REPORT ON HYDROSTATICS AND HYDRODYNAMICS. 141 



sonorous waves. These objections to the old theory have been 

 stated by M. Poisson, who proposes a new mode of considering 

 the problem*. He reasons on an hypothesis which embraces 

 both the case of an open and a closed end, viz. that the velo- 

 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 other on the mode 

 of action of the vibrations on the external air, — to determine 

 which is 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 and loops, and the intervals 

 between them, when a given tone is sounded. To find 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, the stop be very un- 

 yielding, and, in the other, the diameter of the tube be small. 

 Recent researches on this subject, which we shall presently 

 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 cylinders 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 for the 

 relative intensities of light perpendicularly incident, and re- 

 flected at a plane surface, as those given by Dr. Young in the 

 Article Chromatics of the Supplement to the Encyclopcedia 

 Britannica. This subject was afterwards resumed by M. Pois- 

 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 

 theory of light. 



At the last meeting, in May this year, of the Philosophical So- 

 ciety of Cambridge, a paper was read by Mr. Hopkins, in which, 



* Memoires de V Acad^mie des Sciences, Paris, An 1817. 

 t Ibid. torn. X. p. 317. 



