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The main properties of a new bulk metal film resistor have been previously presented at the Electronic Components Conference in Washington, May 6, 1964. In particular, it was shown that this resistor has an extremely low and controllable temperature coefficient of resistance. In the present paper a rigorous mathematical treatment of temperature coefficient changes in bulk metal film resistors due to thermal strains is presented. The resistance change corresponding to these thermal strains is used in resistor design to balance the inherent T.C. of the metal film. Special attention is focused on the contribution of protective coatings to thermal strains. Relationships have been developed between the temperature coefficient changes and the properties and thicknesses of substrate, metal film, and coatings. In this way design parameters and manufacturing tolerances have been prescribed on a fully rational basis.