US Army Sun Compass
The U.S. Army Sun Compass was produced during World War II in the early 1940s by Abrams Instrument Co. of Lansing, MI, designated Model SC-1. In operation, it could determine direction accurately by noting the angle of the sun at a known time of day. It was designed for daylight use, mounted on a vehicle in environments where a magnetic compass might not work properly, such as inside an aircraft or truck due to the metal content or electrical circuits nearby.
The exterior of the box is painted olive drab and the lid is lettered:
C. of E.
"C. of E." is no doubt the U.S. Army Corps of Engineers, responsible for military compasses and other instruments during World War II.
According to researcher François Pineau, in World War II the SC-1 was used in the North African desert by the Long Range Desert Patrol (the famed Desert Rats) and other American, British or Australian units. Other uses were in B-24 Liberator bombers and by Army ground troops in the Philippines. It is reported to have been used through the 1970s for polar region expeditions where magnetic readings are unreliable or in the Sahara desert.
The manual visible in the case is TM 5-9422 War Department Maintenance Manual and Parts Catalog for Compass, Sun, Universal Type, Abrams Model SC-1. The second manual underneath is probably the matching Operator's Manual.