Boscovich, the “vis viva” Debate and the Unitary Law of Force

Fabio Bevilacqua e Angelo Chierico, University of Pavia Boscovich, the “vis viva” Debate and the Unitary Law of Force The sixth volume of the Edizione Nazionale delle Opere e della Corrispondenza di R. Boscovich will be dedicated to a set of small books on natural philosophy which, while preceding the Theoria (Wien 1758, Venice 1763), have unfortunately received much less attention, namely: the De Viribus Vivis (1745), the De Continuitatis Lege (1754), the De Lege Virium (1755), and the De Materiae Divisibilitate (1757). Except for the De Continuitatis there are no existing translations: work is in progress towards an Italian translation of the four booklets and of the Theoria. The unitary law of force appears for the first time in 1745 in the De Viribus Vivis. The well-known dimensional identification with living forces of the areas outlined by the geometrical representation of the law indicates the relevance of Boscovich’ s work for the history of energy conservation. In the De Viribus Vivis there is also the first formal solution of the longlasting “vis viva debate”: quantity of motion deals with effects in time while living force with effects in space. This was prior to d’Alembert’s similar approach which only appeared in the 2nd edition of his Traité de dynamique (1758). But what does Boscovich mean by “vis viva”? Why does he deny its “existence”? He demonstrates a deep knowledge of the contemporary literature and of the various meanings attributed to “vis viva conservation” by various authors, basically conservation during collisions, conservation at given positions and conservation during motions. Among Boscovich’s successors who dealt with various interpretations of the vis viva debate, Lagrange (1788), Helmholtz (1847) and Planck (1887) will be briefly discussed.