would be in the ratio of 2 to 1, and the squares of the velocities in proportion to the quantities of labour from which they originated, or as 4 to 1; and if the forces acquired by their descent were employed in driving piles, their more sudden effects produced would be found to be in that same ratio.
This species of force has been, first by Bernouilli and afterwards by Smeaton, very aptly denominated mechanic force; and when by force of percussion is meant the quantity of mechanic force possessed by a body in motion, to be estimated by its quantity of mechanic effect, I apprehend it cannot be controverted that it is in proportion to the magnitude of the body and to the square of its velocity jointly.
But of this quantity of force Newton no where treats, and has accordingly given no definition of it. If, after defining what he meant by the quantitas acceleratrix, and quantitas motrix he had had occasion to convey an equally distinct idea of the quantitas mechanica resulting from the continued action of any force, he might, not improbably, have proceeded conformably to the definition given by Smeaton, and have added
———quantitas mechanica est mensura proportionalis spatio per quod data vis motrix exercetur;
or, if speaking with reference to the accumulated energy communicated to a body in motion,
———proportionalis quadrato velocitatis quam in dato corpore generat.
But, if we attend to the words of his preface to the first edition of his Principia, he evidently had no need of such a definition;
