62 LECTURE VIII. 



ing motion would be in the direction of the surface of contact, and perpen- 

 dicular to that of the ball impelled. 



Hence it follows, that if we wish to impel a billiard ball * in a given 

 direction, by the stroke of another ball, we have only to imagine a third 

 ball to be placed in contact with the first, immediately behind it in the 

 line of the required motion, and to aim at the centre of this imaginary ball ; 

 the first ball will then be impelled in the required direction, and the second 

 will also continue to move in a direction perpendicular to it. 



By a similar resolution of the motion of an elastic ball, we may deter- 

 mine its path, when it is reflected from a fixed obstacle. That part of the 

 motion, which is in a direction parallel to the surface of the obstacle, re- 

 mains undiminished : the motion perpendicular to it is changed for an 

 equal motion in a contrary direction, and the joint result of these consti- 

 tutes a motion, in a direction which is equally inclined to the surface with 

 the first motion, but on the opposite side of the perpendicular. Of this we 

 have also a familiar instance in the motions of billiard balls ; for we may 

 observe, that a ball rebounds from the cushion in an angle equal to that in 

 which it arrives at it ; and if we wish that our ball, after reflection, should 

 strike another placed in a given situation, we may suppose a third ball to 

 be situated at an equal distance, on the other side of the cushion, and aim 

 at this imaginary ball : our ball will then strike the second ball, after re- 

 flection, with a direct impulse. We here suppose the reflection to take 

 place when the centre of the ball arrives at the cushion, while in fact the 

 surface only comes into contact with it ; if we wish to be more accurate, 

 we may place the imaginary ball at an equal distance beyond the centre of 

 a ball lying in contact with the nearest part of the cushion, instead of 

 measuring the distance from the cushion itself. (Plate V. Fig. 73.) 



When the number of bodies, which meet each other, is greater, and their 

 magnitudes and motions are diversified, the calculation of the effects of 

 collision becomes very intricate, and the problem is scarcely applicable to 

 any practical purpose. Those who are desirous of pursuing the investiga- 

 tion as a mathematical amusement, will find all the assistance that they 

 require in the profound and elegant works of Maclaurin. 



LECT. VIII. ADDITIONAL AUTHORITIES. 



Galileo, Op. i. 957, ii. 479. Wallis, Wren, Huygens, in Ph. Tr. 1668-69-71. In 

 the last, Wallis gives a correct view of momentum. Mariotte, Traite de la Percussion 

 des Corps, 12mo, Par. 1673. Borellus de vi Percussionis, 4to, Lugd. 1686. Saulmon 

 Mairan Molieres, Hist.et Mem. de Paris, 1721, pp. 23 ; 1722, p. 23, 38,40 ; 1726. 

 Gravesande, Essai d'uneNouvelleTheoriedu Choc des Corps fondee sur 1' Experience, 

 12mo, La Haye, 1722. Maclaurin's Fluxions, 2 vols. 4to, 1742. Milner, Ph. Tr. 

 1788, p. 344. Euler, Comm. Petr. v. 159 ; ix. 50. N. Comm. Petr. xv. 414 ; xvii. 

 315. Mem. de Berl. 1745, p. 21. Theoria Motus Corporum Solid. &c. &c. 



* BiUiards, Encyclopedic Methodique, pi. 4 ; Art. Pausmerie, pi. 4, 5 ; Art. 

 Amusemens de Mecanique. Coriolis, Theorie Mathematique du Jeu de Billiard, 8vO. 



