  Let $\mathbf{F}=\left\langle F,R\right\rangle $ be a finite Kripke frame. A
congruence of $\mathbf{F}$ is a bisimulation of $\mathbf{F}$ that is also an
equivalence relation on F. The set of all congruences of $\mathbf{F}$ is a
lattice under the inclusion ordering. In this article we investigate this
lattice in the case that $\mathbf{F}$ is a finite line frame. We give concrete
descriptions of the join and meet of two congruences with a nontrivial upper
bound. Through these descriptions we show that for every nontrivial congruence
$\rho$, the interval $[\mathrm{Id_{F},\rho]}$ embeds into the lattice of
divisors of a suitable positive integer. We also prove that any two congruences
with a nontrivial upper bound permute.
