Volume
Decided: the cub = a cube 1 unc per side ≈ 1.7736 L. Water in it ≈ 1 lib.
Why: volume follows directly from length (no separate definition), it makes the water rule of thumb work, and dozenal fractions of it land close to common drink sizes.
Advantage: volume needs no definition of its own, a cub of water weighs about a lib, and drink sizes stay familiar.
How length leads to area, volume and (through water) mass:
flowchart LR di["dig<br>1.01 cm"] -->|"× 10"| un["unc<br>12.1 cm"] un -->|"× 2"| sp["span<br>24.2 cm"] un -->|"× 10"| p["pace<br>1.45 m"] p -->|"squared, × 1,000"| ag["ager<br>3,646 m²"] un -->|"cubed"| cu["cub<br>1.77 L"] di -->|"cubed"| dc["dig-cube<br>1.03 mL"] cu -->|"of water ≈"| li["lib<br>1.77 kg"] dc -->|"of water ≈"| mli["0;001 lib<br>1.03 g"]
Good size for milk. Dozenal fractions land close to common drink and pub sizes (all ~4% larger):
| Fraction | mL | Close to |
|---|---|---|
| 1 | 1,774 | large milk |
| 0;8 (2/3) | 1,182 | pub jug (AU 1,140) |
| 0;6 (1/2) | 887 | |
| 0;4 (1/3) | 591 | pint (AU 570, UK 568); US 20 fl oz bottle (591) - almost exact |
| 0;3 (1/4) | 443 | schooner (AU 425); 440 mL can |
| 0;2 (1/6) | 296 | pot/middy (AU 285), UK half pint (284); 300 mL bottle |
| 0;1 (a twelfth) | 148 | small glass / wine pour (150) |
Small volumes (kitchen and drinks):
| Fraction | mL | Close to |
|---|---|---|
| 0;06 | 73.9 | quarter cup |
| 0;1 | 148 | half cup |
| 0;2 | 296 | cup (AU 250, US 237) - a bit larger |
| 0;025 | 29.8 | spirit shot (30 mL) |
| 0;01 | 12.3 | standard drink of pure alcohol: 9.7 g ethanol (AU std drink = 10 g) |
| 0;004 | 4.1 | teaspoon (5 mL) |
| 0;001 | 1.03 | a dig-cube, about 1 mL / 1 g of water |
Rainfall
Proposed (not decided): rainfall is measured as a depth in lin (0;1 dig ≈ 0.84 mm; the name is also still proposed), and that's the same number as libs of water per square pace.
- A cub is 0;001 cubic pace, so 1 cub spread over 1 square pace is 0;001 p = 1 lin deep, and a cub of water weighs about a lib. So 1 lin of rain = 1 li of water per p² - just as 1 mm of rain is 1 L (1 kg) per m²
- Gauges keep measuring depth, as they do now; the lib figure is for tanks, roofs and gardens: 10 lin of rain on a 100 p² roof (304 m²) is 1,000 li, which fills 1,000 cu (1 t↑cu, 3.06 m³) of tank
| Rain | mm (dec) | lin |
|---|---|---|
| Light shower | 1 | 1;2 |
| Rainy day | 10 | E;X |
| Heavy storm | 25 | 25;8 |
| Flood rain | 100 | 9X;E |
| Sydney, a year | 1,200 | 9XE |