Statistical mechanics and the partition of numbers I. The transition of liquid helium

The existing theory of ‘Bose-Einstein condensation’ is compared with some results obtained from the theory of partition of numbers. Two models are examined, one in which the energy levels are all equally spaced, the other being the perfect gas model. It is concluded that orthodox theory can be relied upon at very high and at very low temperatures, also that the condensation phenomenon is a real one, but that it is not correctly described by orthodox theory, the position of the transition temperature and the form of the specific heat anomaly both being given wrongly.