\ g \ cm}^{-3}$), the gas is monatomic and $\gamma=5/3$. The value of $K$ is defined such that when the gas is isothermal, $K = c_{\rm s}^2$ with $c_{\rm s} = 2.0 \times 10^4 {\rm \ cm\ s^{-1}}$, and when $\gamma$ changes the pressure is continuous.

Collapse of an initially-static cloud
-------------------------------------

To test that the above equation of state captures the important elements of the gas’s behaviour, spherically-symmetric, one-dimensional (1-D), finite-difference calculations were performed of the collapse of an initially-static molecular cloud core with the above parameters and equation of state. The results are shown in Figure \[bate.static\] (solid line). These results are in good agreement with the results from 1-D calculations incorporating radiative transfer (e.g. Larson 1969; Winkler & Newman 1980a, b).

The three-dimensional (3-D) SPH code was also tested on the same problem to check that the SPH code can indeed accurately resolve the collapse down to stellar densities (Figure \[bate.static\], dotted line). There is excellent agreement between the results from the 1-D finite-difference code and those from the 3-D SPH code.

Collapse of a rotating cloud
----------------------------

Three-dimensional calculations are required if the molecular cloud core is rotating. In Figures \[bate.rotmassdens\] to \[bate.finalstate2\] we present results 