  Although Descartes’s laws of motion go beyond his conservation law in placing further constraints on the directions of bodies, they  nonetheless presuppose that the total quantity of motion of bodies  remains the same. Leibniz is therefore able to argue that Descartes’s laws of motion are untenable because they would lead to violations of the conservation of force as measured by mv2.  Thus, in a letter to Bayle of 1687, Leibniz introduces, as an  example, a case where a ball B moving with 100 degrees of  speed collides head on with a ball C moving with 1 degree of speed. Before the collision the two balls collectively have 101 units of quantity of motion as measure by ms, and 10,001 units of  vis viva as measured by mv2.  According to Descartes’s Third Rule, after the collision the two  balls should move together in the direction of B with a  speed of 50 ½ units. Their quantity of motion will be 101  units as dictated by Descartes’s conservation law, but their quantity of vis viva will be 2(50 ½)2 or  5100 ½ units. Leibniz thus objects that Descartes’s laws of  motion would violate the conservation of vis viva  and with it the principle that the whole cause must be equal to the  entire effect (G III.46).