The Weighing of Liquids: Oil and Water in Communicating Vessels
Why oil floats and rises higher, and the equilibrium of liquids in tubes of equal and unequal bore
Four diagrams on the right show V-shaped communicating vessels of equal and of unequal bore, a U-tube on a stand, and paired cylinders of different diameter, all for a study titled 'On the weighing of liquids.' Leonardo examines a V-shaped balance of two joined tubes holding water with some oil on one side, and argues that the liquid surfaces will not settle level. Because oil is lighter than water it rests on top, and to equal the weight of the water lacking beneath it a greater quantity of oil is needed, so its surface stands higher while the water under it stands lower than the opposite water. A closing case treats oil half as light as water in a third instrument, where the rule holds whatever the bore or quantity.
On this page
Oil floats above water and rises higher in its tube
In the balance a e g of two tubes joined at their lower part, the water and oil surfaces will not sit level. Oil is lighter, so it rests above the water; to equal the weight of the missing water it must occupy more space, so the oil surface stands higher and the water beneath it lower than the opposite water.
Oil half as light as water: the third instrument
If the oil is half as light as water, this third instrument has on one side the water surface level with the center of gravity of the oil. Whatever the thickness of the tubes and whatever the quantity of oil, the rule never departs from this order.
The adversary: surface n m raising surface S t
For the case of communicating vessels of different diameter, Leonardo records the adversary's contention that the surface n m will raise up the opposite surface S t.