2. The Law of Continuity is asserted by Galileo in a particular application; and the assertion which it {222} suggests is by him referred to Plato;--namely[36\3] that a moveable body cannot pass from rest to a determinate degree of velocity without passing through all smaller degrees of velocity. This law, however, was first asserted in a more general and abstract form by Leibnitz[37\3]: and was employed by him to show that the laws of motion propounded by Descartes must be false. The Third Cartesian Law of Motion was this[38\3]: that when one moving body meets another, if the first body have a less momentum than the second, it will be reflected with its whole motion: but if the first have a greater momentum than the second, it will lose a part of its motion, which it will transfer to the second. Now each of these cases leads, by the Law of Continuity, to the case in which the two bodies have _equal_ momentums: but in this case, by the first part of the law the body would _retain all_ its motion; and by the second part of the law it would _lose_ a portion of it: hence the Cartesian Law is false. [Note 36\3: _Dialog._ iii. 150. iv. 32.] [Note 37\3: _Opera_, i. 366.] [Note 38\3: Cartes, _Prin._ p. 35.] 3. I shall take another example of the application of this Law from Professor Playfair's Dissertation on the History of Mathematical and Physical Science[39\3]. 'The Academy of Sciences at Paris having (in 1724) proposed, as a Prize Question, the Investigation of the Laws of the Communication of Motion, John Bernoulli presented an Essay on the subject very ingenious and profound; in which, however, he denied the existence of hard bodies, because in the collision of such bodies, a finite change of motion must take place in an instant: an event which, on the principle just explained, he maintained to be impossible.' And this reasoning was justifiable: for we can form a _continuous_ transition from cases in which the impact manifestly occupies a finite time, (as when we strike a large soft body) to cases in which it is apparently instantaneous. Maclaurin and others are disposed, in order to avoid the conclusion of Bernoulli, to reject the Law of {223} Continuity. This, however, would not only be, as Playfair says, to deprive ourselves of an auxiliary, commonly useful though sometimes deceptive; but what is much worse, to acquiesce in false propositions, from the want of clear and patient thinking. For the Law of Continuity, when rightly interpreted, is _never_ violated in actual fact. There are not really any such bodies as have been termed _perfectly hard_: and if we approach towards such cases, we must learn the laws of motion which rule them by attending to the Law of Continuity, not by rejecting it. [Note 39\3: In the _Encyc. Brit._ p. 537.]