Ullage or ouillage comes from the old French ouiller which is the unfilled head space above a liquid in a container. In manufacturing processes it can also mean any small amount that is left over from a packing process which is insufficient to fill a keg or container. For example 1003 litres of a liquid would fill 200 x 5 litre containers and leave 3 litres of ullage over. Modern computerised stock control and processing systems find ullage a problem to handle. However, I have learned to love it. The ullage can be used for quality control testing, decanted into samples to send to potential clients or sometimes just kept to one side for in house use. When a production process yields the required amount of containers to fill a customer's order and leave a few litres or kilos over everyone is happy. When a process runs short there are problems and questions are asked. In my experience its much better to have a slight excess at the end and a quieter life! Mr Micawber in Oliver Twist by Charles Dickens would certainly agree. A surplus of 6d on his annual accounts brought happiness but a deficit of 6d brought misery. I don't know if astronomers ever used the term ullage but even the ancients know about a surplus in the Lunar yearly cycle and the Solar year. The Solar year is 12.368 lunations, so between twelve and thirteen full Moons. This is sometimes referred to as the over plus of the Moon or the Silver fraction. It comes to 10.875 days, however, the Lunar fraction is more interesting. 0.368 lunations is the fraction 7/19 to within 0.1% accuracy. The fraction 7/19 was obviously known to the architects who designed Stonehenge. The Aubrey Circle and the Sarsen Circle at Stonehenge have diameters of 283 feet and 104 feet respectively which are in the ratio 7/19. Also if we draw a pentagram inside a circle of diameter 13 units the pentagram arms have lengths of 12.368 units. If we add the lengths of all five star arms together we get the number of full Moons in five years 61.82.
The ancient Gaulish Celtic calendar was based on a five year Lunar cycle. This calendar was used in the second century CE but was only rediscovered in fragmentary form in 1897 in Coligny in France. There was an error of 6 hours every five years so about 0.014%. Our current calendar has an error of 0.06% which is why we have leap years to reset the lost day every four years. The ancient Gauls only had to reset 6 hours every five years so arguably had a better system.
Just like the ancient astronomers who looked for symmetry in the night sky the scientist Albert Einstein in our time also looked for symmetry in 1905 when working out his theory of special relativity. Einstein once famously said he had three rules of work. Out of clutter find simplicity. From discord find harmony and in the middle of difficulty lies opportunity.
Like Einstein our ancestors found harmony in discord and realised that the Lunar ullage, or over plus of the Moon, could be explained by the fraction 7/19 and that they could then use this fraction to keep track of time and create a simple effective yearly calendar. Life would never be the same again!