On length of the period of the continued fraction of $n\sqrt{d}$

For a given quadratic irrational $α$, let us denote by $D(α)$ the length of the periodic part of the continued fraction expansion of $α$. We prove that for a positive integer $d$, which is not a perfect square, the sequence $(D(n\sqrt{d}))_{n=1}^{\infty}$ has infinitely many limit points.