Pocket Watch Size Information

18s, 12s, 3/0...  what does this mean?  Below is a table to convert an American pocket watch size to inches and millimeters.  This measurement refers to the size of the movement, as measured at the dial plate, not the case or dial.
Finally, YES they were measured in 30th of an inch, not 32nds!

Size (Lancashire) Inches Millimeters
20s 1 5/6 46.56
18s Common 1 23/30 44.86
17s 1 22/30 44.02
16s Common 1 21/30 43.18
14s Common 1 19/30 41.48
12s Common 1 17/30 39.78
10s Common 1 15/30 38.10
8s Common 1 13/30 36.40
6s Common 1 11/30 34.70
0s Common 1 5/30 29.62
3/0s Common 1 3/30 27.94