2 1 V INTRODUCTORY. [CHAP. I. 



Aitjij 6 : ootaoiis:^nd positions of bodies can be deduced from them, 

 and predictions so made are verified in experience. But in the 

 process of formulation the Science assumes a highly abstract 

 character. The fundamental notions involved have, for the most 

 part, names in common use, such as " force " for example, but the 

 common use of such names is never precise, and for scientific 

 purposes the meaning to be attached to them must be made 

 definite. This is done, as in Geometry, by means of definitions 

 and postulates. Except in the statement of the postulates nothing 

 ought to be taken from experience, all the results ought to be 

 logically deduced. There is thus an abstract logical theory of 

 Mechanics, of the same nature as Geometry, in which all that is 

 assumed is suggested by experience, all that is found is proved by 

 reasoning. The test of the validity of a theory of this kind is 

 its consistency with itself, the test of its value is its ability to 

 furnish rules under which natural events actually fall. In what 

 follows we shall be mainly occupied with the exposition of the 

 theory, we shall not detail the observations and experiments by 

 which the fundamental notions were suggested, nor shall we do 

 more than indicate in particular cases the kinds of natural events 

 bo which applications of our theory can be made. 



2. Motion of a point. We have said that our object is 

 the description of the motions of bodies. The necessity for a 

 simplification arises from the fact that, in general, all parts of a 

 body have not the same motion, and the simplification we make 

 is to consider the motion of so small a portion of a body that 

 the differences between the motions of its parts are unimportant. 

 How small the portion must be in order that this may be the 

 case we cannot say beforehand, but we avoid the difficulty thus 

 arising by regarding it as a geometrical point. We think then in 

 the first place of the motion of a point. 



Motion may be defined as change of position taking place in 

 time. 



In regard to this definition it is necessary to make clear two 

 things: one is the measurement of time, and the other is the 

 meaning of the phrase " change of position." 



3. Measurement of time. Time may be measured by 

 any process which goes on continually. The amount of the 



