  We present a study of hierarchical structure in the Perseus molecular cloud,
from the scale of the entire cloud ($\gtrsim$10 pc) to smaller clumps ($\sim$1
pc), cores ($\sim$0.05-0.1 pc), envelopes ($\sim$300-3000 AU) and protostellar
objects ($\sim$15 AU). We use new observations from the Submillimeter Array
(SMA) large project "Mass Assembly of Stellar Systems and their Evolution with
the SMA (MASSES)" to probe the envelopes, and recent single-dish and
interferometric observations from the literature for the remaining scales. This
is the first study to analyze hierarchical structure over five scales in the
same cloud complex. We compare the number of fragments with the number of Jeans
masses in each scale to calculate the Jeans efficiency, or the ratio of
observed to expected number of fragments. The velocity dispersion is assumed to
arise either from purely thermal motions, or from combined thermal and
non-thermal motions inferred from observed spectral line widths. For each
scale, thermal Jeans fragmentation predicts more fragments than observed,
corresponding to inefficient thermal Jeans fragmentation. For the smallest
scale, thermal plus non-thermal Jeans fragmentation also predicts too many
protostellar objects. However at each of the larger scales thermal plus
non-thermal Jeans fragmentation predicts fewer than one fragment, corresponding
to no fragmentation into envelopes, cores, and clumps. Over all scales, the
results are inconsistent with complete Jeans fragmentation based on either
thermal or thermal plus non-thermal motions. They are more nearly consistent
with inefficient thermal Jeans fragmentation, where the thermal Jeans
efficiency increases from the largest to the smallest scale.
