PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 27 



unaccompanied by normal vibrations, or at least by any which are of sufficient magnitude to 

 be sensible. If we could be sure that the ether was strictly incompressible, we should of 

 course be justified in asserting that normal vibrations are impossible. 



29. If we suppose a = op , and / (/) = C sin — - — , we shall get from (40) 



cXcosct 27r ,. ' c\ 2 cosa . irr 2ir I ' r\ 

 t = cos — (bt - r) a = ; sin — cos — bt — , 



„ c sin a . 27r ., . cX sin a 2 71-.- . cX 2 sina . irr &irf- r\ 



C = ~ , sm — (bt -r) . ^.. „ cos— (or - r) + — „ — - sin- — cos — \bt — ; 



S 47rD6 2 r X V ' 8-n*Db 2 r 2 X V ' 8^- 3 I>6 2 r 3 X X V 2/ \ 



(41) 



and we see that the most important term in {• is of the order — compared with the 



71-r 



leading term in £, which represents the transversal vibrations properly so called. Hence £, 



and the second and third terms in £, will be insensible, except at a distance from O x comparable 



with X, and may be neglected ; but the existence of terms of this nature, in the case of a 



spherical wave whose radius is not regarded as infinite, must be borne in mind, in order to 



understand in what manner transversal vibrations are compatible with the absence of dilatation 



or condensation. 



30. The integration of equations (18) might have been effected somewhat differently by 

 first decomposing the given functions £ , tj , £ > an d ^V^o* w a i nto two parts, as in Art. 8, and 

 then treating each part separately. We should thus be led to consider separately that part 

 of the initial disturbance which relates to a wave of dilatation and that part which relates to 

 a wave of distortion. Either of these parts, taken separately, represents a disturbance which 

 is not confined to the space T, but extends indefinitely around it. Outside T, the two disturb- 

 ances are equal in magnitude and opposite in sign. 



Section III. 



DETERMINATION OP THE LAW OP THE DISTURBANCE IN A SECONDARY WAVE 



OP LIGHT. 



31. Conceive a series of plane waves of plane-polarized light propagated in vacuum in a 

 direction perpendicular to a fixed mathematical plane P. According to the undulatory theory 

 of light, as commonly received, that is, including the doctrine of transverse vibrations, the light 

 in the case above supposed consists in the vibrations of an elastic medium or ether, the vibra- 

 tions being such that the ether moves in sheets, in a direction perpendicular to that of propa- 

 gation, and the vibration of each particle being symmetrical with respect to the plane of 

 polarization, and therefore rectilinear, and either parallel or perpendicular to that plane. In 

 order to account for the propagation of such vibrations, it is necessary to suppose the existence 

 of a tangential force, or tangential pressure, called into play by the continuous sliding of the 



4 — 2 



