Hydraulic Architecture, Volume One, Part Two

HYDRAULIC ARCHITECTURE, BOOK III.

814. A

One takes a curved glass tube ABDI, of which the end A of the smaller branch must be hermetically sealed; through the other end I, one pours mercury to fill the lower part BD of the tube, taking care that no more air enters the branch AB than was there before. This is done so that the air enclosed there remains in equilibrium by its spring original: "ressort"; in 18th-century physics, this refers to the elastic force or pressure of a gas. with 28 inches of mercury, assuming the barometer is at that height in the place where the experiment is performed. Continuing to pour mercury, it will maintain itself at unequal heights in the two branches; for the mercury that passes into the shorter branch AB, coming to occupy a portion of the space of the air found there, which has no opening to escape, will be reduced into a smaller volume. If one supposes that it occupies no more than AF, half of AB, by drawing the horizontal line FG, one will see that the mercury will maintain itself at the height GH of 28 inches. Since the two columns FB and GD are in equilibrium with each other, the spring of the air contained in the space AF will be equal to the weight of 28 inches of mercury GH, plus that of the atmosphere which presses upon the surface HM—consequently, equal to the weight of 56 inches of mercury.

If one continues to pour it, until the air is reduced to the space AK, half of AF, or a quarter of AB, by drawing the horizontal line KL, one will see that the mercury will have risen to the height LO of 84 inches; adding 28 inches for the weight of the atmosphere, one will have 112 inches for the column of mercury equivalent to the force of the spring of the air reduced into the space AK. This proves that its spring increases in the proportion of the weights with which it is loaded, or in the inverse ratio of the decrease of its volume, from which one deduces this general principle:

813. That the product of the space occupied by a certain volume of air, by the load it supports in that state, is always equal to the product of the space where it has condensed by the weight it carries then. This is the first law of thermodynamics for ideal gases, specifically Boyle's Law (or the Mariotte Law in France), expressed as Pressure × Volume = Constant.

Thus, taking the number 28 to express the column of mercury that is in equilibrium with the spring of the air, if the barometer is at that height at the moment of the experiment, one will always have four reciprocally proportional terms, from which it will be easy to find the one that is unknown. Air further possesses this property: when condensed, the force of its spring does not weaken over time. M. de Roberval Gilles Personne de Roberval (1602–1675), a renowned French mathematician and physicist known for his work on the weight of air and the invention of the Roberval balance., having charged an air gun original: "arquebuse à vent"; a rifle that uses compressed air rather than gunpowder to propel a projectile. as usual, left it for sixteen years without touching it; at the end of this time, its effect was as great as if it had been charged on the spot.