(to appear in the Intl. Journal of Engineering Science)

 Robin J. Knops and Amit Acharya

 The relationship between dislocation theory and the difference of linear elastic solutions for two different sets of elastic moduli, derived by Filon in two-dimensions, is generalised to three-dimensions. Essential features are developed and illustrated by the  examples of the edge and screw dislocations. The inhomogeneity  problem is  discussed within the same context and related to Somigliana dislocations, and  in the limit  to the interstitial atom.