S2 LECTURE VIII. 



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 re- 

 bounds 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 reflection, with a direct im- 

 pulse. 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 col- 

 lision becomes very intricate, and the problem is scarcely applicable to any 

 practical purpose. Those who are desirous of pursuing the investigation as a 

 mathematical amusement, will find all the assistance that they rec[uire in the 

 profound and elegant works of Maclaurin. 



