  Two sets of high quality income data are analysed in detail, one set from the
UK, one from the USA. It is firstly demonstrated that both a log-normal
distribution and a Boltzmann distribution can give very accurate fits to both
these data sets. The absence of a power tail in the US data set is then
discussed. Taken in conjunction with detailed evidence from the UK and Japanese
income data, a strong case is made for the mathematically separate treatment of
waged and unwaged income. The authors present a case for preferring the use of
the Boltzmann distribution over the log-normal function, this leads to a brief
review of the work of a number of researchers, which shows that a coherent
theory for the distribution of all income can be postulated.
