INTRODUCTION TO MECHANICS. xiii 



other E, only part of the motion of D, therefore, will be destroyed by it, and 

 the two balls will move on together to d and e, which are less distant from 

 the vertical line than the ball D was before it fell. Still, however, action 

 and re-action are equal ; for the action on E is only enough to make it 

 move through a smaller space, but so much of D's motion is now also 

 destroyed. If the elasticity of the balls be imperfect, the effect will be in- 

 termediate between the effects produced in the cases we have mentioned ; 

 that is to say, the ball struck will rise farther than in the case of non-elas- 

 tic bodies, and less far than in that of perfectly elastic bodies ; and the 

 striking ball will be retarded more than in the former case, but not stopped 

 completely, as in the latter. They will therefore move onwards both after 

 the blow, but not together, or to the same distance ; but in this, as in the 

 preceding cases, the whole quantity of motion destroyed in the striking 

 ball will be equal to that produced in the ball struck. 



Birds, in flying, strike the air with their wings, and it is the re-action 

 of the air which enables them to rise or advance forwards. The force 

 with which their wings strike against the air must equal the weight of 

 their bodies, in order that the re-action of the air may be able to support 

 that weight ; the bird will then remain stationary. If the stroke of the 

 wings be greater than is required merely to support the bird, the re-action 

 of the air will make it rise; if it be less, it will descend: the lark some- 

 times remains with its wings extended, but motionless ; in this state it 

 drops rapidly into its nest. A bird expands his wings when he gives the 

 stroke, the re-action of which is to impel him onward, and contracts them 

 when in the opposite direction. The swimming of fishes is on the same 

 principle ; their fins are expanded and contracted in a like manner; and 

 a man in swimming strikes his hands out to produce the re-action which 

 impels him forward, and turns them edgewise to lessen the effect of the 

 contrary re-action. In rowing, the oars are lifted out of the water after 

 every stroke, so as completely to prevent any re-action in a backward 

 direction ; and even in moving them through the air they are turned edge- 

 wise, or feathered, as it is called, from its resemblance to the action of the 

 feathers of a bird in flying. 



Let us now return to the subject of re-action, on which we have some 

 further observations to make. It is re-action being contrary to action 

 which produces reflected motion. If you throw a ball against a wall, it 

 rebounds ; this return of the ball is owing to the re-action of the wall 

 against which it struck, and is called reflected motion. A ball filled with 

 air rebounds better than one stuffed with bran or wool, for the elasticity of 

 the air re-acts after compression. If the ball be thrown perpendicularly 

 against a wall it returns straight towards the hand, though the action of 

 gravity draws it downwards before reaching it ; but if thrown obliquely 

 upwards, it rebounds still higher. We use the term perpendicular in pre- 

 ference to the more familiar word straight, because straight is a general 

 term for lines in all directions which are neither curved nor bent, and is, 

 therefore, equally applicable to oblique or perpendicular lines. A perpen- 

 dicular line has always a reference to something towards which it is 

 perpendicular; that is to say, that it inclines neither to the one side nor 

 the other, but makes an equal angle on either side. 



Let the line A B (Jig. 4) represent the floor of the room, and the line 

 CD that in which you throw a ball against it: the line CD, you will 

 observe, forms two angles with the line A B, and those two angles are 

 equal. All circles are supposed to be divided into 360 equal parts, called 

 degrees ; the opening of an angle being, therefore, a portion of a circle, 

 must contain a certain number of degrees; the larger the angle, the 



