This is a partial translation of the memoir by Andr?-Marie AMP?RE, entitled 'Th?orie Math?matique des Ph?nom?nes ?lectro-dynamiques Uniquement D?duite de L'Exp?rience', up until the point where he has derived his formula for the force between two elements of electric current. A knowledge of differentiation and integration techniques is required to understand this memoir, as well as a basic knowledge of electricity and magnetism, and, while the level of mathematical knowledge required is not exceedingly high, there is much detail to get through. In parts 2 & 3 of this booklet I have included Maxwell's contribution to the subject, from his 'Treatise', and a few simple geometric applications of Amp?re's formula: more complex problems may require the use of numerical methods of integration.
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