TRANSACTIONS OF SECTION A. 505 



those days may he seen from the enthusiastic hiuguage which the sober-miuded 

 Dr. Humphrey Lloyd allows himself to use about him in his valuable report ou 

 Physical Optics, which he wrote for this Association in I8'3i. 



In passing I would say that the name of Fresnel reminds us of the loss 

 Science, and especially this Section, has sustained since we last met in the death 

 of that illustrious Frencli physicist who devoted his life with such ardour and 

 success to the same field of research — Alfred Cornu. Those of us who had the 

 privilege of being present will recall with a sad pleasure the beautiful address he 

 gave us in Cambridge on the Wave Theory of Light ou the occasion of Sir 

 George Stokes' jubilee. 



Fi-esnel in his analysis bad assumed that when the molecules of the ether are 

 disturbed by the passage of a wave the force of restitution acting upon a mole- 

 cule depends upon that molecules absolute displacement. Cauchy and Neumann 

 and, in England, Green, improved on Fresnel's reasoning, making this force 

 depend not ou the absolute but on the relative displacement ; all these physicists, 

 however, worked on the lines of endeavouring to form au explanation of the 

 propagation of the waves of Light, by treating them as the waves in an elastic 

 medium, akin iu its properties to a solid medium in which the stresses depend 

 on the deformation of the elements. 



MacCullagh agreed with these others in making the forces of restitution depend 

 on the relative displacements as expressed through a certain function V, which 

 represented the potential energy of the medium. In the further development of 

 the theory he, however, diverges from them and adopts a line of his own. Struck 

 by the significance of the fact, to which he seems to have been the first to direct 

 attention, that the vector whose components are 



1 /dv dw\ 1 /dw du\ l/dii du\ 

 2\rf^~ d^)'2\d^~'dz)' '2[dy~d^]' 



which we now, of course, know as the vector of molecular rotational displace- 

 ment, was, so to speak, a physical vector, independent of the choice of our axes of 

 coordinates, he was led to the idea of choosing for the form of V that of a homo- 

 geneous quadric in these three components. It must be admitted that the reasoning 

 by which he attempts to prove the necessity of this assumption is eminently 

 unsatisfactory, and that the assumption itself lay open to an apparently fatal 

 objection urged later by Stokes, that of neglecting to secure the equilibrium of 

 the element of the medium quoad moments. 



Having, however, adopted this form of V, MacCullagh proceeds (making the 

 assumption that while the elasticity of the medium varied the density was every- 

 where the same), by processes of remarkable elegance and simplicity, to develop 

 the laws of wave propagation in a crystal, thus verifying the wave-surface of 

 Fresnel, while at the same time be found himself able to satisfy completely the 

 requirements at the limits. lie could also point to experience, e.ff., the experiments 

 of Brewster and Seebeck, as justifying the simple and beautiful laws which he had 

 succeeded in obtaining. 



Nevertheless the force of Stokes' objection was felt to be so strong that one 

 who reviewed the subject, say thirty years ago, would have regarded MacCullagh's 

 work in Optics as presenting indeed opportunities for beautiful mathematical 

 developments, but lacking sound physical basis. 



The publication, however, of the epoch-making treatise of Maxwell on 

 Electricity and Magnetism entirely changed the aspect of the question, and in 

 particular threw a new light on MacCullagh's assumption. FitzGerald, in 1879, 

 pointed out that the Potential Energy, which in Maxwell's theory was equivalent 

 to the electro-static energy, really was a quadratic function of three variables, which 

 answered to the components of MacCullagh's molecular rotation, and accordingly 

 led to the same difl'erential equations of the motion as MacCullagh had deduced. 



Subsequently Larmor, in his remarkable investigation of the Dynamical Theory 

 of the Electric and Luminiferous Ether, deliberately reconsiders MacCullagh's posi- 

 tion, finds in fact in his equations the starting-point of his own theory. He points 



