[naturalman1975]

I'm looking at the greatcoat sleeve from the 1916 'Private Soldiers' kit.

Somebody would have had a very bad day if they'd called the person wearing that coat 'Private'.

Our Sergeant Major has a crown upon his arm.
And he thinks he's got it on his bloody head.

[NorthMountain]

I’m reluctant to try reading foreign (to me) enlisted rank insignia from 100 years ago, but 3 chevrons (pointed down ... last time we had that in America was 1860s) suggests a sergeant of some sort.