Correction in the equation for the third order upper Kröner bound on the shear modulus of a polycrystalline aggregate of cubic crystals

An algebraic error has been detected in the formula given by Gairola and Kroner for the third order upper bound on the shear modulus of a polycrystalline aggregate of cubic crystals. The correct formula is calculated, and the answer verified by substituting single crystal elastic values into the equation. The fourth order bounds and self-consistent shear modulus are also calculated.