398 schlink: variance of measuring instruments 



as the range, at any given value of the measured quantity, of 

 variation in reading which may be exhibited by the instrument 

 under repeated application of the same value of the quantity 

 being measured, after a steady reading has been attained, the 

 environment remaining unchanged. This quantity represents 

 the range of uncertainty of the indications of the instrument. 

 The specific variance may be defined as the ratio of the range, 

 at any given value of the measured quantity, of variation in 

 reading which may be exhibited by the instrument under repeated 

 application of the same value of the quantity being measured, 

 divided by the measured quantity itself, the same assumptions 

 applying as above as to the attainment of a steady state of 

 indication and as to the maintenance of unchanged environment. 

 This factor has rarely been determined in tests of measuring 

 instruments; ignoring it in their use, as is commonly done, may 

 cause appreciable error, and it is therefore important that it be 

 recognized or expressed. 



In the case of the usual direct-reading instrument, the variance 

 is disclosed in the displacement observed between the upward 

 and downward branches of the hysteresis loop obtained by plot- 

 ting instrument readings (or corrections or errors) against actual 

 values of the measured quantity over a complete cycle of increas- 

 ing and decreasing values. The amount of the variance will de- 

 pend upon the previous history of the instrument and upon the 

 immediately precedent cycles of movement which the instru- 

 ment has undergone. The hysteresis curve obtained by plotting 

 in the manner outlined is a valuable index to the operating char- 

 acteristics of an instrument and leads to the detection of defects 

 in design and workmanship discoverable with certainty in no 

 other way. Figures 1 and 2 illustrate the effect described. In 

 figure 1 it is to be noted particularly that the instrument con- 

 tains no force-measuring elements of the elastic type, the scale 

 in question being a pendulum-operated device, so that the loop 

 shown is not the result of hysteresis of inelasticity. The sources 

 of the hysteresis exhibited are all expressible as backlash or are 

 closely analogous to it. The median line of the loop of figure 1 

 gives the characteristic error of the scale correctable by suitable 



