192 T. A. Hirst on Ripples, 
too, also depends upon the height of the water in the bath; 
so that at first sight it would appear, not only that the latter 
ought to be kept constant throughout one and the same experi- 
ment, but that a separate determination of a should be made in 
each case. 
On setting both jets in action, however, at different. inclina- 
tions, and comparing the two ripples which they produced, it 
was soon found that, however much the radii a and a’ of the 
circles described by the jets might differ in magnitude, the radii 
x and » of the circles described by the cusps of their ripples were 
in all cases nearly equal. This result is confirmed by theory, 
which also shows that the slight difference between the radii 7 
and 7’ is due, solely, to the slight difference between the values 
of the velocities X and X/ with which the waves, produced under 
these different circumstances, are propagated. In fact it fol- 
- lows at once from equation (35) of art. 20, that 
AM or ol 
uw aa? 
and the angular velocity of rotation being the same for each jet, 
their actual velocities u and w’ will clearly be proportional to the 
radii a and a’ of the circles they describe; the above proportion, 
therefore, reduces itself to the simpler one, 
A cD mer te ps) es) alo WA 
and thus verifies the above remark. When one jet descended 
vertically and the other issued horizontally, the difference between 
rand 7’, although still very small, was at a maximum, and the 
cusp of the ripple produced by the vertical jet was always fur- 
thest distant from the axis; from which we may conclude that 
the velocity X is greater when the jet descends vertically into the 
water of the bath, than when it strikes the surface of the latter 
obliquely. When the vertical jet was replaced by a solid cylinder, 
the difference between the positions of the cusps remained about 
the same as before, thus indicating that the velocity X was ap- 
preciably the same for a jet and for a solid cylinder. 
It is also worth noting here, that when the distance, from the 
axis, of the cusp of the ripple produced by the oblique jet ex- 
ceeded the radius (5 inches) of the circle described by the vertical 
jet, the latter produced no ripple whatever. ‘The reason of this 
has already been given in art. 13; and in accordance with the 
statement there made, it was found that in all such cases the velo- 
city of the vertical jet was less than 74 inches per second, which, 
as we shall see, is the mean value of the velocity % with which 
the waves produced by each jet are propagated. Attempts were 
made to regulate the velocity of rotation so that the cusp of the 
