Page:Proceedings of the Royal Society of London Vol 60.djvu/560

 improved apparatus, that the specific heat of water increases with rising temperature. On the assumption that the rate of change is uniform, Neumann calculated the ratio of the specific heats at 100° and 0° to be 10176. The assumption made is now known to be incorrect, but it cannot be said that Neumann's experimental result has been much improved upon by later investigators. Although nearly all fields of physical science have at different times been successfully treated by Neumann, his fame chiefly rests on his theo retical investigations in optics and electricity. After Fresnel's fundamental researches, which had shown the possibility of ex- plaining the niost complicated optical phenomena by the undulatory theory, it became necessary to connect that theory more closely with the conditions of wave-propagation in ordinary elastic bodies. In other words, an elastic solid theory of the ether formed the next step to be taken, and the name of Neumann will always remain associated together with that of Cauchy, McCullagh, and Green in the early efforts to found a truly dynamical theory of light. In the first paper, "Theorie der doppelten Strahlenbrechung abgeleitet aus den Glei chungen der Mechanik," Neumann obtains a wave-surface identical with that deduced somewhat earlier by Cauchy. In the case of biaxal crystals it does not agree with that of Fresnel. It consists of three sheets, one of them being due to the longitudinal wave. The difference of the two other sheets with Fresnel's surface is, however, more nominal than real, for as Stokes pointed out, in his Report on Double Refraction, the difference may, by proper adjustment of the constants, be made to show itself only in the tenth place of decimals. The same report gives full details on the comparison between the theories of Cauchy, Neumann and Green. A further important contribution to optics was made in the year 1835 under the title "Theoretische Untersuchungen der Gesetze, nach welchen das Licht an der Grenze zweier vollkommen durchsichtigen Medien reflectirt und gebrochen wird." This paper raises the difficult ques tion of the mathematieal expression for the conditions which must hold at the surface separating two crystalline media. For well con sidered reasons Neumann adopts the view that the density of the ether is the same in all media, and follows out this hypothesis to its logical consequences. The same problem was treated at the same time by McCullagh by very different and simpler methods, but the results of both investigators were identical. Neumann fnrther con firmed his equations by experiment. The general acceptance of the electromagnetic theory has now considerably changed our point of view, but the historical importance of Neumann's work must be con ceded in spite of certain defects which may, with justice, be urged against it.

Several further papers treated of optical subjects, amongst which,