Let $M(t_{0},t_{1})$ be the Observability Gramian for an LTVC System on the pair $(t_{0},t_{1})$. It has the following properties: 1. $M(t_{0},t_{1})$ is symmetric and positive semidefinite for $t_{1}>t_{0}$. 2. $M$ satisfies the matrix differential equation: $$\begin{cases} \frac{d}{dt}M(t,t_{1})=A(t)M(t,t_{1})+M(t,t_{1})A^{\top}(t)-C(t)C^{\top}(t) \\ \\ M(t_{1},t_{1})=0 \end{cases}$$ 3. $M$ satisfies $$M(t_{0},t_{1})=M(t_{0},t)+\Phi_{A}^{\top}(t,t_{0})M(t,t_{1})\Phi_{A}(t,t_{0})$$