  We establish an exact differential equation for the operator describing
time-dependent measurements continuous in time and obtain a series solution.
Suppose the projection operator $E(t) = U(t) E U^\dagger(t)$ is measured
continuously from t = 0 to T, where E is a projector leaving the initial state
unchanged and U(t) a unitary operator obeying U(0) = 1 and some smoothness
conditions in t. We prove that the probability of always finding E(t) = 1 from
t = 0 to T is unity. If $U(t) \neq 1$, the watched kettle is sure to `boil'.
