142 Mr. 0. Reynolds on Thermal Transpiration 



and the heat involves the diversion of part of the energy into 

 the forms of radiation, convection, &c, in fact into other 

 forms than wave propagation. 



4. The fourth condition is that the wave surface propagated 

 from each physical centre within the medium be one which 

 can be represented by an equation of which the parameters 

 are linear quantities of the form at, bt, &c, where a, b, &c, 

 are constant velocities. This obviously includes the wave- 

 surface with two or three sheets in crystals, as well as 

 the spherical wave-surfaces of monotropic media. It also 

 includes such waves as are thrown off by an advancing 

 missile, whether in a monotropic or crystalline medium — a 

 kind of wave which probably exists in the aether : and 

 innumerable others. In fact, the theorem is one of perfect 

 generality, and makes it possible physically to resolve any 

 motion however complex which pervades a given space into trains 

 of absohdely uniform plane waves, provided the four conditions 

 enumerated above are fulfilled. The second and third of these 

 conditions are equivalent to saying that the displacements 

 must be such as are not affected by the second order of diffe- 

 rential coefficients, and that in general external forces must not 

 intervene. These conditions are essential where the motion 

 is a real physical one, and where the resolution is intended to 

 be into real ptrysical waves. But if the problem be merely 

 kinematical they need not be attended to. This corresponds 

 to the similar statement that has to be made in regard to 

 applications of Fourier's theorem, &c. 

 I am, Gentlemen, 



8 Upper Hornsey Rise, Yours vei 7 faithfully. 



London, N. G. JOHNSTONE StONEY. 



1897, January 16. 



XXII. Thermal Transpiration and Radiometer Motion. 

 By Osborne Reynolds*. 



IN Fart I. of a paper, contributed to the Phil. Mag. for 

 November 1896, by Mr. W. Sutherland, there are 

 references (pp. 373, 374) to my paper " On certain Dimen- 

 sional Properties of Matter in the Gaseous State " (Phil. 

 Trans. R.S. part ii. 1879). 



t, and provided it do not disturb the uniformity of the plane waves. 

 These requirements are approximately fulfilled in air, so that the theorem 

 applies approximately to sound waves in air, which means that the plane 

 waves into which sound waves in air may be resolved are approximately 

 uniform. 



* Communicated by the Author, 



