A particle in inertial frame $S$ has coordinates $(t, x)$, whilst the coordinates are $\left(t^{\prime}, x^{\prime}\right)$ in frame $S^{\prime}$, which moves with relative velocity $v$ in the $x$ direction. What is the relationship between the coordinates of $S$ and $S^{\prime}$ ?

Frame $S^{\prime \prime}$, with cooordinates $\left(t^{\prime \prime}, x^{\prime \prime}\right)$, moves with velocity $u$ with respect to $S^{\prime}$ and velocity $V$ with respect to $S$. Derive the relativistic formula for $V$ in terms of $u$ and $v$. Show how the Newtonian limit is recovered.