few millimetres, it is seen to rise as a slender column of the same diameter to a height of perhaps 30 or 40 cm. Sometimes the column disappears without visible disturbance of the air; more often it ends in a small vortex column. When the pressure is raised, the column shortens until finally the funnel-shaped vortex attaches itself to the nozzle. At a pressure of about one-fifth of an atmosphere there appears again a jet 2 or 3 cm. long. As the pressure rises still further, the jet becomes longer and more distinct and suddenly exhibits thin, bright, and fairly equidistant disks to the number of perhaps 10 or 12, crossing the jet perpendicularly. The first disks have exactly the diameter of the nozzle, but they diminish as the jet attenuates. Under still higher pressures the interval between the disks increases, and at the same time the jet is seen to swell out between them. These swellings further increase and oblique markings develop which hardly admit of merely verbal description.
Attributing these periodic features to stationary sound waves in the jet, Emden set himself to determine the wave-length (X), that is the distance between consecutive disks, and especially the pressure at which the waves begin to develop. He employed a variety of nozzles, and thus sums up his principal results:
1. When air, carbonic acid, and hydrogen escape from equal sufficiently high pressures, the length of the sound waves in the jet is the same for the same nozzle and the same pressure.
2. The pressure at which the stationary sound waves begin to develop is the same in air, carbonic acid, and hydrogen, and is equal to '9 atmosphere.
This is the pressure-excess behind the nozzle, so that the whole pressure there is T9 atmosphere. The environment of the jet is at one atmosphere pressure.
Emden, comparing his observations with the theory of Saint-Venant and Wantzel, then enunciates the following conclusion: The critical pressure, in escaping from which into the atmosphere the gas at the nozzle's mouth moves with the velocity of sound, is equal to the pressure at which stationary sound waves begin to form in the jet. So far, I think, Emden makes out his case; but he appears to over-shoot the mark when he goes on to maintain that after the critical pressure-ratio is exceeded, the escaping jet moves everywhere with the same velocity, viz. the sound-velocity; and that everywhere within it the free atmospheric pressure prevails. He argues from what happens when the motion is strictly in one dimension. It is true that then a wave can be stationary in space only when the stream moves with' the velocity of sound; but here the motion is not limited to one dimension, as is shown by the swellings between the disks. Indeed the propagation of any wave at all is inconsistent with uniformity of pressure within the jet.l as of the particles of fluid with each other, is more directly shewn by an experiment on the continuance of a column of mercury, in the tube of a barometer, at a height considerably greater than that at which it usually stands, on account oi the pressure of the atmosphere. If the mercury has been well boiled in the tube, it may be made to remain in contact with the closed end, at the height of 70 inches or more " (Young's Lectures, p. 626,1807). If the mercury be wet, boiling may be dispensed with and negative pressures of two atmospheres are easily demonstrated.