Dumaresq Deflection (or, less ambiguously, Speed-Across) is the speed component of the enemy's motion relative to one's own ship which is perpendicular to the line of sight. That is, it is the speed with which he seems to move left or right across the line of fire. It was sometimes referred to simply as deflection, although that can be an ambiguous term used to refer to the angular measure of gun deflection (or "scale" in American parlance). Gun deflection was intended to place the shell on target after factors that cause lateral deviation of shell or target during time-of-flight.
Naval gun sights were designed to permit the sighting telescopes to be angled in pitch and yaw so that proper elevation and deflection could be established to hit the target while it was centred in the telescopic sights. These angles were usually established by sightsetting equipment.
A dumaresq or similar device would often be used to convert the relative motion of the firing and target ships and the target bearing to a range rate and a dumaresq deflection. The dumaresq deflection could then be converted to a Gun Deflection suitable for aiming by reference to a graphic chart that related the two variables at any given gun range.