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The three principal elastic constants, K11, K11, and K33, of the eutectic nematic liquid crystal mixture E7 have been determined as a function of temperature by following changes in the anisotropy of turbidity of a magnetically aligned specimen. The agreement with values of K22 obtained by a previous capacitance-voltage method is excellent, whereas the values of K11 and K33 derived from the absorption coefficients are systematically higher.