  Let $Q(\alpha)$ be the simplest cubic field, it is known that $Q(\alpha)$ can
be generated by adjoining a root of the irreducible equation
$x^{3}-kx^{2}+(k-3)x+1=0$, where $k$ belongs to $Q$. In this paper we have
established a relationship between $\alpha$, $\alpha'$ and $k,k'$ where
$\alpha$ is a root of the equation $x^{3}-kx^{2}+(k-3)x+1=0$ and $\alpha'$ is a
root of the same equation with $k$ replaced by $k'$ and $Q(\alpha)=Q(\alpha')$.

Number Theory;Algebraic Geometry