You have a Lewis or NIG model, built in 1903.
1938-39
1985 371871501 - 371882000
The value of a 16 gauge double barrel Ithaca shotgun with the serial number 461934 is determined by its condition. This gun in excellent condition is valued at 325.00 as of 2014.
Made in 1949
Made in 1968
It sounds to me that you have a Ithaca Flues model double barrel shotgun.With the serial number that you provided,your shotgun was made by Ithaca in 1917.
$317
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.
1946
According with Ithaca's web page range 371453501 to 371536500 is from 1975.
Forearm iron and watertable are the easiest places to obtain this info
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.