44 schunk: hysterbsis of indicating instruments 



taining in the experiment, are highly reproducible and invariant 

 in themselves, even in the presence of very considerable instrumental 

 friction and the resulting so-called unreliability of indication. 



2. If the instrument is used therefore under the conditions 

 hereinbefore specified as defining the manner of its calibration, 

 the positiveness and certitude of its indications over a very 

 large portion of its range of indication are enormously increased, 

 as compared with the results of operation in the ordinary and 

 unregularized manner. 



3. The middle portion of the calibration loop while in general 

 exhibiting the largest absolute range of variability or variance 

 of indication, in the ordinary manner of operation of the instru- 

 ment, is the region most useful for obtaining results of the high- 

 est relative precision in the cyclic manner of operation above 

 outHned. 



4. Knowing the operational history of the instrument subse- 

 quent to regularization,^ accurate reduction of a given indica- 

 tion can be carried out by this method with complete elimina- 

 tion of first-order variance. 



5. The limiting values of the variant (casual or nonrepetitive) 

 errors of such an instrument can be accurately set down upon 

 the performance of a calibration of the type referred to, for any 

 given range of operation in question, since the major loop corre- 

 sponding to that range circumscribes and completely encloses 



^ In this connection it is clear that one of the factors tending to make the history 

 of the instrument movement uncertain can be eliminated by application of critical 

 or over-critical damping, since the effect of this expedient is to obviate the more 

 or less irregular and indeterminate oscillations of the indicator about its rest point, 

 which would normally depend upon the rate and manner of change of the independent 

 variable during its application. The utility of such damping is especially marked, 

 for instance, in the case of the controlled use in the laboratory, of automatic weigh- 

 ing scales which commonly revert to zero between weighings, since in such cases, 

 the damping assures approach to the rest point over an acctuately determinate 

 functional path. In this connection it should be mentioned that critical or over- 

 critical damping will be definitely disadvantageous if regular reversion of the instru- 

 ment to its zero cannot be depended upon. Moreover, if the scale in question is 

 to be used without correction of its readings, its adjustment to critical or over- 

 critical damping implies that the calibration of the dial shall have been performed 

 with respect to the curve of increasing readings, while the application of simple 

 additive corrections, if they are to be used, is to be carried out with reference^to the 

 same branch of the hysteresis loop. 



