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We apply the Tremaine-Weinberg method of pattern speed determination to datacubes of CO emission in six spiral galaxies from the BIMA SONG survey each withan ISM dominated by molecular gas. We compare derived pattern speeds withestimates based on other methods, usually involving the identification of apredicted behavior at one or more resonances of the pattern(s). In two cases(NGC 1068 and NGC 4736) we find evidence for a central bar pattern speed thatis greater than that of the surrounding spiral and roughly consistent withprevious estimates. However, the spiral pattern speed in both cases is muchlarger than previous determinations. For the barred spirals NGC 3627 and NGC4321, the method is insensitive to the bar pattern speed (the bar in each isnearly parallel to the major axis; in this case the method will not work), butfor the former galaxy the spiral pattern speed found agrees with previousestimates of the bar pattern speed, suggesting that these two structures arepart of a single pattern. For the latter, the spiral pattern speed found is inagreement with several previous determinations. For the flocculent spiral NGC4414 and the ``Evil Eye'' galaxy NGC 4826, the method does not support thepresence of a large-scale coherent pattern. We also apply the method to asimulated barred galaxy in order to demonstrate its validity and to understandits sensitivity to various observational parameters. In addition, we study theresults of applying the method to a simulated, clumpy axisymmetric disk with nowave present. The TW method in this case may falsely indicate a well-definedpattern.Comment: 54 pages with 23 figures, accepted for publication in Ap

Pattern Speeds of BIMA SONG Galaxies with Molecule‐dominated Interstellar Mediums Using the Tremaine‐Weinberg Method