"Eastman" Arms seems to be a misreading of Eastern Arms Co, from worn markings.
Eastern Arms was a house brand for either Sears or a major hardware store. It's hard to be positive a hundred years later, and both stories are likely. They were manufactured by either J. Stevens Arms, Iver Johnson, Meriden Firearms, or Harrington & Richardson (H&R) under license (the contract went to the lowest bidder each year), and branded "Eastern."
They are worth very little to collectors, only worth a little for their functionality. They sell used online and at stores for about $100 (in 2012). They have not been in production for decades.
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