396 schlink: variance of measuring instruments 



ideal, but we may define instrumental accuracy numerically 

 in terms of the error or correction corresponding to various 

 values of the quantity to be measured. The error arising from 

 whatever source, observed in an* indication of the instrument, 

 divided by the true value of the measured quantity, may be 

 termed the inaccuracy at a given reading, the negative term 

 being justifiable on the basis of custom and ease of application. 

 With this in mind, it is seen that accuracy may be expressed as the 

 ratio of the value of the quantity being measured to the error of 

 the instrumental indication at that value (this of course being 

 the reciprocal of the quantity defined above) . The ratio express- 

 ing instrumental accuracy, while not of value in the ordinary 

 use of instruments, will be of service in rating the performance of 

 an instrument. 



Sensitivity defined and distinguished from immediacy of response. 

 Any instrument showing a change of reading for any change, 

 however great, in the quantity being measured may be said to 

 be sensitive. This term again requires expression in numerical 

 terms in order to be of value in studies of measuring instruments. 

 Statements of sensitivity of instruments are often erroneously 

 based upon that change in the value of the measured quantity 

 producing the smallest perceptible response in the indication of 

 the instrument. This method of expression is by no means a 

 satisfactory one, since it disregards the factor of sluggishness or 

 passiveness in instrument performance, a matter more fully 

 discussed later — and moreover involves the error of personal 

 judgment of the observer. The rating of sensitivity on the 

 basis of the purely incidental dimension of some part, such as 

 the length of a pointer or an arbitrarily graduated scale over which 

 the pointer moves, is also unsatisfactory, since the pointer length 

 or the graduation interval is subject to wide change within the 

 discretion of the designer, making comparison of the sensitivity 

 of different instruments unreliable and dependent upon factors 

 of a purely accidental character. A better basis, in instruments 

 having a rotating or oscillating indicator, would be the angular 

 deflection of the indicator per unit change of the measured quan- 

 tity — for example, in a balance, the angular deflection of the rest 



