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Dimensional analysis is supposed to prevent such errors.

In dimensional analysis, that confusingly becomes joules, the same unit as energy.

"One of our early attempts," he said, "was simply to put this in as a volume factor, so that the left-hand side of the equation, below the line, would read—" He scribbled again on the paper and held it up: md = K d3ft2 "Unfortunately, as you can perhaps see," Dr. O'Connor said, "the equation would not stand up under dimensional analysis."