The formula then becomes I = Ioe kt (2) where e is the base of Napierian logarithms, and k is a constant which is practically the same as j for bodies which do not absorb very rapidly.
Similarly the continued fraction given by Euler as equivalent to 1(e - 1) (e being the base of Napierian logarithms), viz.
In 1873 Charles Hermite proved that the base of the Napierian logarithms cannot be a root of a rational algebraical equation of any degree.3 To prove the same proposition regarding 7r is to prove that a Euclidean construction for circle-quadrature is impossible.
The two systems of logarithms for which extensive tables have been calculated are the Napierian, or hyperbolic, or natural system, of which the base is e, and the Briggian, or decimal, or common system, of which the base is io; and we see that the logarithms in the latter system may be deduced from those in the former by multiplication by the constant multiplier /loge io, which is called the modulus of the common system of logarithms.
., and the value of its reciprocal, log e io (by multiplication by which Briggian logarithms may be converted into Napierian logarithms) is 2.302585092994 0 45 68401 799 1 4