and for unit of length m2. Hence if T=mv2 the theorem is true. If we suppose a portion of the tube to be straight, and the whole to be moving with velocity v parallel to this line, and against the motion of the cord, we shall have the straight part of the cord reduced to rest, and an undulation, of any, but unvarying, form and dimensions, running along it with the linear velocity

velocity

m

Suppose the cord stretched by an appended mass of W pounds, and suppose its length / feet and its own mass w pounds. Then T=Wg, lm=w, and the velocity of the undulation is

() When an incompressible liquid escapes from an orifice, the velocity is the same as would be acquired by falling from the free surface to the level of the orifice.

For, as we may neglect (provided the vessel is large compared with the orifice) the kinetic energy of the bulk of the liquid; the kinetic energy of the escaping liquid is due to the loss of potential energy of the whole by the depression of the free surface. Thus the proposition at once.

(k) The small oscillations of a liquid in a U tube follow the

harmonic law.

The tube being of uniform section S, a depression of level, x, from the mean, on one side, leads to a rise, x, on the other; and if the whole column of fluid be of length 2a, we have the mass 2aSp disturbed through a space x, and acted on by a force 2Sxgp tending to bring it back. The time of oscillation is therefore (§ (a)) 2π

and is the same for all liquids whatever be their densities.

a

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