The Universal Rarity Scale

I propose the Universal Rarity Scale-one that is mathematically sound in its progression and relationship among its divisions, and one that will be applicable to any series. Stated simply, it is a geometric progression of numbers, rounded off for convenience in use, with each category containing about twice as many members as the 'preceding category. The proposed Universal Rarity Scale uses a simple geometric progression of numbers, as 1, 2, 4, 8, 16, 32, etc. (see the rightmost of each number pair):

PROPOSED SCALE DRAFT:

Universal Rarity Scale-1 = 1 known, unique

URS-2 = 2 known

URS-3 = 3 or4

URS-4 = 5 to 8

URS-5 = 9 to 16

URS-6 = 17 to 32

URS-7 = 33 to 64

URS-8 = 65 to 128

URS-9 = 129 to 256

URS-10 = 257 to 512

URS-ll = 513 to 1,024

URS-12 = 1,025 to 2,048

URS-13 = 2,049 to 4,096

URS-14 = 4,097 to 8,192

URS-15 = 8,193 to 16,384

URS-16 = 16,385 to 32,768

URS-17 = 32,769 to 65,536

URS-15 = 65,537 to 131,072

URS-19 = 131,073 to 262,144

URS-20 = 262,145 to 524,288

URS-21 = 524,289 to 1,048,576

URS-22 = 1,048,577 to 2,097,152

URS-23 = 2,097,153 to 4,194,304

URS-24 = 4,194,305 to 8,388,608

URS-25> = same progression

The suggestion was made to me by John Croon, and seconded by J. Alan Bricker, that the Universal Rarity Scale could be simplified by rounding off the numbers in higher categories. For example, URS-16 could be 16,000 to 31,999; URS-17 could be 32,000 to 64,999, etc. While this takes the DRS away from precise mathematics, it makes it easier to use. Thus, I give the final form of the URS as follows:

THE UNIVERSAL RARITY SCALE Universal Rarity Scale-O = None known

URS-l = I known, unique

URS-2 = 2 known

URS-3 =3 or4

URS-4= 5 to 8

URS-5 = 9 to 16

URS-6 = 17 to 32

URS-7 = 33 to 64

URS-8 = 65 to 124

URS-9 = 125 to 249

URS-10 = 250 to 499

URS-11 = 500 to 999

URS-12 = 1,000 to 1,999

URS-13 == 2,000 to 3,999

URS-14 =4,000 to 7,999

URS-15== 8,000 to 15,999

URS-16 = 16,000 to 31,999

URS-17= 32,000 to 64,999

URS-18 = 65,000 to 124,999

URS-19 = 1,25,000 to 249,999

URS-20 = 250,000 to 499,999

URS-21 = 500,000 to 999,999

URS-22 = 1,000,000 to 1,999,999

URS-23 = 2,000,000 to 3,999,999

URS-24 = 4,000,000 to 7,999,999

URS-25 = 8,000,000 to 15,999,999

URS-26>= same progression

Application of the Universal Rarity Scale

For the numismatist, the Universal Rarity Scale permits accuracy not hitherto known, For example, an 1884 trade dollar (10 known) is URS-5, while an 1885 (5 known) is URS-4. The 1870-S $3 and 1873- CC No Arrows dime, each of which is unique, are each URS-1 The 1873-S Liberty Seated dollar, of which none is known to exist, is URS-O.