SIXTH LECTURE.
Heat Radiation.   Statistical Theory.

Following the preparatory considerations of the last lecture
we shall treat today the problem which we have come to recognize
as one of the most important in the theory of heat radiation:
the establishment of that universal function which governs the
energy distribution in the normal spectrum. The means for the
solution of this problem will be furnished us through the calcu¬
lation of the entropy >S of a resonatot placed in a vacuum filled
with black radiation and thereby excited into stationary vibra¬
tions. Its energy U is then connected with the corresponding
specific intensity ^, and its natural frequency v in the radiation
of the surrounding field through equation (47):

^. = ~2U.                                    (48)

When S is found as a function of U, the temperature T of the
resonator and that of the surrounding radiation will be given by:

^'-=^                                       (49)

dU     T'                                      ^^^^

and by elimination of U from the last two equations, we then
find the relationship among ^„ T and v.

In order to find the entropy S of the resonator we will utilize
the general connection between entropy and probability, which
we have extensively discussed in the previous lectures, and inquire
then as to the existing probability that the vibrating resonator
possesses the energy U. In accordance with what we have seen
in connection with the elucidation of the second law through

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