If you look at WWII pictures, you will notice
that almost all female servicewomen wear their garrison caps the same way
-- primarily angled on the right side of their head, in a style tending
to cover part of the right portion of their hairstyle. This is because
women were ordered to wear their headgear in the same exact manner prescribed
for male personnel. . The reason why the right side was chosen is
connected with the traditional courtesy of rendering military salutes.
The custom originated from the medieval practice of European knights to
tip their helmet visors -- normally closed for hostile combat -- upwards
to greet friendly knights. The right hand was used specifically to show
that the knight's fighting arm was not holding a weapon.
from Army Regulations AR 600-37 43, April 1945 showing correct wear
of the garrison cap
During World War II, an individual soldier
(male or female) saluted in the American military with the tip of the closed
forefingers of the extended right hand touching either the corner of the
service cap visor, or the forehead just below the garrison cap.
With the garrison cap angled to the right side,
the fingers touch just below the lowest part of the garrison caps. Because of this closeness, sometimes the fingers
may brush the bottom fringe of the cap itself, as wartime photographs demonstrate.