31*2 SCIENTIFIC NEWS. 



and reft cvio- &«mt>lanre to those of li^ht, but their theory is attended 

 ooun . w j t | 1 morp diffi cu |ty. As the velocity of sound is very small, 



it might be questioned how far it depended on a simple law. 

 Messrs. Lagrange and Euler, who first treated this problem, 

 s«.pp- s d ir in a particular case to depend only on its dis- 

 tance mm the centre of mot on. M . Poreson has just de- 

 monstrated generally, in a very Ingenious manner, that the 

 lav is alwa.. the same: that the movement is propagated 

 by spherical undulations with the same velocity in every 

 di e< n • bni that the vibration of panicles situate at the 

 same mom nt in the sonorous wave are made with unequal 

 rapidity, according to a law depending on the nature of 

 the prim.- r\ a^ital'ion ; and consequently, that the intensity 

 of the sound, which depends on the velocity of these vibra- 

 tions, is too* found to be different in different parts of the 

 sonorous wave. The velocity in a given radius decreases in 

 the ratio of the di tame; whence it follows, if the intensity 

 be propoj io a to the square of the velocity, it must de- 

 crease in ihe proportion of the sQuaie of th distance. 



Only iwo determinate roots of the, general equation had 

 been found, but the formulae of Mr. Poisson comprise an 

 inn. ite number, by wh ch may be verified all the theorems 

 he has obta'ned n the general case, to which he first paid 

 attention. He afterward considers the case where there are 

 several causes of a simultaneous vibration* and without 

 affecting the generality qf the root, he decompose* it so, 

 that the different parts answer to the different centres; 

 ivhich leads him to give in a novel and irgenious manner the 

 theory of the reflexion of sound, and production of echoes; 

 / and to show what would take place between opposite and 



parallel planes. By a similar method he explains whjit 

 must occur in the far ifftpre diffcult case, where the mass of 

 air set in motion is inclt^ed in an ellipsoid, tie demon- 

 strates, that the sound, which originates in one of the foci, 

 is reflected toward the other, maki.^g the angle of reflection 

 equal to that of incidence, and following the same laws as 

 light. The-e results are conformable with what we have 

 learned by experience of elliptical faults, but it was very 

 difficult to demonstrate them mathematically, which Mr, 

 pci^on has done in a new and ingenious manner. 



It 



