EVOLUTION OF QUARTZ CRYSTAL CLOCK 



519 



the direct counterpart of circular error, for in all other cases the restoring 

 force varies linearly with displacement in the region of operation and not as 

 a sine function of it. 



In the early stages of pendulum clock development it was not necessary 

 to consider the arc error because other errors were of greater magnitude. 

 But it is by no means a negligible factor, and in all precision timing by 

 pendulums it must be accounted for, either by allowing for an arc correction, 

 as is done commonly in geodetic survey work, or by keeping the arc small 

 and precisely controlling it. According to F. Hope-Jones^, referring to the 

 master pendulum in the famous Synchronome free-pendulum clock: "A 

 variation of only 0.01 mm. in the excursion of the bob or 2 sees, of arc will 

 by circular error alter the rate by 0.00145 sec. per day, — and if it arose un- 



0.5 t.O 1.5 2.0 2.5 



LARGEST ANGLE FROM VERTICAL IN DEGREES 



Fig. 4 — Relation between arc and rate of pendulum. 



perceived and was steadily maintained, it would produce an accumulated 

 error of half a second in a year, so the necessity for this close observation 

 is obvious." 



The control of arc has almost invariably been accomplished by keeping 

 constant the amount of energy applied per swing so that the actual ampli- 

 tude obtained is that value for which all of the applied energy is dissipated 

 in the pendulum system. In a sense this method of control of arc puts a 

 penalty on improvements in design that would reduce the friction, because 

 the better a pendulum becomes in this respect the less stable becomes the 

 arc control. Since even the best pendulums develop unexplainable small 

 changes in arc, it has been common practice in some observatories to record 

 the arc frequently and to make allowance for changes in it when making 

 the most precise time determinations. 



The inherent constancy of rate of a pendulum, with small or constant 

 amplitude of swing, depends to the one-half powxr on the stability of l/g. 



