1910
The Ithaca side by side 12 gauge serial 188650 was made in 1927.
1904
If this is an old side by side it would be a Baker model made in 1886. Serial numbers of Ithaca shotguns for that year were 2448 - 4101.
I would say that you have a Ithaca model flues double barrel shotgun that was made in the year 1923,with the serial number that you provided.
The double is the last model NID (New Ithaca Double) mfg by Ithaca. This one was mfg in 1927. Depending on condition and gauge you may have a very desirable shotgun.
The gauge is stamped on the water table by the serial number. It is a Flues model made in 1924.
This ia an Ithaca Gun Co. "Crass" model double and was made in 1896. REFERENCE: the Reference Center pages at www.ithacagunrepair.com - 02-16-07 SPR.
There's a list of serial numbers by year at http://ithacagunrepair.com/page5/page23/
Made in 1919. Either a Flues or NIG model. Value depends on condition, but probably around $350.
If the shotgun is a hammerless double, it is a Baker Model produced in 1899 (per Dixie Gun Works, Ithaca Serialization Guide) That serial should be a 1926 production NID. sales@countrygunsmith.net
1950
1947