Minor quick tidbits on the dd for reference.
If it has the markings on the rib in the side or a "two-line" on top it is a type I, on the side is a 1st model, on the top 2nd model. (E. Remington)
If there is a on line address on the top (Remington Arms) this is a Type II, third model (unless it includes UMC) which it becomes a type III 4th model, if the rib is gone it's a mono-block (quite scared) it's a 5th model.
Type I, 1st model's are serials. (Around 2,000 made, 3 actual variations)
Type I, 2nd model are NOT serials, two runs (~18,000) made from 1-9999 and then repeated.
Type II, 3rd model has 6 variations, the 1st variation is a serial number this is referred to as a "short-line" because of the obvious words start and end 1/2 or so from sight/hinge (others are 1/4 or so). They made approximately 3,000 of these, they are simply serials because they change the variation before they started the run from 1-9999, repeat, repeat.
Type III Remington UMC's, they have real serials (although at the end they got a bit goofy with letters), starting in 1921 they also marked the month/date code on the lug under the barrel.