As suggested by one of the commentators on my last question, I am going through Bohr's Nobel prize lecture in order to understand how quantum mechanics was developed.

The lecture describes Planck's observations on radiations. I'd like to know how it was concluded from these observations that energy can only change in discrete amounts and also the derivation of Planck's formula.

The lecture then goes on to Einstein's idea about the restricting condition for vibrational energies of atoms and the specific heats of crystals. Can anyone describe exactly what Einstein's idea was about the specific heats of crystal, how that accentuated the concept of discrete energy variation and how it led to further development of QM?