the collapse of Jeans-unstable clumps being delayed significantly, enough particles should be used so that the Jeans length/mass is always resolved.

How many particles are necessary to ensure that the Jeans length/mass is resolved? With SPH, the spatial resolution is given by the smoothing length which is usually variable in time and space. The smoothing lengths are set by ensuring that each particle contains a certain number of neighbours, $N_{\rm neigh}$, or equivalently a fixed mass, within two smoothing lengths. Thus, in contrast to a grid-based code which has spatially-limited resolution, SPH has mass-limited resolution which [*automatically*]{} gives greater spatial resolution in regions of higher density. Therefore, with SPH, it is necessary to ensure that the minimum resolvable mass is always less than the Jeans mass. In practice, Bate & Burkert found that a Jeans mass should always be represented by at least $\approx 2 N_{\rm neigh}$ particles.

Collapse of a Molecular Cloud to Stellar Densities {#collstellar}
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The mass-limited resolution of SPH is ideal for studying the collapse and fragmentation of molecular cloud cores because there is a minimum Jeans mass in the problem (Figure \[bate.tmr\]). By contrast, there is no minimum Jeans length. This is a problem for 