In his 1961 papers, Hayashi showed that the convective envelope of a star is determined by: E = 4 π π G 3 / 2 ( μ μ H k ) 5 / 2 M 1 / 2 R 3 / 2 P T 5 / 2 where E is unitless, and not the energy. Modelling stars as polytropes with index 3/2—in other words, assuming they follow a pressure-density relationship of P = K ρ ρ 5 / 3 —he found that E = 45 is the maximum for a quasistatic star. If a star is not contracting rapidly, E = 45 defines a curve on the HR diagram, to the right of which the star cannot exist. He then computed the evolutionary tracks and isochrones (luminosity-temperature distributions of stars at a given age) for a variety of stellar masses and noted that NGC2264, a very young star cluster, fits the isochrones well. In particular, he calculated much lower ages for solar-type stars in NGC2264 and predicted that these stars were rapidly contracting T Tauri stars.