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 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,
