How it began
The idea came to the Belgrade mathematician Mihailo Petrovic in 1892. His work on the machine was announced in 1896 by Ljubomir Kleric, and the first paper appeared in 1897. Serbian and French publications followed in 1898 and a perfected version in 1899. Petrovic, of the Grand School in Belgrade, designed and conceived the device. It was constructed to his design by a French specialist in precise mechanisms whose name is not recorded.
How it works
The machine rests on an analogy between the solutions of certain differential equations and the behavior of a liquid when a body is dipped into a vessel filled with it. It has an arithmetic unit made of a specially shaped vessel of fluid, a precisely defined body and a float. An input unit and an output unit of one or several rotating cylinders are connected with the float, and they trace the result. The final version used a clock mechanism turning at constant speed. It handled first-order differential equations, including Riccati equations.
What changed first
The hydrointegrator was shown at the World Exhibition in Paris in 1900, in the Serbian Pavilion designed by architect Milan Kapetanovic. It was fully functional and was demonstrated to visitors. The device was awarded a gold medal. Petrovic had published accounts of it in Paris and in an American journal as well as in Serbia.
What lasted
The Serbian Academy project on Petrovic calls the device the first analog computing machine to work on the principle of fluid flow. In 1936 Lukyanov proposed a later hydro integrator that solved the Fourier partial differential equation of heat conduction through an analogy with liquid moving in capillary tubes. In 1980 Professor Dragan Trifunovic and architect Gradimir Bosnic made a reconstruction of the Petrovic machine. It is kept in the Mathematical Office of the Faculty of Forestry in Belgrade.
