4 INSTRUMENTATION IN SCIENTIFIC RESEARCH 



quantity. The fractional error is F f = F/Q , which is approximately 

 equal to F\Q' \ the percentage error is ^percent = F/Qo x ^0. 



The error is usually complex. It is practical to distinguish the 

 following components: 



scale error. ( 1) The observed output may deviate from the cor- 

 rect output by an amount which is constant throughout the entire 

 range of the instrument (additive constant, zero displacement). (2) 

 The observed output may deviate from the correct value by a con- 

 stant factor. ( 3) The experimentally observed transfer function may 

 deviate from that postulated by theory (nonconformity) . In partic- 

 ular, if a linear relationship between input and output quantity is 

 postulated but not experimentally realized, the error is called non- 

 linearity, or nonlinear distortion. (4) The output may depend not 

 only upon the applied input but also upon the past history of the 

 element, i.e., upon the input formerly applied to the element 

 (hysteresis error) . 



dynamic error. The output does not follow the variations with 

 time of the input precisely or it depends upon time functions such 

 as a time derivative or the frequency of the input quantity. 



noise and drift. A signal originating in the element and varying 

 with time appears at the output terminals or is superimposed on the 

 output signal. The magnitude of this noise or drift output is, in prin- 

 ciple, independent of the magnitude of the signal applied to the input. 

 If information is available about the statistical nature of the noise 

 output, it is possible sometimes to distinguish between the desired 

 output signal and the undesirable noise. 1 



If a human observer reads the output, he is a part of the instrument 

 system, and his reaction must be included in the consideration of 

 errors. For instance, a scale error can be caused by parallax in scale 

 reading, or a dynamic error can be caused by the observer's reaction 

 time or psychological anticipation of an expected result (the 

 "personal equation" in the observation of passage instruments in 

 astronomy). 



3. Response to Environmental Influences. The performance of an 

 instrumentation element is fully described by the transfer function 

 and the errors, as mentioned above, providing the instrument is in 

 a constant environment and is not subjected to external disturb- 

 ances. If instruments are subjected to environmental influences such 

 as changes of temperature, pressure, or acceleration, changes of mag- 

 netic or electric fields, or changes of the supply voltages, variations 



1 K. S. Lion and D. F. Winter, Electroencephalog. and Clin. Neurophysiol., 5, 

 109 (1953). 



