what are these buttons?

[brandywine]

I posted this in the Native American thread and someone removed it because I suppose it is not a tool or weapon. But , anyhow, in my quest to find out what it is I will pose the question to the button experts.

This sat on the shelf of my wife's family for decades. No information or history. It is not for sale and I never intend to sell it so I'm not looking for value...just plain information. You guys have any thoughts?

Thank you in advance!

 

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[wvwildman]

looks like a chines hat

 

[SCdigger]

Indian Wars era Federal Eagle buttons...