proceedings: philosophical society 449 



The subject of map projections is a very wide one and some of the 

 considerations have their roots extending far into the fertile soil of pure 

 mathematics. A careful working out of the results for any one pro- 

 jection forms a good exercise in the practical application of mathematical 

 knowledge. 



Discussion. — This paper was discussed by Messrs. Sosman and Wm. 



Bowie. 



Adjournment took place at 9.53 p.m. and was followed by a social 

 hour. 



819TH MEETING 



The 819th meeting was held at the Cosmos Club, May 10, 1919, 

 President Humphreys in the chair; 40 persons present. 



The minutes of the 818th meeting were read in abstract and approved. 

 The first paper was presented by Mr. F. J. Schlink On the nature of 

 the inherent variability of measuring instruments. 



This paper treats of those characteristics of the performance of an 

 indicating measuring instrument, on account of which the instrument 

 fails to give identical readings for repeated applications of the same 

 value of the quantity being measured. Variable errors introduce 

 serious difficulties, and the obtaining of a high degree of freedom from 

 variability in instrument operation, although it has not until very re- 

 cently been given any general or systematic consideration, is likely 

 to be very much more important than mere smallness of calibration 

 error. A means of defining the variability of measuring instruments, 

 either indicating or integrating, with respect to random observations 

 in caUbration, is illustrated, in which, the characteristics of the instru- 

 ment, as regards dispersion of readings, are set forth by reference to 

 *the surface defined by a family of probability curves. 



The concepts of resilience and the cychc state with respect to instru- 

 ment operation are next introduced and it is shown by experimental 

 results on a typical indicating instrument of considerable mechanical 

 complexity that when once cyclic or regularized operation is set up, 

 the indications lie upon a hysteresis loop which, while defining a zone 

 of uncertainty or variance, is in itself definite and reproducible with 

 high precision, provided that the successive increments of the inde- 

 pendent variable are appHed aperiodically and in the absence of jarring 

 or vibration, in such manner as to avoid all overshooting of the final 

 reading. This method is directly apphcable only in the absence of 

 appreciable transient after-effects in the operation of the instrument. 



The causes of instrumental hysteresis maybe either elastic or mechan- 

 istic; the nature and effect of the latter are illustrated and explained. 

 The type of calibration that would obtain in the absence of friction 

 has been determined by the study of instruments subjected to vigorous 

 jarring and the relation between cyclic and acyclic calibration was thus 

 made evident. An experiment was shown using a crude type of auto- 

 matic weighing scale which served to demonstrate the determinate 

 nature of the hysteretic lag in the un vibrated, aperiodic condition of 



