The paper is an exposition of the theoretical analysis made by the author of the experimental work of Woodbury, Canby and Lewis, on the Nature of Flame Movement in a Closed Cylinder, the results of which were published in THE TRANSACTIONS for the first half of 1921. No experimental evidence is presented by the author that has not been derived previously by other investigators.The relation of pressure to flame travel is derived first, the relation of mass burned is considered and a displacement diagram constructed, described and analyzed. The break of the flame-front curve, called the “point of arrest,” enters prominently into the discussion and computations; the pressure in the flame-front is studied; the reaction-velocities are calculated; and general comments are made.The mathematical analysis is supplementary to the paper itself and includes the calculations for the relation of pressure to flame travel, pressure drop in the flame-front, and the actual and the theoretical reaction velocities.The paper is an exposition of the theoretical analysis made by the author of the experimental work of Woodbury, Canby and Lewis, on the Nature of Flame Movement in a Closed Cylinder, the results of which were published in THE TRANSACTIONS for the first half of 1921. No experimental evidence is presented by the author that has not been derived previously by other investigators.The relation of pressure to flame travel is derived first, the relation of mass burned is considered and a displacement diagram constructed, described and analyzed. The break of the flame-front curve, called the “point of arrest,” enters prominently into the discussion and computations; the pressure in the flame-front is studied; the reaction-velocities are calculated; and general comments are made.The mathematical analysis is supplementary to the paper itself and includes the calculations for the relation of pressure to flame travel, pressure drop in the flame-front, and the actual and the theoretical reaction velocities.