DY is a code for September 1930 or 1974, the 510 was only manufactured from 1939 to 1962 the #4 designates the barrel as a fire damaged or blown up non-returnable firearm. Check your markings.
The bottom of the barrel, left of center, just in front of the stock.
The Remington Model 4 was made from 1890-1933. Check the barrel on the left side for letter markings (2 letters, just forward of the receiver) that are the code to date barrel was made. You may also check with Remington.
The Remington Model 41 was made from 1936-1939, they will have the date code stamped on the left side of the barrel. You can look up this code at the Remington Society of America, I will add a related link to this answer with it.
Date code is stamped on the barrel, left side in front of receiver. Check Remington Society of America for the codes.
Remington didn't make a model 55 rifle, nylon or otherwise. Autoloader, lever, or Bolt, Clip or Tub, letters on left side of barrel?
The right barrel is mod. The left is full. front trigger fires the right barrel. The back one fires the left.
They are date code stamped on the barrel on left side in front of receiver. A barrel location diagram and the date code table (month/year) is available on the Remington Society of America.
Look at the barrel code letters on the left side of the barrel in front of receiver. Look these up on the Remington Society of America site under the manufactures date link.
If the letters apear on the left side of the barrel above the reciver it will help you scipher the date of manufactor.
After 1920 Remington stamped a date code on the left side of the barrel in front of the receiver. The diagram and date code table is on the Remington Society of America.
Best left to a gunsmith.
Left side right in front of receiver, see related links for diagram and table.