54 ELEMENTS OF SCIENCE 



there is no friction, and if the body W ascends from 

 B to A i.e., if it rises through the distance CA the 

 weight P descends through a distance equal to BA ; and 

 by comparing P with W it will be found that 



As P : W : : AC : AB. 



Consequently, by diminishing the height of the plane, 

 as compared with the length, the force P may be made 

 as small as we please, compared with W, the resistance 

 to be overcome. 



We have hitherto considered force with respect rather 

 to its statical effects as equilibrating other forces ; but 

 force is manifested in its most interesting aspect in 

 producing motion in imparting motion to what we call 

 matter the study of which is dynamics. 



We must now consider a little more fully the subject 

 of motion, and particularly that of bodies moving under 

 the action of forces. 



Motions may vary as to their velocity, and these 

 differences may be expressed by numerical or other 

 symbols. The idea of velocity involves the ideas of 

 time and length and direction as we speak of a body 

 moving in a given direction at the rate of " ten miles 

 an hour," and the unit of velocity can be defined 

 only by reference to the unit of length and the unit of 

 time. 



" Velocity " is sometimes called the " intensity of 

 motion," but the quantity of the motion of any body, 

 which is called its " momentum," is very different 

 from its velocity, and refers jointly to the amount of 

 matter of which a moving body consists as well as 

 to its velocity. Thus if two bodies are moving with equal 

 velocity, the quantity of motion in each corresponds 

 with -its mass, and if two bodies of equal mass are in 



