Undulatory Theory of Light. 421 



places of equilibrium ; and suppose the circle to be a section 

 of tile sphere of the influence of the molecule which occupies 

 its centre; then, the intervals between \^\a. \. 



the molecules being greater in the ho- 



rizontal than in the vertical direction, * 

 it is manifest that the sums in general \ 

 will vary according to the directions of 

 the coordinates, and that, when the '- 

 planes of the coordinates are parallel \ 



to the planes which form the paral- 



lelopipeds, the sums of the second class 



will have for every positive term an equal negative term, and 



consequently that these sums will vanish. 



If the molecules of the aether and those of a transparent 

 body form a compound vibrating medium, and if the obser- 

 vations just made be regarded as having reference only to the 

 molecules of the body, the consequences will still be the same. 

 (See paper at p. 270 of vol. viii.) 



(3.) Since no light can be discovered to arise from the dis- 

 placements f *, we will neglect them, and then the equations 

 (3,) of the paper at p. 7 of vol. viii. become 



d^l f 1 ('•) 



~de = '"2: |4>W A^ + .J/(r)(Aj/A>, + A2A?) Azj- 



Putting 



A >) = -y- A X + -r^— . —_ + Sec. 

 dx dx"- 2 



and substituting these values in the previous equations, it is 

 obvious that the principal sum of the second class (art. ]) is 

 2 . \{/ (r) A ^-^ A j/ A ::. Now y and z may be taken in any di- 

 rections which are perpendicular to x and to one another ; 

 and if the directions be so chosen as to make this sum vanish^ 

 we may neglect the other sums of this class, and then the sub- 

 stitution will transform the equations into the second and third 

 of the equations (2.) at p. 272, and the velocities of the waves 

 will be determined by the formulae previously deduced in the 

 paper at p. 500. 



(4.) Suppose then x,,y,,z,, to be rectangular coordinates, 

 and the axis of x^ to be fixed in the medium ; suppose the plane 

 of X and j/ to coincide with this axis; and suppose the mole- 

 cules to be so arranged that the turning of the coordinates 

 round it would not sensibly affect the values of the sums. la 

 * Airy's Math. Tracts, p. 340, art. 101. 



