NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Lars Bergman
Date: 2023 Nov 17, 14:37 -0800
Bob Goethe asked "Around when was the 32-point compass phased out in favor of compasses with a 360° face?"
Wrangel, in his "Lärobok i teoretisk och praktisk navigation" (Textbook of Theoretical and Practical Navigation), 2nd edition 1910, writes, in a foot note, "Compass roses marked in 360° are nowadays somewhere coming into use". Admiralty Manual of Navigation 1922, seems to use 360° in general.
The point compass was still in use for many years after that, especially for steering compasses. When using traverse calculations, the quadrantal system, e.g. N34°W or S57°E were used at least until the middle of the last century.
So the answer is probably that 360° compasses were introduced between 1910 and 1920 for new vessels, but old vessels did keep their old compasses for the rest of their lifes.
Lars
