resolution length/mass approaches the Jeans length/mass, collapse is artificially delayed due to viscous forces, softening of gravitational forces, or a combination of both. A good example is the collapse of an isothermal filament [@Trueloveetal97]. Such a filament should collapse without limit to a filamentary singularity without fragmenting. However, if the collapse perpendicular to the major-axis is delayed, small density perturbations along the filament may have enough time to grow to non-linear amplitudes and fragments may form along the bar.

Bate & Burkert [@BatBur97] first demonstrated the need for the Jeans mass criterion using self-gravitating SPH calculations. With SPH, the problem can be understood by considering the gravitational and pressure forces between two particles within a marginally Jeans-stable clump of gas of radius $R\approx h$ (Figure \[bate.forces\]). SPH codes typically soften the gravitational forces between neighbouring particles, using either the Plummer force law or kernel softening [@GinMon77; @HerKat89; @Benz90]. The characteristic gravitational softening length, $\epsilon$, may or may not be equal to the SPH hydrodynamic smoothing length, $h$, depending on the specific implementation. If $\epsilon=h$, the ratio of the gravitational and pressure forces between two particles is approximately constant for particle with separations $\simless h$. Thus, a Jeans-unstable clump of gas 