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The development of the circular dividing engine in England is traced from Henry Hindley and Jesse Ramsden through the improvements introduced by Ramsden's successors to the self-acting engine of William Simms. Particular emphasis is given to the invention, evolution and transmission of the methods used to achieve accuracy in: dividing the wheel; ratching the teeth and matching them to the endless screw; and mounting the cutter. The procedures adopted by Ramsden and Troughton for correcting initial dividing marks are also described.