186 Lord Rayleigh on the Discharge of 



with observation, since the places of maximum retardation 

 act after the manner of a convex lens. Although a complete 

 theory of the optical effects in the case of a symmetrical jet 

 is lacking, there seems no reason to question Emden's 

 opinion that they are natural consequences of the consti- 

 tution of the jet. 



But although many features are more or less perfectly 

 explained, we are far from anything like a complete mathe- 

 matical theory of the jet escaping from high pressure, even 

 in the simplest case. A preliminary question is — are we 

 justified at all in assuming the adiabatic law as approximately 

 governing the expansions throughout ? Is there anything 

 like the " bore " which forms in front of a bullet advancing 

 with a velocity exceeding that of sound ?* It seems that 

 the latter question may be answered in the negative, since 

 here the passage of air is always from a greater to a less 

 pressure, so that the application of the adiabatic law is 

 justified. The conditions appear to be simplest if we suppose 

 the nozzle to end in a parallel part within which the motion 

 may be uniform and the velocity that of sound. But even 

 then there seems to be no reason to suppose that this state of 

 things terminates exactly at the plane or* the mouth. As the 

 issuing gas becomes free from the constramino- influence of 

 the nozzle walls, it must begin to expand, the pressure at the 

 boundary suddenly falling to that of the environment. 

 Subsequently vibrations must set in ; but the circumstances 

 are not precisely those of Prandtl's calculation, inasmuch as 

 the variable part of the velocity is not small in comparison 

 with the difference between the mean velocity and that of 

 sound. It is scarcely necessary to call attention to the 

 violence of the assumption that viscosity may be neglected 

 when a jet moves with high velocity through quiescent air. 



On the experimental side it would be of importance to 

 examine, with more accuracy than has hitherto been attained, 

 whether the asserted independence of the discharge of the 

 pressure in the receiving vessel (supposed to be less than a 

 certain fraction of that in the discharging vessel) is absolute, 

 and if not to ascertain the precise law of departure. To this 

 end it would seem necessary to abandon the method followed 

 by more recent workers in which compressed gas dis- 

 charges into the open, and to fall back upon the method of 

 Saint-Venant and Wantzel where the discharge is from 

 atmospheric pressure to a lower pressure. The question is 



* Proc. Roy. Soc. A. vol. lxxxiv. p. 247 (1910) ; Scientific Papers, 

 vol. v. p. 346. 



