Correct Wear of Garrison Caps
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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. 
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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. 
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.Plate from Army Regulations AR 600-37 43, 
April 1945 showing correct wear of the garrison cap 
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Picture Source: Photograph from June 1944 published in: A Woman's War in the South Pacific. Lady G.I. by Irene Brion, 1997 ..... 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. 

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More information about saluting can be found here: How to Salute?

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So if you go out and take part in reenactment events, you will authenticate your impression if you take care to wear your garrison cap on the right side.
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Picture Source: WWII WAC recruitment posterWWII Women Marines recruitment posterPicture Source: Air Force Magazine Cover, October 1944Picture Source: Official U.S. Navy Photograph now in the collection of the National Archives

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