The rule
The rule states that over the first period the quantity increases by 1/12. Then in the second period by 2/12, in the third by 3/12, in the fourth by 3/12, fifth by 2/12 and at the end of the sixth period reaches its maximum with an increase of 1/12. The steps are 1:2:3:3:2:1 giving a total change of 12/12. Over the next six intervals the quantity reduces in a similar manner by 1, 2, 3, 3, 2, 1 twelfths.Applications
In many parts of the world the tides approximate to a semi-diurnal sine curve, that is there are two high- and two low- tides per day. As an estimate then each period equates to 1 hour, with the tide rising by 1, 2, 3, 3, 2, finally 1 twelfths of its total range in each hour, from low tide to high tide in about 6 hours, then the tide is decreasing by the same pattern in the next 6 hours, back to low tide. In places where there is only one high and one low water per day, the rule can be used by assuming the steps are 2 hours. If the tidal curve does not approximate to a sine wave then the rule cannot be used. This is important when navigating aExample calculations
Tides
If a tide table gives the information that tomorrow's low water would be at noon and that the water level at this time would be two metres aboveDaylength
If midwinter sunrise and set are at 09:00 and 15:00, and midsummer at 03:00 and 21:00, the daylight duration will shift by 0:30, 1:00, 1:30, 1:30, 1:00 and 0:30 over the six months from one solstice to the other. Likewise the day length changes by 0:30, 1:00, 1:30, 1:30, 1:00 and 0:30 each month. More equatorial latitudes change by less, but still in the same proportions; more polar by more.Caveats
The rule is a rough approximation only and should be applied with great caution when used for navigational purposes. Officially produced tide tables should be used in preference whenever possible. The rule assumes that all tides behave in a regular manner, this is not true of some geographical locations, such as Poole Harbour or the Solent where there are "double" high waters or Weymouth Bay where there is a double low water. The rule assumes that the period between high and low tides is six hours but this is an underestimate and can vary anyway.References
{{DEFAULTSORT:Rule Of Twelfths Twelfths, rule of Tide tables de:Gezeitenrechnung#Zwölftel-Regel