• DOI:10.1017/S0007087400002934
• Corpus ID: 145513749

Daniel Bernoulli and the Vis Viva of Compressed Air

@article{Pacey1967DanielBA,
  title={Daniel Bernoulli and the Vis Viva of Compressed Air},
  author={Antony Pacey and Sara J. Fisher},
  journal={The British Journal for the History of Science},
  year={1967},
  volume={3},
  pages={388 - 392}
}

• A. Pacey, S. J. Fisher
• Published 1 December 1967
• Engineering
• The British Journal for the History of Science

T H E tenth section of Daniel Bernoulli's Hydrodynamica, in which he discussed the behaviour of air and other "elastic fluids", is well known because in it, Bernoulli put forward a kinetic theory which is closely similar to the modern one. The kinetic theory occupies the first few pages of the section; but further on, Bernoulli continued his investigation of elastic fluids in a manner which anticipated modern ideas in an even more striking and significant way. The important passage began with a study of the efflux of air from a vessel in which it was held under pressure, and this involved Bernoulli in a calculation of the vis viva stored in the compressed air. He could have used his kinetic theory to do this, but he said that the vis viva contained in a compressed elastic body was not to be explained "by assuming an internal fluid motion . . . but because these bodies by virtue of their elasticity are capable of producing an upward motion in other heavy bodies. To speak, therefore, of vis viva contained in a compressed elastic body simply means the potential ascent which the elastic body can impart to another body".3 Thus Bernoulli ensured that the vis viva of compressed air was understood in terms of a potential motion rather than the existing motions of the corpuscles of air, and at the same time he made the calculation of this quantity independent of his kinetic theory. Bernoulli went on to consider the compression of air in a vertical cylinder under the action of a piston, which was at first in equilibrium when loaded with a weight p. When a further weight, P, was added, the piston began to move downwards towards a new equilibrium position. At some intermediate point, GH, at a distance (x) from the starting point, the piston had a velocity (V). If the total length of the cylinder measured from the first position of the piston was (a), the pressure of the air would