Bestimmung der Genauigkeit der Beobachtungen is the second of the three major pieces that Gauss wrote on statistical hypothesis generation. It continues the methodological tradition of Theoria Motus, producing estimates by maximizing probability density, however absence of the change-of- variables theorem causes technical difficulties that compromise its elegance. In Theoria Combinationis, Gauss abandoned the aforementioned method, hence placing Bestimmung der Genauigkeit at a crossroads in the evolution of Gauss’s statistical hypothesis generation methodology. The present translation is paired with a preface discussing the piece and its historical context.