and then derived Planck's law for E(v, T)by standard manipulations—and there-
with concluded his paper without further comments.
Bose considered his Ansatz (Eq. 23.13) to be 'evident' [B3]. Nothing is further
from the truth. I venture to guess that to him the cell counting (Eq. 23.13) was
the perfect analog of Boltzmann's particle counting (Eq. 23.6) and that his cell
constraint, hold Zs fixed, was similarly the analog of Boltzmann's particle con-
straint, hold N fixed. Likewise, the two Lagrange parameters in Eq. 23.14 are
his analogs of the parameters in Eq. 23.8. Bose's replacement of fixed N by fixed
Zs already implies that N is not conserved. The final irony is that the constraint
of fixed Z^5 is irrelevant: if one drops this constraint, then one must drop Xs in Eq.
23.14. Even so, it is easily checked that one still finds Planck's law! This is in
accordance with the now-familiar fact that Planck's law follows from Bose statis-
tics with E held fixed as the only constraint. In summary, Bose's derivation intro-
duced three new features:
He then maximized W as a function of the p\ holding Zs and E fixed so that
is the total number of photons. Next Bose introduced his new coarse-grained
counting:
(23.13)
(23.14)
(23.9)
(23.10)
(23.11)
(23.12)
and
which incorporate the constraints (a) hold N fixed and (b) hold E fixed.
Bose. Partition Zs into numbers psr, where p"r is defined as the number of cells
which contain r quanta with frequency if. Let there be Ns photons in all with this
frequency and let E be the total energy. Then
A LOSS OF IDENTITY: THE BIRTH OF QUANTUM STATISTICS 427
where C is a constant and W^ follows from the extremal conditions(23.8)