On the Reflexion and Refraction of Light, 415 



vessel, which may be infinitely distant all round, exactly 

 fulfils the condition of zero velocity for the condensational- 

 rarefactional wave; while it has a definite rigidity and 

 elasticity of form, and a definite "velocity of distortional wave, 

 which can easily be calculated with a fair approximation to 

 absolute accuracy. 



3. Green, in his original paper " On the Reflexion and Re- 

 fraction of Light," had pointed out that the condensational - 

 rarefactional wave might be got quit of in two ways, (1) by 

 its velocity being infinitely small, (2) by its velocity being 

 infinitely great. But he curtly dismissed the former and 

 adopted the latter, in the following statement : — " And it is 

 not difficult to prove that the equilibrium of our medium 

 would be unstable unless A/B > 4/3. We are therefore com- 

 pelled to adopt the latter value of A/B*," (<x> ) " and thus to 

 admit that in the luminiferous ether, the velocity of trans- 

 mission of waves propagated by normal vibrations, is very 

 great compared with that of ordinary light/' Thus originated 

 the " jelly " theory of ether, which has held the field for fifty 

 years against all dynamical assailants, and yet has failed to 

 make good its own foundation. 



4. But let us scrutinize Green's remark about instability. 

 Every possible infinitesimal motion of the medium is, in the 

 elementary dynamics of the subject, proved to be resolvable 

 into coexistent condensational-rarefactional wave-motions. 

 Surely, then, if there is a real finite propagational velocity for 

 each of the two kinds of wave-motion, the equilibrium must 

 be stable ! And so I find Green's own formula f proves it to 

 be provided we either suppose the medium to extend all through 

 boundless space, or give it a fixed containing vessel as its 

 boundary. If, left to itself in space, there be a bubble of air 

 contained in the ordinary film, in which we suppose the 

 tension to be constant however much it may expand or 

 shrink, it will come to stable equilibrium in the form of a 

 globe of such size that the pressure inwards on the air due to 

 the tension of the film is equal to the air-pressure outwards. 

 But if instead of being constant, the tension of the film varies 

 as t ] ~ K (t denoting its thickness) the equilibrium will be stable^ 

 or unstable according as k is positive or negative. A finite 



* A and B are the velocities of the condensational and distortional 

 waves respectively ; suppose for a moment the density of the medium 

 unity. 



t Collected Papers, p. 253 ; formula (C). 



% Provided instability of the film itself (by thicker parts having- greater 

 contractile force than thinner parts) is artificially guarded against by 

 keeping it arbitrarily of uniform thickness. 



2 F 2 



