The source counts distribution of radio-sources from a radio-astronomical survey is the cumulative distribution of the the number of sources (N) brighter than a given flux density (S)
Early work on cataloguing radio sources had as an aim the determination of the source counts distribution to help decide between cosmological models
For a uniform distribution of radio sources at not too large redshift (ie in a 'steady-state, Euclidean universe') the slope of the cumulative distribution of log(N) versus log (S) would be -1.5,
Data from the early Cambridge 2C survey (published 1955) apparently implied a (log(N),log(S)) slope of nearly -3.0. This appeared to invalidate the Steady State theory of Hoyle and co-workers. Unfortunately many of these weaker sources were subsequently found to be due to 'confusion' (the blending of several weak sources in the side-lobes of the interferometer, to give a response like one stronger one.)
By contrast, analysis from the contemporaneous Mills Cross data (by Slee and Mills) were consistent with an index of -1.5.
The immediate interest in testing the Steady-State theory through source-counts was reduced by the discover of the 3K background radiation in the mid 60s, which essentially confirmed the Big-Bang model.
Later radio survey data have shown a complex picture - source counts show the effects of both density and luminosity evolution of the principal radio sources over cosmic timescales.
