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If one is to have a complete and satisfying understanding of the theory of the torsion balance, it is essential to have clearly in mind a physical picture of the quantities involved. Most authors assume either that their readers are well versed in the differential geometry of surfaces in a Euclidean three-dimensional space or that a discussion of surface curvature is far beyond the reader's ability to grasp. Too often is neither of these true. The writer attempts to present a mathematical discussion of this matter in which only the bare fundamental concepts of the differential calculus are needed.
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