640 ELECTRICAL MEASUREMENTS 



Consequently, with the critically damped oscillograph, the ratio 

 of the amplitude of the deflection due to a given harmonic to the 

 value it would have if the instrument were perfect, that is, with- 

 out inertia and without damping, is given by 



The free period of the movable system is T = 2ir -/- and if 

 the periodic time of the phenomena under investigation is T, 



1 



Rn = 



or 



T" = ^/E~^ (6) 



Suppose the natural period of the movable system is J^,ooo 

 second and that 60-cycle phenomena are being investigated. 

 Then for the fundamental and the ninth and the twenty-first 

 harmonics, 



= - 9999 



'" 2 



1 + 0.0081 

 ^21 = 0.956 



These departures from exact proportionality are negligible in 

 almost all cases. 



As another example, suppose that it is desired to reproduce 

 the fifth harmonic to within 1 per cent. Then 



# 5 = 0.99 



That is, for the assigned degree of accuracy the frequency of 

 the vibrator should be 50 times that of the phenomena under 

 investigation, or the rate of the vibrator should be 3,000 per 

 second when dealing with the fifth harmonic in a 60-cycle circuit. 



