According to the simple hydraulic theory of jets, each particle of a jet moves independently along a parabolic trajectory. Therefore a steady jet has a parabolic shape. We wish to consider how these results are modified by surface tension. For simplicity we will consider a two-dimensional jet of incompressible fluid.

In the author's paper “Drift” (Lighthill 1956) there are mistakes which need correction. Equation (28) should read $\phi \sim -\frac {m}{4\pi U_r}\;\; as \;\; r \rightarrow \infty$ (28) since the definition of the disturbance potential ϕ (p. 35) states that the full velocity potential is U(x + ϕ). Hence by (18) equation (29) for the asymptotic form of the secondary flow due to a source should read $v_x = -\frac {Amy} {4 \pi U (y^2 + z^2)} \left(1 + \frac{\chi}{r}\right),\;\;\;\; v_y = -\frac {Am}{4\pi Ur}, \;\;\;\; v_z=0$ (29) where as well as the U's a 4π was accidentally missing from the version printed and a y misprinted as x.

With the increasing popularity of combustion driving in strong shock tube experiments, the possibility of detonation must be considered seriously. In addition to the extreme and relatively well-known conditions associated with a detonation, there exists a phase during the transition from a flame to a detonation during which pressures and velocities of propagation can exist which are higher than those associated with the fully formed detonation. This has been discussed theoretically by Oppenheim (1952) and has been shown experimentally by several workers. A luminous front having a higher than detonation velocity has been observed by Bone, Fraser & Wheeler (1936) and others. J. B. Smith (1949), using calibrated burst diaphragms at the end of a pipe, has observed reflected pressures in fuel gas-air, acetylene-air, and hydrogen-air mixtures which were approximately four times greater than those associated with a reflected normal detonation. Turin & Huebler (1951), using quartz pressure transducers in the side of a tube, observed pressures during this transition process about three and a half times higher than those at a later time when detonation was fully developed. They worked with Toledo natural gas. Mooradian & Gordon (1951) also have clear indications of this phenomenon with hydrogen-air mixtures.

An expression is obtained for the jump in the vorticity across a gasdynamic discontinuity in an inviscid flow. This result generalized results of Truesdell (1952) and Lighthill (1957) for the vorticity behind a steady curved shock in a uniform flow and that of Emmons (1957) for the vorticity jump across a steady flame. The derivation is a dynamical one, and no assumptions on the composition or thermodynamic properties of the fluid are made. The jump in vorticity in the steady flow case is found to depend upon the jump in density and upon gradients along the discontinuity surface of the tangential velocity component and of the normal mass flow. An analogous result is found with unsteady flow.

It is shown that the interpenetration of two ionized streams is arrested, as a rule, not because of individual collisions between particles belonging to opposite streams, but because the whole system of charged particles is unstable. The smallest wavelength of an unstable oscillation is λmin where $\lambda_{min} = \surd \left(\frac {\pi m_0 U^2}{2N \epsilon^2}\right) \left(1 - \frac {U^2}{c^2} \right) ^{-\frac {3}{4}}$ Here ± U are the velocities of the undisturbed streams, and N is the density of electrons in each.

A further calculation for the non-relativistic case deals with the amplification of the plasma oscillations present in two colliding streams. It is shown that these grow rapidly and that $\tau_{crit} \surd (m_0 U^2|\pi N \epsilon^2$ is the distance of interpenetration achieved before the counterstreaming of the electrons is brought to a halt. The value of τcrit depends only insensitively on the ratio of the internal plasma energy densities Tpl to the kinetic energy densities Tkin in the streams. For example, τcrit = 9·0 when Tpl:Tkin = 1:10, and τcrit = 19·0 when Tpl : Tkin = 1:105.