We present an analysis of ~3.5 square degrees of submillimetre continuum and extinction data of the Perseus molecular cloud. We identify 58 clumps in the submillimetre map and we identify 39 structures (`cores') and 11 associations of structures (`super cores') in the extinction map. The cumulative mass distributions of the submillimetre clumps and extinction cores have steep slopes (alpha ~ 2 and 1.5 - 2 respectively), steeper than the Salpeter IMF (alpha = 1.35), while the distribution of extinction super cores has a shallow slope (alpha ~ 1). Most of the submillimetre clumps are well fit by stable Bonnor-Ebert spheres with 10K 5 - 7 mag), although Bonnor-Ebert models suggest that we should have been able to detect them at lower column densities if they exist. These observations provide a stronger case for an extinction threshold than that found in analysis of less sensitive observations of the Ophiuchus molecular cloud. The relationship between submillimetre clumps and their parent extinction core has been analyzed. The submillimetre clumps tend to lie offset from the larger extinction peaks, suggesting the clumps formed via an external triggering event, consistent with previous observations. ; Comment: 38 pages, 12 figures, accepted by Astrophysical Journal slight changes to original due to a slight 3" error in the coordinates of the SCUBA map