Measurement of Time. 371 



upon (1) which reads : " The period occupied by the 

 happening of some definite process in a definite system is 

 defined to be 1" Now, if this " definite process " stood for 

 a single particular process covering a single interval of time, 

 obviously nothing could be done with (1), (2), (3). It 

 would amount to as much as giving on a straight a pair of 

 points, 0, A, calling OA the " segment 1/' and declaring 

 any segment LN to be the sum of the (adjacent) segments 

 LM and MN. This would never enable us to say what is a 

 segment 2, or 3, and so on. 



But, if I well grasp his meaning, Dr. Campbell under- 

 stands by " definite process," a process such as a fall or a 

 complete oscillation, happening now, or five minutes hence 

 or to-morrow, and so on. This, however, amounts not to 

 solving the problem of measurement, but to massacring it 

 at its very root, or else it amounts to a concealed assumption 

 of uniformity of (in this case) the succession of a discrete 

 set of events. To make my meaning clear, let that standard 

 process be a complete oscillation of a pendulum (to-and-fro) 

 marked by an audible click at its beginning and at its end. 

 Then Dr. Campbell defines all the intervals between a click 

 and the next click as equal to one another, zeroth to first 

 = first to second = fifth to sixth, and so on. But this means 

 either the setting up of an indefinite series of entirely 

 arbitrary time-scale divisions, or else contains the tacit 

 belief in the uniformity of the succession of the clicks. 

 Such a procedure per se would not deserve the name of 

 chronometry ; it would be chronoscopy pure and simple. 

 I say, per se, i. e. without relating the pendulum-oscillations 

 to some fundamental kinematical and dynamical principles. 

 With such support the scale would ce^se to be merely 

 chronoscopic ; but then it would indirectly rest upon some 

 continuous uniform motion as the fundamental concept of 

 the very science (mechanics) which is its support. If so, 

 however, then it is preferable to utilize directly a uniform 

 motion (instead of a uniform succession of discrete clicks), 

 say, a uniform spinning — which brings ns back to both of 

 our old principles. In fact, Huyghens, who certainly pre- 

 ceded everybody in applying the pendulum to chronometry, 

 used it only as an auxiliary, intervening in his mechanism 

 at discrete instants, and he utilized for rigid subdivision the 

 continuous spinning motion of his wheels. (Such also is 

 the only role of the pendulum in our modern clocks.) That 

 our last remarks are by no means superfluous can be seen 

 from Dr. Campbell's embarrassment when, having dealt very 

 rapidly with !i integral numerals," he looks for fractional 



2 B2 



