The Number of Radio-active Transformations as Determined by Analysis of the Observations

It is known that the expression for the nth product of a series of radio-active transformations is properly represented as the sum of n terms of the type a_ne^-λ_nt. When n is known, the coefficients a_n and λ_n are determinable with comparative ease. The present Paper finds a criterion for determining n, the number of transformations, when this is not known from a priori considerations. This consists in the successive evaluation of a system of simple determinants easily constructed from the observations. The value of n is at once found from the order of the particular member of the system that vanishes.