INSTRUMENTS ILLUSTRATING KINEMATICS. 71 



and an inch square, if it were stretched to seven feet long, still 

 remaining an inch square. Thirdly, we may have a change of 

 shape produced by the sliding of layers over one another, a mode 

 of deformation which is easily produced in a pack of cards ; this 

 is called a shear. By appropriate combinations of these three, 

 every change of size and shape may be produced ; or we may 

 even leave out the second element, and produce any strain what- 

 ever by a dilatation or contraction, and two shears. 

 Dynamics. We have already said that the change of motion of a 

 body depends upon the position and state of surrounding bodies. 

 To make this intelligible it'will be necessary to notice a certain 

 property of the three kinds of motion of a point which we 

 described. 



The combination of velocities may be understood from the case 

 of a body carried in any sort of cart or vehicle in which it moves 

 about. The whole velocity of the body is then compounded of 

 the velocity of the vehicle and of its velocity relative to the vehicle. 

 Thus, if a man walks across a railway carriage his whole velocity 

 is compounded of the velocity of the railway carriage and of the 

 velocity with which he walks across. 



When the velocity of a body is changed by adding to it a 

 velocity in the same direction or in the opposite direction, it is 

 only altered in amount ; but when a transverse velocity is com- 

 pounded with it, a change of direction is produced. Thus, if a 

 man walks fore and aft on a steamboat, he only travels a little 

 faster or slower ; but if he walks across from one side to the other, 

 he slightly changes the direction in which he is moving. 



Now, in the parabolic motion of a projectile, we found that 

 while the horizontal velocity continues unchanged, the vertical 

 velocity increases at a uniform rate. Such a body is having a 

 downwards velocity continually poured into it, as it were. This 

 gradual change of the velocity is called acceleration ; we may say 

 that the acceleration of a projectile is always the same, and is 

 directed vertically downwards. 



