. Looking in imagination to the extension of 
our curves leftwards from the middle of the diagram, we find an 
exact counterpart of what we have been examining on the right. 
Thus we see an initial elevation, symmetrical on the two sides 
of a convex crest, of height L41 above the undisturbed level, 
sinking in the middle and rising on the two flanks. The crest 
becomes less and less convex till it gets down to height IT, when 
it becomes concave ; and two equal and similar wave - crests 
