
Planck had proposed that
E_{tot} = N E,
where 'E_{tot}' is the total energy of
all the oscillators, 'N' is an integer number and
'E' is the arbitrarily small lump of energy. In
order for the calculations to succeed, Planck discovered
that he had to choose the size of the energy lumps
to be proportional to the frequency of the radiation,
i.e.:
E = h f,
where 'f' is the oscillator frequency and 'h' is
a constant which Planck hoped would eventually become
infinitely small. 



Planck struggled to understand
the physical interpretation of his equation. Eventually,
he decided that a radical step was needed and adopted a
mathematical interpretation, where the energy of the oscillators
was divided into small lumps to make the calculations more
meaningful. He expected that the lumps could (mathematically)
be made to become infinitely small as the calculations proceeded. 