REPORT ON HYDROSTATICS AND HYDRODYNAMICS. 141 



«nnnrous waves. These objections to the old theory have been 

 Ttedby M Poisson, who proposes a new mode of considenng 

 ?he problem*. He Reasons on an hypothesis which embraces 

 both the case of an open and a closed end, viz tha the ^elo- 

 city at each is in a constant ratio to the condensation This 

 ratio will be very large for the open end, and a very small frac- 

 tion for the closed end. Its exact value in the latter case de- 

 pends on the elasticity of the stop, and in the ot^er on the mode 

 of action of the vibrations on the external an-,--to determine 

 whichl a problem of great difficulty, which M Poisson has 

 forborne to meddle with! His theory is not competent to assign 

 a priori either the series of tones or the gravest that can be 

 sounded by a tube of given length, but is more successful in 

 determining the number of nodes ..d loops and the in -va^s 

 between them, when ^ given tone is sounded. To J^d the di- 

 stances of the nodes and loops from the extremities of the tubes 

 he has recourse to the hypotheses of the old theory, which 

 make the closed end the position of a node, and the open end 

 the position of a loop. This, he says, will not be sensibly dif- 

 ferent from the truth, if, in the one case, tje stop be very un- 

 yielding, and, in the other, the diameter of the tube be sma^l. 

 Recent researches on this subject, which we shall presentiy 

 speak of, show that when the diameter is not very small the 

 position of the loop is perceptibly distant from the open end. 



The latter part of M. Poisson's memoir contains an applica- 

 tion of the principles of the foregoing part to the vibrations of 

 air in a tube composed of two or more cyhnders of different dia- 

 meters, and to the motion of two different fluids superimposed 

 in the same tube. In the course of this latter inquiry, the au- 

 thor determines the reflection which sound experiences at the 

 junction of two fluids ; and by an extension of like considerations 

 to luminous undulations, obtains the same expressions tor the 

 relative intensities of hght perpendicularly incident, and re- 

 flected at a plane surface, as those given by Dr. Young m tfie 

 Article Chromatics of the Supplement to the Eneyclop^dm 

 Britannica. This subject was afterwards resumed by M. 1 ois- 

 son at greater length in a very elaborate memoir On the Mo- 

 tion of two Elastic Fluids superimposed f, which is chiefly 

 remarkable for the bearing which the results have upon the 



*^ Auhe laft meeting, in May this year, of the Philosophical So- 

 ciety of Cambridge, a paper was read by Mr. Hopkms, m which, 



• Memoir es de V Acad^mie des Sciences, Paris, An 1817. 

 f Ibid. torn. X. p. 317. 



