ASTRONOMY OF EIGHTEENTH CENTURY. 277 



of forces. In dynamics, which became a science onty in, the hands of 

 Newton, in 1687, the beginning of the eighteenth century witnessed a 

 very singular controversy concerning the measure of the force pos- 

 sessed by moving bodies. Leibnitz gave to the force of a moving 

 body the appellation of vis viva, living force, in order to distinguish 

 it from the force of bodies not actually moving, but having only a 

 tendency to move, which he called dead force. Mathematicians were 

 divided into two opposite camps on the question. Leibnitz and the 

 German philosophers took one side ; the English ranged themselves 

 on the other. France was divided by two scientific leaders in the dis- 

 pute, the celebrated female mathematician, the Marquise du Chatelet 

 on one side, and Clairaut, the distinguished member of the Academy 

 of Sciences, on the other. The mode of estimating pressure or dead 

 force was at no time a matter of dispute ; but with regard to moving 

 bodies, Leibnitz in 1686 raised the question by a publication bearing 

 the title, " Demonstrations of a Remarkable Error of the Cartesians 

 and others in estimating the Moving Forces of Bodies." He points 

 out that a body, after falling freely from rest through a space of 4 feet, 

 has a velocity only double of that acquired by falling i foot ; and 

 as these velocities directed upwards would carry the body to the re- 

 spective heights 4 feet and i foot, therefore he said as the forces are 

 proportional to the height to which they carry the bodies, it follows 

 that the double velocity corresponds with a quadruple force, and so on. 

 That is, the forces are as the squares of tJie velocities. It was objected 

 to this doctrine by the Cartesians that the effect should not be esti- 

 mated in this way, for the time required in each was as the simple 

 velocity. J. Bernoulli entered into correspondence with Leibnitz on 

 this subject, and he came over to the views of the German philosopher. 

 When in 1724 the French Academy of Sciences offered a prize for the 

 best dissertation on the communication of motion, it was carried off 

 by an opponent of the Leibnitzian vis viva. The dispute was renewed, 

 and many were the arguments and replies on one side and the other. 

 We need here notice only an experiment brought forward by the 

 partizans of the vis viva. This consisted in allowing bodies of the 

 same size and figure to fall from various heights into soft clay, and 

 then measuring the depths to which they penetrated. The results 

 showed that these depths were proportional to the height of the fall 

 and the weight of the bodies jointly, that is, to \hzproduct of the weight 

 into the square of the velocity. However; the dispute waxed warm, and 

 Clairaut, Herman, Kcenig, Madame du Chatelet, Voltaire, Maupertuis, 

 S'Gravesande, Dr. A. Clarke, and others entered into it. The question 

 continued to be agitated until D'Alembert published his treatise on 

 Dynamics in 1743, in which he shows that it is merely a question of 

 words, and that in some cases it is desirable to measure forces in the 

 one way, in the other cases in the other way. The term vis viva is 

 now applied to the product of the square of the velocity of a moving 



