Actually, the use of that particular emblem on US Navy buttons dates from the 1840s through May 1941, when an order was issued to have the eagle's head facing toward the eagle's right.
To be able to time-date your button, we need a well-focused closeup photo showing your button's back, with a read-able backmark (maker's/dealer's company name).
I will be equally as gracious whenever you need to post a correction to something I've said. That's going to happen. I do not know everything there is to know. (Nobody does.)
For anybody here who doesn't already know:
As a companion to the Tice book on American Military buttons (which almost entirely stops after 1865), I recommend the book "Record of American Uniform and Historical Buttons, Bicentennial Edition" by Alphaeus H. Albert. Its 511 pages contain over 2,000 photos. It is available online at civil war relic dealers' websites for about $45.
NHBenz, that book's photos and info on the various versions of US Navy buttons from the Revolution to the present stretches from page 85 to page 106. (For example, the info on the 1941 change-order is on page 103, with photos on page 104.)
Not a good idea to soak 2 piece buttons as there is no way to get what you are soaking it in, out of the button right away. Please let it not be olive oil. It will turn your button black and steadly leak oil like a sunken oil tanker
There is a forum here that has very good tips on proper button cleaning.
Button in this condition should not be hard at all hard too read backmark. if you hayent cleaned the back just do it the same way you cleaned the front!