After his father had been pardoned by Cardinal de Richelieu for his dissent and given the office of royal tax commissioner for the province of Haute Normandie, Pascal went with him to Rouen in 1640; in the same year his first mathematical publication, the Essai pour les Coniques (Essay on conical sections), appeared. Two years later he invented a calculating machine, which he had originally conceived to help his father with his tax work; this remarkable achievement was far in advance of the industrial skills required to produce it, although various versions were made and demonstrated to scientific colleagues, prominent politicians and members of the aristocracy.

2 The debate over the vacuum

Between 1646 and 1648, Pascal became embroiled in the fierce European debate concerning the existence of the vacuum. Torricelli’s experiment with a barometer, which involved placing a tube of mercury upside down in a bowl of mercury, had been made public in France by Mersenne in 1644, and had given rise to many competing interpretations. Nearly all of these had recourse to the notion of atmospheric pressure as an explanation, and there was general agreement that the space at the top of the tube contained some kind of rarefied and invisible matter, which was consistent with the Aristotelian adage natura abhorret vacuum.

In 1647, Pascal published his Expériences nouvelles touchant le vide (Experiments on the vacuum); this was the summary of a series of experiments he conducted with Pierre Petit, using variously sized and shaped tubes and different liquids. Through them he was able to determine the quantity of water and mercury that could be supported by air pressure and the size a siphon had to be in order to function. He also set out in this summary the reasons why there was no rarefied and invisible matter occupying the space above the column of liquid supported in the barometer, but did not feel able yet to affirm the existence of a vacuum.