470 T. H. Havelock. 
Turning now to the wave portion of the surface elevation, the change from 
(6) to (10) consists in replacing — P,(«9q’,) by 
aa (o/s) — Po? (Ko9's)}- (15) 
Ko (Y'1 
In fig. 3 curves have been drawn for the quantity 
{Po (p — k) — Py 4 (p)}/k, (16) 
on a base 7p, for several values of hk. 
There are several points of interest in these curves. Since k = d/2xA, the 
relative effect of smoothing out a sharp corner over a given range is less the 
Fic. 3.—Curves of {P,~!(p — k) — P,—1(p)}/k for different values of k. 
smaller the ratio of d to A, as might be expected. In the curves for the smaller 
values of k, although there is some diminution of amplitude, the more notice- 
able effect is the displacing of the troughs and crests to the rear, an effect 
which would increase the apparent interference length of the model. For the 
larger values of k, from about & = 2, there is a pronounced lessening of the 
amplitudes. 
On the convention already described, in calculating these curves from (16) 
the first term is zero until after p = k, and hence within the range k, the curve 
is simply the value of — P,(p) . /k. This quantity has a first maximum 
numerically, at about p = 2-54, and this may be observed in the curves for 
= 3. 4,5, 6. Further, in the curves for the higher values, the effect of later 
maxima of the same quantity may be noticed; for instance, with k = 6 the 
range of continuous variation of slope is practically equal to the effective wave- 
length, and so subsidiary interference phenomena of this nature are obtained. 
