114 J. W. Davis — Motion of Compressible Fluids. 



Note. On page 177, volume x of the Memoirs of the Man- 

 chester Literary and Philosophical Society, 1887, in a para- 

 graph of a paper entitled " On the Flow of Gases," read before 

 the Society November 17, 1885, Professor Osborne Reynolds 

 notes that, when a gas is flowing through a channel of variable 

 section, the pressure at every point of the channel may have 

 in general either of two unequal values ; whereas, if the fluid 

 were incompressible, the pressure could have but one value. 

 This is the only published notice the present writer has seen 

 of the dual values that occur in problems relating to the 

 motion of compressible fluids. The apparent governing effect 

 of the velocity of sound upon the behavior of compressible 

 fluids, is set forth in an interesting manner by Professor 

 Reynolds in the paper just mentioned, and by Hugoniot in a 

 communication published in Comptes Rendus, page 1178, 

 volume ciii, 1886, in the case considered by these authors of a 

 flow through an orifice or minimum section. The present 

 writer has recently been perplexed by meeting with the dual 

 values in several problems. Professor Horace Lamb of Man- 

 chester, England, who courteously examined one of the prob- 

 lems, and rendered the solution more definite by employing 

 the method of discussing the intersections of the curves (2), 

 (4), as followed in this paper, expressed the decided opinion 

 that only those values which are continuous with the observed 

 or assumed values at a given point belong to the problem in 

 hand. Impressed by this statement, the writer set about 

 inquiring into the meaning of the values that appear, only to 

 be disregarded, with the result, arrived at in the foregoing 

 paper, that they belong to a separate motion related to the 

 actual motion, as the branches of a hyperbola are related, by 

 having the same equations and the same parameters. 



