2 PROFESSOR STOKES, ON THE DYNAMICAL THEORY OF DIFFRACTION. 



i 



Lastly, good reasons may be assigned why the intensity should be measured by the square of 



the coefficient of vibration ; but it is not necessary here to enter into them. 



In this way we are able to calculate the relative intensities at different points of a diffrac- 

 tion pattern. It may be regarded as established, that the coefficient of vibration in a 

 secondary wave varies, in a given direction, inversely as the radius, and consequently, we are 

 able to calculate the relative intensities at different distances from the aperture. To complete 

 this part of the subject, it is requisite to know the absolute intensity. Now it has been 

 shewn that the absolute intensity will be obtained by taking the reciprocal of the wave length 

 for the quantity by which to multiply the product of a differential element of the area of the 

 aperture, the reciprocal of the radius, and the circular function expressing the phase. It 

 appears at the same time that the phase of vibration of each secondary wave must be accele- 

 rated by a quarter of an undulation. In the investigations alluded to, it is supposed that 

 the law of disturbance in a secondary wave is the same in all directions ; but this will not 

 affect the result, provided the solution be restricted to the neighbourhood of the normal to 

 the primary wave, to which indeed alone the reasoning is applicable; and the solution so 

 restricted is sufficient to meet all ordinary cases of diffraction. 



Now the object of the first part of the following paper is, to determine, on purely 

 dynamical principles, the law of disturbance in a secondary wave, and that, not merely in the 

 neighbourhood of the normal to the primary wave, but in all directions. The occurrence of 

 the reciprocal of the radius in the coefficient, the acceleration of a quarter of an undulation, 

 and the absolute value of the coefficient in the neighbourhood of the normal to the primary 

 wave, will thus appear as particular results of the general formula. 



Before attacking the problem dynamically, it is of course necessary to make some suppo- 

 sition respecting the nature of that medium, or ether, the vibrations of which constitute light, 

 according to the theory of undulations. Now, if we adopt the theory of transverse vibra- 

 tions — and certainly, if the simplicity of a theory which conducts us through a multitude of 

 curious and complicated phenomena, like a thread through a labyrinth, be considered to carry 

 the stamp of truth, the claims of the theory of transverse vibrations seem but little short of 

 those of the theory of universal gravitation — if, I say, we adopt this theory, we are obliged 

 to suppose the existence of a tangential force in the ether, called into play by the continuous 

 sliding of one layer, or film, of the medium over another. In consequence of the existence 

 of this force, the ether must behave, so far as regards the luminous vibrations, like an elastic 

 solid. We have no occasion to speculate as to the cause of this tangential force, nor to 

 assume either that the ether does, or that it does not, consist of distinct particles ; nor are we 

 directly called on to consider in what manner the ether behaves with respect to the motion oi 

 solid bodies, such as the earth and planets. 



Accordingly, I have assumed, as applicable to the luminiferous ether in vacuum, the 

 known equations of motion of an elastic medium, such as an elastic solid. These equations 

 contain two arbitrary constants, depending upon the nature of the medium. The argument 

 which Green has employed to shew that the luminiferous ether must be regarded as sensibly 

 incompressible, in treating of the motions which constitute light *, appears to me of great force. 



• Camb. Phil. Trans. Vol. vn. p. 2. 



