  In this paper, we study a weak law of large numbers for the total internal
length of the Bolthausen-Szmitman coalescent. As a consequence, we obtain the
weak limit law of the centered and rescaled total external length. The latter
extends results obtained by Dhersin & M\"ohle \cite{DM12}. An application to
population genetics dealing with the total number of mutations in the
genealogical tree is also given.
