In 1643, the Italian physicist and mathematician, Evangelista Torricelli, who for a few months had acted as Galileos secretary, conducted a celebrated experiment in Florence. He demonstrated that a column of mercury in an inverted tube can be supported by the pressure of air outside of the tube, with the creation of a small section of vacuum above the mercury. This experiment essentially paved the way towards the invention of the barometer, as well as drawing the attention of Robert Boyle, then a "skeptical" scientist working in England. Boyle was inspired by Torricellis experiment to investigate how the elasticity of air responds to varying pressure, and he did this through a series of experiments with a setup reminiscent of that used by Torricelli. Boyle published his results in 1662.  
Later on, in 1676, the French physicist Edme Mariotte, independently arrived at the same conclusions of Boyle, while also noting some dependency of air volume on temperature. However it took another century and a half for the development of thermometry and recognition of the absolute zero temperature scale, which eventually allowed the discovery of temperature-dependent gas laws.