  In their 1960 book on finite Markov chains, Kemeny and Snell established that
a certain sum is invariant. The value of this sum has become known as {\it
Kemeny's constant}. Various proofs have been given over time, some more
technical than others. We give here a very simple physical justification, which
extends without a hitch to continuous-time Markov chains on a finite state
space.
  For Markov chains with denumerably infinite state space, the constant may be
infinite and even if it is finite, there is no guarantee that the physical
argument will hold. We show that the physical interpretation does go through
for the special case of a birth-and-death process with a finite value of
Kemeny's constant.
  Keywords: Kemeny's constant; discrete-time Markov chains; continuous-time
Markov chains; passage times; deviation matrix.
