and Spontaneous Diffusion of Sound and Light. 253 



motion at P applies to every portion of the fluid surrounding 

 A. Here, then, is the explanation of that diffusion of the effect 

 of any disturbance which it was proposed to account for. 



The rate of transmission of the effect of the disturbance has 

 to be calculated from the laws of the elementary motions, with- 

 out respect to any arbitrary mode of disturbance. This I 

 have done by the solution of Proposition XIV. in pages 214- 

 224 of my treatise on the Principles of Mathematics and 

 Physics, obtaining thereby the result that the theoretical 

 value exceeds the observed value by 17 '5 feet. The excess 

 may with probability be ascribed to the circumstance that 

 the air is not, as supposed in the theory, a simple fluid of 

 perfect elasticity, but composite and loaded with vapour. 



It would appear from the foregoing argument that the 

 method of determining velocity of propagation in an elastic 

 fluid from assumed conditions of the motion of the fluid, which 

 was first adopted by Newton, and afterwards virtually fol- 

 lowed by Lagrange and Poisson, is defective in principle, 

 and that the exact method must be derived from the general 

 equations of fluid-motion. Also it seems that the rapid 

 alternate generations of heat and cold in a series of aerial 

 vibrations does not, as has been generally supposed, sensibly 

 affect the rate of propagation. 



The results above obtained relative to the diffusion of sound 

 by aerial vibrations equally pertain to the diffusion of light 

 by setherial vibrations, on the hypothesis, which I adopt, that 

 the aether is a perfect fluid defined by the equation p — a 2 p, 

 a 2 being absolutely constant. 



The motion of the air defined by the series for the function 

 <£, obtained in the manner already stated, is required for as- 

 certaining the character of spontaneous aerial vibrations 

 pertaining to the phenomena of sound, and for obtaining the 

 laws of the harmonic series which is applied in the theory of 

 music. 



The motion of the aether defined by the spontaneous series 

 for/, obtained as before stated, together with that for (/>, is 

 necessary for ascertaining the character of a ray of light, the 

 laws of transverse vibrations and of polarization, and the mode 

 of derivation of a polarized ray from a ray of common light. 



I think it right to mention here that the assertion that the inte- 

 grability oiudx + vdy + wdz indicates rectilinear motion, which 

 I made at an early stage of my hydrodynamical researches, 

 is adverted to by Professor Stokes in his Report on hydro- 

 dynamics contained in his recently published ' Mathematical 

 and Physical Papers,' vol. i., and is with good reason objected to 

 in page 161. I had not, at that time, arrived at the conception of 



