The Bernoulli numbers of the second kind are defined by means of the following generating function
The numbers have been called the Cauchy numbers of the first kind. These numbers satisfy the following relation
The first few of these numbers are given by . These numbers are related to Euler’s constant, and th harmonic numbers, , that is
The Bernoulli numbers of higher-order are defined by means of the following generating function
For the numbers are called the Nörlund numbers or the Cauchy numbers of the second type, may be determined by the generating function
Relations between the numbers and are given by
The author gives a formula expressing the Bernoulli numbers of the second kind as 2-adically convergent sums of traces of algebraic integers. By using this formula, the author proves the formulae and conjectures of Adelberg concerning the initial 2-adic digits of these numbers. He also gives many relations on these numbers and Nörlund numbers or the Cauchy numbers of the second type.