118 Sir W. Thomson on Cauchy's and Green's 



May of that year, to the French Academy of Sciences and 

 the Cambridge Philosophical Society. Stokes, in his Report 

 on Double Refraction,* has given a perfectly clear account 

 of this explanation. It has been but little noticed otherwise, 

 and somehow it has not been found generally acceptable ; 

 perhaps, because of a certain appearance of artificiality and 

 arbitrariness of assumption which might be supposed to dis- 

 credit it. But whatever may have been the reason or reasons 

 which have caused it to be neglected as it has been, and 

 though it is undoubtedly faulty, both as given by Cauchy 

 and by Green, it contains what seems tome, in all probability, 

 the true principle of the explanation, and which is, that the 

 ether in a doubly refracting crystal is an elastic solid, 

 unequally pressed or unequally pulled in different directions, 

 by the unmoved ponderable matter. 



5. Cauchy's work on the wave-theory of light is compli- 

 cated throughout, and to some degree vitiated, by admission 

 of the Navier-Poisson false doctrine f that compressibility is 

 calculable theoretically from rigidity ; a doctrine which Green 

 sets aside, rightly and conveniently, by simply assuming 

 incompressibility. In other respects Cauchy's and Green's 

 " Second Theories of Double Refraction " as Stokes calls 

 them, are almost identical. Each supposes ether in the 

 crystal to be an intrinsically aeolotropic elastic solid, having 

 its aelotropy modified in virtue of internal pressure or pull, 

 equal or unequal in different directions, produced by and 

 balanced by extraneous force. Each is faulty in leaving 

 intrinsic rigidity-moduluses (coefficients) unaffected by the 

 equilibrium-pressure, and in introducing three fresh terms, 

 with coefficients (A, B, C in Green's notation) to represent 

 the whole effect of the equilibrium-pressure. This gives for 

 the case of an intrinsically isotropic solid, augmentation of 

 virtual rigidity, and therefore of wave-velocity, by equal pull + 

 in all directions, and diminution by equal positive pressure 

 in all directions ; which is obviously wrong. Thus definitively, 

 pull in all directions outwards perpendicular to the bounding 



* British Association Report, 1862. 



t See Stokes, 'On the Friction of Fluids in Motion and on the Equili- 

 brium and Motion of Elastic Solids,' Canib. Phil. Trans., 1845, §§ 19, 20 ; 

 reprinted in Stokes 'Mathematical and Physical Papers,' vol. i. p. 123; 

 or Thomson and Tait's ' Natural Philosophy,' §§ U84, 686 ; or ' Elements,' 

 §§ 655, 656. 



X So little has been done towards interpreting the formulas of either 

 writer that it has not been hitherto noticed that positive values of 

 Cauchy's G, H, I, or of Green's A, B, C, signify pulls, and negative 

 values signify pressures. 



