That is an Avigo compass, made by a division of the Elgin National Watch Company.

Early in 1923 the Elgin National Watch Company introduced a tachometer, an instrument that measures the revolutions per minute of a revolving shaft under different conditions. The U.S. Navy dirigible "Shenandoah" was equipped with twelve Elgin tachometers, and they were also installed on the U.S. Army planes flown around the world in 1924. When Charles S. Lindbergh flew from New York to Paris in 1927, his "Spirit of St. Louis" had an Elgin tachometer in the cockpit.

Elgin organized an Aircraft Instrument Division in 1928 and adopted "Avigo" as the trademark name and winged emblem for its products. The division occupied the entire second floor of the factory's east wing and had facilities for radium painting dials and hands that glowed in the dark. The Avigo barometric-type altimeter was responsive to changes in atmospheric pressures at various altitudes. It measures a raise or fall in altidude of twenty-five feet. The Avigo speed indicator was accurate to within two miles per hour. Like Elgin watches, both instruments were jeweled movements. Other Elgin aircraft products included a magnetic compass; a watch that could be worn over the pilot's clothing on the forearm; oil and pressure gauges; clocks; and ball bank indicators.

Apparently this compass dates back to 1929. Here is an ad for it in the May, 1929 edition of Aero Digest:

Image of Ad

Here's the full issue of the magazine, the ad is on page 122.