A HIGH PRECISION STANDARD OF FREQUENCY 507 



1,000 (/4 - /i), 1,000 (/4 - /2), 1,000 (u - /3). (2) 

 The mean of these numbers is 



l,000(/4-- ^' + ^^ + ^^ )- (3) 



If we subtract each of the original three recorded numbers from the 

 mean we obtain 



1,000 (/:- ^^ + ^^ + ^'^ ) = 5„ (4) 



1,000(/. -^^i^+^) = 5„ (5) 



l,000(f,-(l±4±^)=8,. (6) 



Thus we may compute readily the performance of each of the four 

 oscillators referred to the mean of the three similar primary oscillators. 

 It is obvious that the accuracy of intercomparison of the three similar 

 oscillators does not in any way depend upon the constancy of oscillator 

 No. 4. For convenience in reducing the results, however, it is con- 

 trolled as carefully as the others. 



The records and computed results for approximately ten hours are 

 given in Table 1. During this time the largest relative variation 

 between any two of the four oscillators taken in pairs was 5 parts 

 in 10^. The random variations between 1,000 second periods appear 

 to be in the order of one or two parts in a hundred million. These 

 random variations are superposed on slow drifts of a quasi-periodic 

 nature probably caused by temperature changes in the circuit and 

 amounting to less than one part in ten million. In addition to these 

 effects a slow, steady drift is expected due to a settling-down of the 

 oscillator circuit and the crystal in its mounting as well as due to 

 aging of the vacuum tubes and even of the crystal itself. The effects 

 of aging can, of course, only be determined after long continued 

 operation. 



It is preferable in some cases to refer the performance of each of 

 the four oscillators to the mean performance of all four. This is in 

 the event that all four oscillators are equally reliable in which case the 

 mean of all four makes a better reference standard than the mean of 

 any three. If we designate the numbers 



1,000 (/4 -/i), 1,000 (/4 -/2), and 1,000 (J, -/a) 



