grammas pocket watch

Inherited from my Grandmother, I think it is from early 1900's. I cannot tell what was engraved on outside back, only can see slightly, maybe some type of animal/bird.
The emblem/stamp on inside back reads Wadsworth 14ct, Pilot guaranteed 15 years and the engraved number 233667. Then there seems to be hand scribed numbers 36635ED and 3127 with an A under it, also another number 03720k.
The inside of watch reads Elgin Nat'l Watch Co., USA under it. And the number 8387895 and 15 jewel.. also says Safety Pinion.
If anyone can give me any info, it would be much appreciated.