206 harper: thermometric lag 



Electrical thermometers. — Electrical thermometers in common use 

 fall into one of two classes, thermo-electric or resistance. Some 

 form of galvanometer is necessary as an indicator for either, and 

 the lag of this galvanometer is part of the total lag of the system, 

 in fact often the only part which is appreciable. 



Galvanometer lag. — From the fundamental equation of motion 



of a galvanometer, critically damped, it can be shown that the 



deflection follows an impressed e.m.f., changing linearly with 



time, so as to lag behind it by a constant time, numerically 4 X 



Moment of Inertia of Moving System .... 



-=— — ; — — „ . — — — — ^ . This expression is simply 



Damping Coefficient (critical). 



related to the period, T, of the system when oscillating absolutely 

 free, giving to the lag of the galvanometer the extremely simple 

 form X = T/t seconds. For T may be substituted, without appre- 

 ciable error, the period of the system when oscillating much under- 

 damped, for this does not differ materially from T until the con- 

 ditions are closely those of critical damping. 



Resistance thermometers. — The equations developed from (1) 

 have been found to represent fairly well the behavior of resistance 

 thermometers as well as of mercurial thermometers, in approach- 

 ing the temperature of a medium in which immersed. They were 

 employed in determining the lag, in ice or well-stirred water, of 

 a number of such thremometers. Thermometers of the Callendar 

 type depart somewhat from following these equations, the depar- 

 ture being of the same general nature as that observed in the case 

 of a Beckmann thermometer. The two term formula?, with appro- 

 priate constants, proved to be rather better than the simpler ones, 

 and may be said to be an empirical second approximation to the 

 statement of the behavior of a Callendar type instrument. While 

 a definite interpretation of all the various constants is lacking, 

 a reason for such a double lag is in evidence. The temperature 

 of the platinum coil is partly determined by that of the inner 

 surface of the containing tube, of which the lag is relatively small, 

 and partly by that of the support for the coil, of which the lag 

 is relatively great. 



The Callendar type of resistance thermometer was found to 

 be slow in comparison with the average mercurial instrument. 



