when a massive circumbinary disc is formed, the PBE code tends to over-estimate the separation, and under-estimate the mass of the circumbinary disc and the binary’s mass ratio. Thus, if anything, the evolutionary curves in Figures \[bate.uniform\] and \[bate.1r\] tend to under-estimate the binary’s mass ratio and the mass of the circumbinary disc.

The Properties of Binary Stars
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The aim of developing the PBE code was to make it possible to predict some of the properties of binary stars and, by comparing these to the observed properties of binary systems, to constrain the initial conditions for binary star formation.

In order to obtain predictions about the properties of binaries we note that, generally, the initial mass of a ‘seed’ binary is smaller for those binaries with smaller separations. This relationship between a ‘seed’ binary’s mass and its separation is observed from fragmentation calculations [@Boss86; @BonBat94b] and is easily understood from a Jeans-mass argument [@Bate2000]. In order for fragmentation to occur, the Jeans length at the time of fragmentation must be less than or approximately equal to the separation of the binary which is formed. However, for a constant temperature, the Jeans mass depends linearly on the Jeans length. Thus, 