The paper concerns itself primarily with the acoustical specifications necessary for intelligible speech transmission through radiating enclosures, such as gas masks, placed on the front of the head. The results apply to enclosures whose internal dimensions are small by comparison with the wave‐lengths significant for speech. Transmission through larger enclosures is in general poor. A speech transmitting device for a gas mask will ordinarily consist of a diaphragm, a perforated protective cover, and an exhaust valve. The acoustical system, however, must include the cavity between the mask and the face. The enclosures considered here radiate through a circular constriction, a set of perforations, or a diaphragm; specifications for the more complicated case of a diaphragm and cover have not been obtained, but may be inferred from the data presented here. The enclosures all behave as Helmholtz resonators when tested on an artificial voice. They may be specified acoustically by the resonant frequency, and a quantity related to the inertance of the acoustical system. It has been found convenient to express this property of a set of perforations or of a diaphragm in terms of an effective diameter: the diameter of the circular constriction that results in the same resonant frequency for the enclosure, or, in other words, has the same inertance. The intelligibility obtainable through an enclosure increases when either the resonant frequency or the effective diameter is increased. In general, the intelligibility will be satisfactory if the resonant frequency is at least as high as 1500 cycles per second, provided that the effective diameter is at least 1.25 inches.