1-4] TIME. 3 



process that is effected in any interval of time is supposed to 

 be measurable, and the measure of this amount can be taken to 

 measure the interval, so that equal intervals of time are those in 

 which equal amounts of the process selected as time-measurer 

 take place, and different intervals are in the ratio of the measures 

 of the amounts of the process that take place in them. In any 

 interval of time many processes may be going on. Of these one 

 is selected as a time-measurer; we shall call it the standard 

 process. " Uniform processes " are such that equal amounts of 

 them are effected in equal intervals of time, that is, in intervals 

 in which equal amounts of the standard process are effected. 

 Processes which are not uniform are said to be " variable." It is 

 clear that processes which are uniform when measured by one 

 standard may be variable when measured by another standard. 

 The choice of a standard being in our power, it is clearly desirable 

 that it should be so made that a number of processes uncontroll- 

 able by us should be uniform or approximately uniform ; it is also 

 clearly desirable that it should have some relation to our daily 

 life. The process actually adopted for measuring time is the 

 average rotation of the Earth relative to the Sun*, and the unit 

 in terms of which this process is measured is called the "mean 

 solar second." In the course of this book we shall assume that 

 time is measured in this way, and we shall denote the measure of 

 the time which elapses between two particular instants by the 

 letter t, then t is a real number (in the most general sense of the 

 word " number ") and the interval it denotes is t seconds. / 



4. Determination of Position. Position of a point relative 

 to a set of points f is not definite until the set includes four points 

 which do not all lie in one plane. Suppose 0, A, B, G to be four 

 such points ; one of them, 0, is chosen and called the origin, and 

 the three planes OBC, OCA, OAB are the faces of a trihedral 

 angle having its vertex at 0. The position of a point P with 

 reference to this trihedral angle is determined as follows: we 

 draw PN parallel to 00 to meet the plane AOB in N, and we 

 draw NM parallel to OB to meet OA in M ; then the lengths 

 OM , MN, NP determine the position of P. Any particular length, 

 e.g. one centimetre, being taken as the unit of length, each of these 



* See Chapter XIII. 



t The phrase " position of a point " means its position relative to other points. 



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