In his Theory of Observations, T. N. Thiele has introduced the semi- invariants (or cumulaats) into statistical mathematics. These functions, endowed with remarkable properties, have found only few applications in statistics. It is, however, surprising that their interest for theoretical physics has not been recognized from the origin of quantum mechanics. In order to indicate this, a generalized defimtion of cumulants is given which is adaptable to functional analysis, and some problems of theoretical physics where their utilization appears natural are mentioned. It appears that an implicit use of cumulants has been made in modern theories. (tr-auth)