These sizes are being given in what is known as "Lancashire gauge". As with all wacky system of units, it is of British origin, but was taken up by American manufacturers. The system has increments of (of all things!) 1/30 of an inch. That is correct: 1/30 (not 1/32).
A size "0" watch is (for no particular reason I guess) 1 5/30 inch in size. Each added 1/30 of an inch increments the size number, and smaller watches likewise decrement the number for each 1/30 of an inch.
The size of a watch measures the movement, not the case. The measurement is taken on the part of the movement just behind the dial (the narrowest part of the dial side of the lower plate.
A table follows. Unit conversions are as follows:
| Watch Size | Fraction Inch | Decimal Inch | Ligne Size | Millimeter |
| 18 | 1 inch 23/30 | 1.766 | 19.87 | 44.86 |
| 17 | 1 inch 22/30 | 1.733 | 19.50 | 44.02 |
| 16 | 1 inch 21/30 | 1.700 | 19.12 | 43.17 |
| 15 | 1 inch 20/30 | 1.666 | 18.75 | 42.33 |
| 14 | 1 inch 19/30 | 1.633 | 18.37 | 41.48 |
| 13 | 1 inch 18/30 | 1.600 | 18.00 | 40.63 |
| 12 | 1 inch 17.30 | 1.566 | 17.62 | 39.79 |
| 11 | 1 inch 16/30 | 1.533 | 17.25 | 38.94 |
| 10 | 1 inch 15/30 | 1.500 | 16.87 | 38.09 |
| 9 | 1 inch 14/30 | 1.466 | 16.50 | 37.25 |
| 8 | 1 inch 13/30 | 1.433 | 16.12 | 36.40 |
| 7 | 1 inch 12/30 | 1.400 | 15.75 | 35.55 |
| 6 | 1 inch 11/30 | 1.366 | 15.37 | 34.71 |
| 5 | 1 inch 10/30 | 1.333 | 15.00 | 33.86 |
| 4 | 1 inch 9/30 | 1.300 | 14.62 | 33.01 |
| 3 | 1 inch 8/30 | 1.266 | 14.25 | 32.17 |
| 2 | 1 inch 7/30 | 1.233 | 13.87 | 31.32 |
| 1 | 1 inch 6/30 | 1.200 | 13.50 | 30.47 |
| 0 | 1 inch 5/30 | 1.166 | 13.12 | 29.63 |
| 00 or 2/0 | 1 inch 4/30 | 1.133 | 12.75 | 28.78 |
| 3/0 | 1 inch 3/30 | 1.100 | 12.37 | 27.93 |
| 4/0 | 1 inch 2/30 | 1.066 | 12.00 | 27.09 |
| 5/0 | 1 inch 1/30 | 1.033 | 11.62 | 26.24 |
| 6/0 | 1 inch | 1.000 | 11.25 | 25.39 |
| 7/0 | 29/30 | .966 | 10.87 | 24.55 |
| 8/0 | 28/30 | .933 | 10.50 | 23.70 |
| 9/0 | 27/30 | .900 | 10.12 | 22.85 |
| 10/0 | 26/30 | .866 | 9.75 | 22.01 |
| 11/0 | 25/30 | .833 | 9.37 | 21.16 |
| 12/0 | 24/30 | .800 | 9.00 | 20.31 |
| 13/0 | 23/30 | .766 | 8.62 | 19.47 |
| 14/0 | 22/30 | .733 | 8.25 | 18.62 |
| 15/0 | 21/30 | .700 | 7.87 | 17.77 |
| 16/0 | 20/30 | .666 | 7.50 | 16.93 |
| 17/0 | 19/30 | .633 | 7.12 | 16.08 |
| 18/0 | 18/30 | .600 | 6.75 | 15.23 |
| 19/0 | 17/30 | .566 | 6.37 | 14.39 |
| 20/0 | 16/30 | .533 | 6.00 | 13.54 |
| 21/0 | 15/30 | .500 | 5.62 | 12.69 |
| 22/0 | 14/30 | .466 | 5.25 | 11.85 |
| 23/0 | 13/30 | .433 | 4.87 | 11.00 |
| 24/0 | 12/30 | .400 | 4.50 | 10.15 |
| 25/0 | 11/30 | .366 | 4.12 | 9.31 |
| 26/0 | 10/30 | .333 | 3.75 | 8.46 |
Tom's notes / tom@mmto.org