schlink: variance of measuring instruments 397 



position of the beam per unit addition of load to the load pan, the 

 first expressed in radians, and the second in grams. Actual 

 measurements of sensitivity will, of course, be restricted to small 

 deflections so that variations in its value over the range of de- 

 flection are negligible. 



The frictional resistance to turning or sliding within an instru- 

 ment has an important bearing upon the concept of sensitiveness. 

 The effect of frictional resistances is to retard or delay the motion 

 of the indicating element for both increasing and decreasing values 

 of the quantity being measured, and to prevent response of the 

 instrument reading to certain small changes in the measured 

 phenomenon. Its existence requires the modification of the 

 ordinary concept of sensitivity since otherwise the determination 

 of the sensitivity of an instrument would depend upon the absolute 

 rather than the relative magnitudes of the quantities entering 

 into the observation. During the period in which change of the 

 measured quantity is proceeding without the occurrence of any 

 motion of the indicator, owing to the effect of static friction, appli- 

 cation of the ordinary definition of sensitivity would give a zero 

 value for that quantity. It seems necessary, then, to separate the 

 sluggishness factor from the insensitiveness factor and define sen- 

 sitivity thus : Sensitivity in an instrument is the rate of change 

 in the indication of such instrument with respect to change in 

 thequantity being measured, it being necessarily assumed for the 

 purposes of this definition that friction and lost motion in the 

 mechanism have been eliminated' or are negligible. (A similar 

 postulate applies to the determination of the scale value in instru- 

 ments graduated directly in the units of the quantity being 

 measured.) We have thus distinguished between passiveness (or 

 sluggishness) and instrumental insensitiveness, a distinction that 

 so far as known to the writer, has not hitherto been set forth. 

 The amount of the least alteration in the value of the measured 

 quantity producing instrumental response, divided by the initial 

 value of the measured quantity may be called the passivity 

 of the instrument at that point. 



Variance defined and illustrated. Passiveness, defined above, 

 is a special case of the phenomenon of variance, which is defined 



