  Both Poincar\'e in his 1900 Festschrift paper \cite{Poincare} and Einstein in
his 1905 \textsl{Annalen der Physik} article \cite{Einstein} were led to
$E=mc^2$ by considering electromagnetic processes taking place in vacuo.
Poincar\'e's treatment is based on a generalization of the law of conservation
of momentum to include radiation. Einstein's analysis relies solely on energy
conservation and the relativity principle together with certain assumptions,
which have served as the source of criticism of the paper beginning with Max
Planck in 1907. We show that these objections raised by Planck and others can
be traced back to Einstein's failure to make use of momentum considerations.
Relevance of our findings to a proper understanding of Ives' criticism of
Einstein's paper is pointed out.
