Jim,
The order of sorting Washington/Franklins is a personal choice, but I would suggest sorting based on design, appearance (printing method and shade), then type, perforations and watermark last of all. Production changes in the Washington/Franklin series were driven by an increase in the demand for stamps coupled with severe quality control problems. Initially, imperforate and hand assembled coil stamps were produced to meet the emerging use of affixing machines by businesses. The rotary press made high volume production of coils stamps possible as businesses increasingly used the machines for mass mailings. Offset stamps were printed to fill gaps in stamp production related to World I shortages. The various types of rotary and offset printings were directly related to difficulties printing acceptable looking stamps using unmodified flat plate dies.
The general appearance of Washington/Franklin stamps is often distinctive enough to be able to group them, especially with experience. Using a divide and conquer technique, once the stamps are grouped into sheet stamps, coils and imperforate, then they can be grouped by design, printing method, perforations and finally watermark: Separate the stamps by design and denomination For 1, 2 and 3 cent stamps, pick out the tall rotary sheet stamps (1 cent only) , the wide coil waste stamps (1 and 2 cent) and the offset stamps. The rotary press stamps have a distinctive appearance and can be distinguished from flat plate stamps using a horizontal coil or rotary sheet stamp as a size gauge. Note that booklet pane singles are a bit wider and perhaps a bit shorter than a standard sheet stamp, but not as wide as a rotary. The 2 cent is easier because coil waste stamps are type III (or rarely type II). The offset stamps have distinctive shades and appearance, generally with more unprinted area, especially a white ring inside the toga button. One-off checks include checking bluish paper for one and two cent stamps (the others are truly rare), perf 11 two cent stamps (rarer yet) and the perf 11 single line watermarked #461 (distinctive red shade, often found in with perf 10 stamps). Also, the 1 cent offset is perf 11 or 12½. Check 2 cent perf 11 stamps (and the unwatermarked imperf Schermack) for the distinctive and heavily inked toga button of a type Ia. Do not confuse with the strong toga button outline of any 2 cent offset. For 1, 2 and 3 cent stamps, pick out the wide rotary perf 11 x 10 or perf 11 sheet stamps (2 cent are type III or type II and the 3 cent is type II only). All 1912 flat plate 2 cent stamps are type I except for the type Ia #500.
Separate coil stamps by appearance: Flat plate coils have more saturated color, printing offset on the back and practically no ink wash or joint line smears. Rotary coils are wider or taller and always have perforations aligned between rows. Many used flat plate coils are faked by trimming a sheet stamp and most perf 12 coils are faked by trimming or adding perforations to an imperf stamp. A significant percentage of unused 1 and 2 cent perf 8½ and perf 10 coils are also fakes.
Almost all of the coils will also have to be checked for a watermark to determine their identity. The best on-line reference for types is the 1847usa.com Washington Franklins Worksheet Main Page. It has practically all of the type differences in a convenient and useful format. I recommend a 15 power glass for typing, but 10 power may be sufficient.
Regarding rarity, used #519 examples are extremely rare (I have never found one) as are not previously noticed carmine 5 cent #505 or #467 used. There should be more used #461 examples floating around, but they are rare (I have found one and perhaps a second). The easiest stamps to find are the coil waste #538 and #540 and sometimes a #595 (rare). The type II #539 is exceedingly rare, but may exist in a mix somewhere. Finding #500 is the easiest to find once your eyes are trained to spot them. I have picked out more than 80 from mix and maybe 10 #540 since I started looking years ago. The most recent one was during a Law and Order commercial break about a week ago.
Finally, the true rarities deserving mention are the compound perforated 10 x 12 and 12 x 10 1, 2 and 5 cent stamps and the perf 10 top or bottom varieties. I havent found any, but years ago, I found the used discovery copy of the #459 (2 cent imperf rotary coil) with United States Automatic Vending Machine private perforations.
Good luck in your search.
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