The nature phenomenon of light and heat radiation is surely one part of the
origin for all life in the world. And it belongs to the human being inspired by the
inquiring mind to explore all measurable details, in order to develop a coherent
understanding in terms of mathematics.
One simple example, but starting with a sketch about a pseudo problem:
Usually the spectral energy distribution emitted from a cavity of a black-body is
measured as a function of the wave length of the light or the heat respectively.
On the other hand Planck´s radiation formula is given as a function of the
frequency. The difference between both presentations is the irritating fact that
each has its own maximum and that the one does not correspond to the other.
The exact solution of this problem is a logarithmic scale of either the wave
length or the frequency. A further advantage of a logarithmic argument scale
is a unified presentation of all analyzed historical measurement values as
demonstrated in this book.
And particularly a logarithmic frequency scale makes it more clear to understand
the spectral intensity relations: If for instance we consider the spectral distribution
as a “melody”, then this “melody” remains unchanged by changing the temperature,
because all individual “sound” frequencies change directly proportional to the
temperature, or with other words: Stefan-Boltzmann´s law of the dependency of the
intensity upon the temperature raised up to the fourth power is valid not only for the
total radiation but also for each individual “tone” of the “melody”. This is universally
valid from the lowest temperatures until some thausends of Kelvin.
A certain feature of this book is the investigation on Planck´s foundation of the
radiation formula. Special care has been taken by replacing the abridged formula
by the complete approximation formula of the Scottish mathematician James
Stirling. Furthermore are applied the complete permutation binominal coefficient
including the “-1”, Gauss´s formula of the “Handbook of Mathematics of Bronshtein
and Semendyayev, a hypergeometric series, the Gamma function and an own finite
expansion of an applied Gauss-integral.
All calculations are carried out by means of a computer with Mathcad.
And some more details are summarized on the whole page of number 4 of
this book, while all following pages are written in German, also because of the
frequently used German reports.