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XXXI I. On the Instability of Gaseous Jets. By Joseph H. 

 T. Roberts, M.Sc, and E. Meigh, M.Sc, University of 

 Liverpool *. 



A 8 a result of some experiments on the flow o£ gases 

 through tube*, the writers were led to consider how 

 the phenomena of flow would be modified as the tubes were 

 made shorter and shorter, until they ultimately approximated 

 to holes in infinitely thin plates. It is well known that if 

 the pressure causing a gas to flow through an orifice into an 

 atmosphere be increased beyond a certain critical value the 

 flow becomes irregular, and also that under certain circum- 

 stances the gaseous jet may exhibit a sensitiveness to sonorous 

 vibrations, a familiar example of such sensitiveness being 

 that of the sensitive gas-flame. Most experimenters upon 

 sensitive flames appear to have used the pin-hole steatite 

 burner, or a drawn-out glass tube, but there is reason to 

 believe that greater sensitiveness can in general be obtained 

 with jets from holes in very thin plates, and these jets are 

 more immune from the influence of disturbances other 

 than ? onorcus vibrations. 



The instability or sensitiveness of a jet depends upon the 

 vorticity. Before proceeding to describe experiments upon 

 jets, it will be well to discuss the theory f, and to see what 

 a priori reason there is to expect that the jet from a tube 

 will, in general, be more stable than one from a hole in a 

 thin plate. 



" In the ideal case of abrupt transitions of velocity, consti- 

 tuting vortex sheets, in frictionless fluid, the motion is always 

 unstable, and the degree of instability increases as the wave- 

 length of the disturbance diminishes. 



4 ' The direct application of this result to actual jets would 

 lead us to the conclusion that their sensitiveness increases 

 indefinitely with pitch. It is true that, in the case of certain 

 flames, the pitch of the most efficient sounds is very high, 

 not far from the upper limit of human hearing ; but there 

 are other kinds of sensitive jets on which these high sounds 

 are without effect, and which require for their excitation a 

 moderate, or even a grave pitch. 



'*A probable explanation of the discrepancy readily suggests 

 itself. The calculations are founded upon the supposition 

 that the changes of velocity are discontinuous — a supposition 

 that cannot possibly agree with reality. In consequence of 

 fluid friction, a surface of discontinuity, even if it could ever 



* Communicated by the Authors. 

 + Rayleigh, ' .Sound/ vol, ii. ch. xxi. 



