This thesis is concerned with the estimation of the strength of a radioactive source when decay is rapid so that the usual assumption of a Poisson distribution of counts is not applicable. We distinguish two main cases according as the background radiation is small or large.

In the former case the common procedure of simply subtracting off a constant background radiation is adequate. If the background radiation is neglected altogether the method of maximum likelihood may be used to estimate both source strength and decay-constant for counts taken at any arbitrary times. The large-sample variances and covariances of these estimates are obtained and the procedure is illustrated on an actual set of experimental results.

When the background radiation is large their randomness should be taken into account. The exact distribution of counts is the sum of two independent variates, one a binomial and one a Poisson. However, a normal approximation with the same mean and variance will often suffice. We draw attention to a procedure due to Tandberg who considered the problem of obtaining a single optimum count. The method of maximum likelihood applied in conjunction with the assumption of normality of total counts is compared with his method in a numerical example. The possibility of taking two counts is also considered and the source strength is estimated by a least squares approach.