Theoretical Optics since 1840. 539 



a later date to give it a mechanical basis. In this attempt he 

 failed. " If we reflect," says Stokes, " on the state of the 

 subject as Fresnel found it and as he left it, the wonder is 

 not that he failed to give a rigorous dynamical theory, but 

 that a single mind was capable of effecting so much." 



Between the days of Fresnel and Stokes great men had 

 worked at the subject. Navier, Poisson, and Cauchy in 

 France ; Neumann in Germany ; MacCullagh in Dublin ; 

 and George Green in Cambridge, had all contributed their 

 share, and the results were somewhat confusing. 



MacCullagh and Neumann, treating the aether as an elastic 

 solid, had obtained on certain hypotheses FresnePs laws for 

 reflexion and refraction, and his theory of double refraction. 

 Green, using a somewhat different method, had shown, 

 apparently, that the tangent law was only an approximation 

 to the truth, while the wave-surface could only be deduced 

 from the true equations of an aeolotropic elastic solid by some 

 forced and improbable relations between the constants. 



According to all the theories, two waves in general can 

 traverse an elastic medium, the one travelling with velocity 

 V A/p, the other with velocity VB/p where A and B are 

 two constants. Of these the first consists of longitudinal, the 

 second of transverse vibrations ; and since there is no evidence 

 of the former wave in optics, the constant A must either 

 vanish or be infinite. 



Neumann's theory assumed A to vanish ; Green had shown 

 that for an elastic solid with free boundaries the condition of 

 stability demanded that A — 4/3 B should be positive, and 

 hence he assumed A to be infinite. On this view of the aether 

 he was clearly right. Such was the position of the problem in 

 1839, the year in which the papers of Green, MacCullagh, 

 and Cauchy were published. Stokes' earliest paper on the 

 subject, written when he was 26 years old, deals with the 

 properties which we must assign to the aether if we are to 

 explain the facts observed. To propagate transverse waves 

 it must behave to light motions as an elastic solid ; the con- 

 stancy of the length of the year, and other astronomical 

 results, show that it opposes no sensible resistance to the 

 motion of the earth and the planets, for such motions it has 

 the properties of a perfect fluid. 



He distinguishes — the fact is well-known now, but it was a 

 great step then — between the two kinds of elasticity, rigidity 

 and resistance to compression. B is a measure of the rigidity, 

 A — 4B/3 of the resistance to compression. For a fluid, 

 then, which is practically incompressible, the ratio of A to B 

 may be very great, as Green requires it, while in Stokes' 



