While in St Petersburg he made one of his most famous discoveries when he defined the simple nodes and the frequencies of oscillation of a system. He showed that the movements of strings of musical instruments are composed of and infinite number of harmonic vibrations all superimposed on the string.

A second important work which Daniel produced while in St Petersburg was one on probability and political economy. Daniel makes the assumption that the moral value of the increase in a person's wealth is inversely proportional to the amount of that wealth. He then assigns probabilities to the various means that a person has to make money and deduces an expectation of increase in moral expectation. Daniel applied some of his deductions to insurance.

Undoubtedly the most important work which Daniel Bernoulli did while in St Petersburg was his work on hydrodynamics. Even the term itself is based on the title of the work which he produced called Hydrodynamica and, before he left St Petersburg, Daniel left a draft copy of the book with a printer. However the work was not published until 1738 and although he revised it considerably between 1734 and 1738, it is more the presentation that he changed rather then the substance.

This work contains for the first time the correct analysis of water flowing from a hole in a container. This was based on the principle of conservation of energy which he had studied with his father in 1720. Daniel also discussed pumps and other machines to raise water. One remarkable discovery appears in Chapter 10 of Hydrodynamica where Daniel discussed the basis for the kinetic theory of gases. He was able to give the basic laws for the theory of gases and gave, although not in full detail, the equation of state discovered by Van der Waals a century later.

Daniel Bernoulli was not happy in St Petersburg, despite the obvious scientific advantage of working with Euler. By 1731 he was applying for posts in Basel but probability seemed to work against him and he would lose out in the ballot for the post. The post was neither one in mathematics nor physics but Daniel preferred to return to Basel and give lectures on botany rather than remain in St Petersburg. By this time his younger brother Johann(II) Bernoulli was also with him in St Petersburg and they left St Petersburg in 1733, making visits to Danzig, Hamburg, Holland and Paris before returning to Basel in 1734.

Daniel Bernoulli submitted an entry for the Grand Prize of the Paris Academy for 1734 giving an application of his ideas to astronomy. This had unfortunate consequences since Daniel's father, Johann Bernouuli, also entered for the prize and their entries were declared joint winners of the Grand Prize. The result of this episode of the prize of the Paris Academy had unhappy consequences for Daniel. His father was furious to think that his son had been rated as his equal and this resulted in a breakdown in relationships between the two. The outcome was that Daniel found himself back in Basel but banned from his father's house. Whether this caused Daniel to become less interested in mathematics or whether it was the fact that his academic position was a non mathematical one, certainly Daniel never regained the vigour for mathematical research that he showed in St Petersburg.

Although Daniel had left St Petersburg, he began an immediate correspondence with Euler and the two exchanged many ideas on vibrating systems. Euler used his great analytic skills to put many of Daniel's physical insights into a rigorous mathematical form. Daniel continued to work on polishing his masterpiece Hydrodynamica for publication and added a chapter on the force of reaction of a jet of fluid and the force of a jet of water on an inclined plane. In this chapter, Chapter 13, he also discussed applications to the propulsion of ships.

The 1737 prize of the Paris Academy also had a nautical theme, the best shape for a ship's anchor, and Daniel Bernoulli was again the joint winner of this prize, this time jointly with Poleni. Hydrodynamica was published in 1738 but, in the following year Johann Bernoulli published Hydraulica which is largely based on his son's work but Johann tried to make it look as if Daniel had based Hydrodynamica on Hydraulica by predating the date of publication on his book to 1732 instead of its real date which is probably 1739. This was a disgraceful attempt by Johann to gain credit for work which was not his and at the same time to discredit his own son and shows the depths to which the bad feeling between them had reached.

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