Let $C$ be a smooth real quartic curve in ${\mathbb{P}}^2$. Suppose that $C$ has at least $3$ real branches $B_1,B_2,B_3$. Let $B=B_1\times B_2\times B_3$ and let $O\in B$. Let ${\tau }_O$ be the map from $B$ into the neutral component Jac$\left(C\right){\left(ℝ\right)}^0$ of the set of real points of the jacobian of $C$, defined by letting ${\tau }_O\left(P\right)$ be the divisor class of the divisor $\sum P_i-O_i$. Then, ${\tau }_O$ is a bijection. We show that this allows an explicit geometric description of the group law on Jac$\left(C\right){\left(ℝ\right)}^0$. It generalizes the classical geometric description of the group law on the neutral component of the set of real points of...