The force on Ampere's bridge with straight ends (a current carrying n-shaped wire frame) due to the remainder of the circuit is derived correctly from Ampere's original differential force law for the first time without any amending factors. The theory is in reasonable agreement with the variation of the force as a function of the diameter of the wire as measured by Moyssides and Pappas1 (J. Appl. Phys. 59 (1986)). The force on Ampere's bridge with bent ends is also derived. These results differ from measurements by 20-30%. However, if a small systematic experimental error is postulated, there is agreement with the theory.