Statistics, as governed by the asymptotic calculus of probabilities, in the manner propounded by Condorcet at the end of the 18th century, and pursued by Laplace and his school, was gradually put in abeyance, as early as the 1830s, by statisticians who sought their methods, and the legitimacy of their practice, from other approaches – at the same time as the field was being abandoned by mathematicians, drawn as they were to other theories and pursuits. Virtually alone in this respect, Jules Bienaymé stood his ground as a defender of the Laplacian statistical theory, to which he brought further developments on a number of points. The recent uncovering of family archives now allows the lineaments of an isolated, albeit remarkable, body of work to be brought into sharper focus. The two unpublished papers presented here are drawn from this archive. The first, sent in 1855 to the French Académie des sciences morales et politiques, provides a fair illustration of the manner in which this author sought to cut down to size the excessive claims being made, regarding statistics as practiced in his time. The second paper, addressed in 1842 to the Société philomatique, gives a glimpse of his own personal endeavours and achievements in the field, anticipating as they do on current statistical theory.