54 Lord Rayleigh on the Creations of Fluid 
of the stationary wave into its progressive components may 
be effected. 
In the actual experiment two sets of stationary waves are 
combined; and the analytical expression is 
cos{KX + nt) + cos{kx— nt) + cos {Ky + nt) + cos {icy— nt), . (3) 
which is equal to 
2 cos kx cos nt + 2 cos icy cos nt, . . . . (4) 
or to 
. k(x + v) k{x — v) , /CN 
4 cos ij) cos v y ' cos nt (5) 
If, as before, we write kx 1 -\-nt for kx, we get 
cos {kx' + 2nt) + cos kx' + 2 cos Ky cos nt. . . (6 ) 
The eye, travelling forward with the velocity n/te, sees mainly 
the corresponding progressive waves, whose appearance, how- 
ever, usually varies with y, i. e. along the length of a ridge or 
furrow. If the effect could be supposed to depend upon the 
mean elevation only, this complication would disappear, as we 
should be left with the term cos kx' standing alone. With the 
semi-opaque coloured water the variation along y is evident 
enough; but the experiment may be modified in such a manner 
that the ridges and furrows appear sensibly uniform. For 
this purpose the coloured water may be replaced by milk, 
lighted from above, but very obliquely. The appearance of a 
set of (uniform) ridges and furrows varies greatly with the 
direction of the light. If the light fall upon the plate in a direc- 
tion nearly parallel to the ridges, the disturbance of the surface 
becomes almost invisible ; but if, on the other hand, the inci- 
dence be perpendicular to the line of ridges, the disturbance 
is brought into strong relief. The application of this principle 
to the case before us shows that, when the eye is travelling 
parallel to x, the ridges and furrows will look nearly uniform 
if the incidence of the light be also nearly parallel to x ; but 
if the incidence of the light be nearly parallel to y, the ridges 
will show marked variations along their length, and in fact be 
resolved into a series of detached humps. The former con- 
dition of things is the simplest, and the most suitable as the 
subject of measurement. 
In order to see the progressive waves it is not necessary to 
move the head as a whole, but only to turn the eye as when 
we look at an ordinary object in motion. To do this without 
assistance is not at first very easy, especially if the area of the 
plate be somewhat small. By moving a pointer at various speeds 
until the right one is found, the eye may be guided to do what 
