Sir Howard Douglas (1776-1861), a noted British military officer and author, received a British patent (#3461) for this "reflecting circle or semicircle" in 1811. William Cary, who made the first examples of this instrument, noted that it combined a protractor with a reflecting system as used in a sextant. He also noted that it was "particularly useful in military survey, where the true situations of objects can at once be determined, and the sketch corrected at the same time
that it is taken." Instruments of this sort were still available at the end of the century. The signature on this example refers to either George Dollond (fl. 1820-1852), or to George Dollond II (fl. 1852-1866). The horizontal arc extends 140 degrees, is graduated to 30 minutes, and read by vernier to single minutes. The straight limb has a linear scale which is divided into tenths by a diagonals. This scale is not in Imperial or metric units, and differs from that in Douglas' original instrument.
Ref: Mr. Cary, "Description of the Patent reflecting Semicircle, invented by Sir Howard Douglas, Bart," Philosophical Magazine 38 (1811): 186-187 and plate VI.
"Howard Douglas" in Dictionary of National Biography, vol. 5, pp. 1203-1206.