403 Mr. O'BRIEN, ON THE PROPAGATION OF LUMINOUS WAVES 



It is evident that on this supposition a, /3, 7 will be of some such 

 form as c sin — (vt — px — qy — n) (where p 2 + q* + ,s* = 1) ; hence the 



X 



second differential coefficients of a, /3, 7 will evidently be of the same 



€ C 



order of magnitude as — , the fourth differential coefficients as -j, and 



X X 



so on. 



Again, it is evident that Sx, Sy, 1% are of the same order of mag- 

 nitude as r, and rj"(r) as f{r) (for if we suppose f(r) = Mr" 1 + Nr n + &c. 

 then rf'{r) = mMf™ + nA r r" + &cc), hence in the equation (6) the part 

 involving second differential coefficients is of the same order of mag- 



r* 



nitude as 2y(r) - c; the part involving fourth differential coefficients 

 X 



as 2/Xr) -4 c, and so on. 

 X 



Now we know that the molecular forces of all ordinary bodies are 

 quite insensible at the smallest distances that can be measured ; and 

 therefore they must be so at the distance X, which, though small, is 

 yet measurable; hence we may suppose that the particles of ether 

 exercise no sensible force at the distance X, and this being the case, 



2y*(r)— c must be extremely small compared with ^,J"(r)—^c, since r 

 X X 



is the distance between two particles which exercise a sensible force 



on each other. I think we are quite justified in this supposition by 



analogy, especially if we consider how much more minute the ethereal 



particles must be than those of matter ; for I can scarcely conceive 



that the delicate particles of ether can exercise a sensible force at a 



greater distance than the comparatively gross particles of matter do. 



Besides, observation seems to shew that all colours are propagated with 



equal velocity in vacuum : now if the particles of ether exercise a 



sensible force at the distance X this cannot be the case, for then that 



part of the equation which involves fourth and higher differential 



coefficients cannot be neglected, and it is well known that if that 



part of the equation be sensible, different colours must be propagated 



with different velocities ; hence if it be true, as it most probably is, 



