150 EMPIRICAL TOOLS AND EMPIRICISM 



mometers, thermocouples, and the hke. Cahbrating these at the fixed 

 points, we contrive to assure the equivalence of the alternate denota- 

 tions of "temperature." 



How shall we extend the range of application of the concept 

 "temperature"? The extension above 1200° C presents no serious 

 problems. Here we use a radiation pyrometer diat can be calibrated, 

 at fixed points established with the gas thermometer, over a range of 

 several hundred degrees. We then extrapolate the relation between 

 pyrometric and thermometric readings into the range where only 

 pyrometric measurements are possible. This extrapolation proves ex- 

 tremely useful and generally satisfactory; i.e., the data so obtained 

 "make sense." But now consider the extension below ca. — 265 °C. As 

 before, we extrapolate a relation, between the readings of some de- 

 vice and the readings of the gas thermometer, into the range in 

 which only the new device can be used. Here a drastically different 

 situation materializes: most of the attempted extrapolations prove un- 

 satisfactory, and we easily recognize their inadequacy. That is, the 

 "temperatures" so secured "don't make sense." We encounter discon- 

 tinuities, inversions, and anomalies difficult to explain save on the 

 assumption tliat most of the extrapolations were ill advised. Fortu- 

 nately some extrapolations survive this test, and with them we make 

 a deep penetration of the region close to absolute zero. 



Many such cases give abundant evidence that in die long term any 

 failures of denotative equivalence, due to unsound extrapolations of 

 the relations of equivalence, will become recognizable and rectifiable. 

 Thus even a primary denotation may be called into question. Today 

 we adopt the gas thermometer to establish a scale of temperature we 

 consider far superior to those of the liquid-in-glass thermometers 

 originally primary only as a matter of historical accident. A com- 

 paratively recent revision of the primary denotation of "electric 

 charge" now pins it to an electromechanical device (distantly re- 

 lated to an integrator-galvanometer) instead of the silver coulom- 

 eter. What is primary and what is secondary may thus change with 

 time, and often the distinction loses its clarity. To be sure ii—i1^side the 

 range in which both primary and secondary denotations are deploy- 

 able— we encounter some inconsistency between the measurements 

 they yield, we will adjust the relation between them to bring the 

 second into conformity with the first. But, meeting contradictions and 

 anomalies outside the range in which direct comparison of suppos- 



