and their relation to the Velocities of Currents. 189 
a point of inflexion 2, whose coordinates are r= We G=1 —7 
(equivalent to 12° 17! 44” nearly), it commences and continues 
ever after to turn its concavity towards the centre O, which 
point it approaches asymptotically. In comparing the fore- 
eoing results with those of experiment, the above curve was found 
to be of service. 
Experiments. 
22. I proceed to describe a few experiments which will serve 
to verify the general principles upon which the foregoing results 
are based, though they are by no means sufficiently complete 
and accurate to decide, fully, the interesting question as to the 
velocities of differently shaped waves. 
23. The experiments on the ripples produced by a jet or solid 
cylinder rotating in still water were made with the modification 
of Barker’s mill represented in section by fig. 1, PL IV. DCC’D! 
is a tin tube 17 inches long and 2 inches in diameter, whose 
lower extremity, contracted to a diameter of 1 inch, is soldered 
into a hollow brass cap DD'E'E. Into this cap three brass 
tubes are fitted; one vertical, projecting 6 inches into the inte- 
rior of the tin tube, and closed at its upper extremity by a plate 
F of hard steel; and two, D B and D! B’, horizontal, in the same 
straight line, about 44 inches long, —5ths of an inch in diameter, 
and terminated by two brass caps A B and A’ B’, which slide 
over the tubes and can be removed at pleasure. In each cap 
a lateral aperture is made, into which can be fitted either a smaller 
brass tube suitable for the issue of a jet 7th of an inch in 
diameter, or a solid brass cylinder of the same diameter, which 
completely prevents the efflux of water. The whole weight of 
the portion of the instrument thus far described, and of the 
water it may contain, is supported by a steel pin OF about 
8 inches long, whose hardened and pointed upper extremity enters 
a small cavity in the centre of the steel plate i, whilst its lower 
extremity is screwed firmly into a lead weight. MN, placed 
at the bottom of a bath PQRS. By this arrangement, the 
water in the tin tube issuing at one or both of the orifices A, A! 
causes a rotation unaccompanied by sensible cscillations, and the 
issuing jets of water, by falling into the water in the bath, pro- 
duce the ripples whose forms are to be examined. When a con- 
stant velocity of rotation is required, it is merely necessary to 
retain the same depth of water in the tin tube; and this can be 
done either by regulating, with a cock, the supply of water enter- 
ing at H, or by carrying a siphon through H to a reservoir kept 
at a constant level. When necessary, too, the water in the bath 
can be kept at a constant level by similar means. 
