# Boyle’s law

Boyle’s law is the principle that, at constant temperature, the volume occupied by a gas is inversely proportional to pressure (at least until the pressure gets extremely high). In symbolic terms, PV = k, where k is a constant. The pioneering scientist and amateur theologian Robert Boyle published this law in 1662, in his New Experiments Physico-Mechanical, Touching the Air (2nd edition): Whereunto is added a defence of the authors explication of the experiments against the objections of Franciscus Linus and Thomas Hobbes. The chart above shows the data he collected, together with a diagram of his apparatus and a scan of his original data table (cleaned up from an image in the Wellcome Collection).

Boyle’s apparatus involved an uneven U-shaped tube, sealed at the short end, and with mercury in the “U.” Further mercury was added to the long end, in order to compress the air in the short end to a specified volume. The pressure in each case (in inches of mercury) was the measured amount in the long end of the tube, plus 29.125 inches for atmospheric pressure.

Boyle’s experimental work was excellent, with all errors less than 1% (on my calculation). This is shown visually by the close fit of his experimental datapoints to the line PV = 351.9. His arithmetic was not quite so good – column “E” in his original table showed his predicted pressure, calculated laboriously using fractions. Seven of the 25 entries are incorrect. For example, using his approach, the 7th entry should be 1398 / 36 = 38 5/6, but Boyle has 38 7/8.

Home replications of Boyle’s work generally involve weights, a large syringe, some precarious balancing, and the fact that the air column sitting on a square centimetre weighs about 1.03 kg. Like so:

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