IX 



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 to be 1-0176. 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 most 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 Tint ersuchun gen 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 mathematical 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 further 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, 



