EMPIRICAL TOOLS AND EMPIRICISM 149 



type, through relations involving only certain independently deter- 

 minable characteristics of the galvanometer, e.g., the dimensions, ar- 

 rangement, and number of windings in its coil, the strength of its 

 magnet, the disposition of its mechanical system, and so forth. With 

 these colligative relations in hand we can now establish an inde- 

 pendent secondary denotation for "electric charge." That is, making 

 no reference to silver coulometers, we can build integrating galva- 

 nometers and graduate their scales to read directly and accurately 

 in coulombs. 



Extrapolation. The way now lies open to a gain far weightier than 

 mere operational convenience. Each "equivalent" denotation reflects 

 the existence of one or more colligative relations joining different sets 

 of data. Throughout the broad range in which galvanometric and 

 coulometric results can be compared, we find them well correlated 

 by relations we then dare extrapolate to situations in which only 

 galvanometric measurements can be made. Provisionally conven- 

 tionalizing the relations— incorporating them in my definition of 

 charge— I graduate my galvanometer dial to read "electric charge" on 

 a scale I assume everywhere consistent with that originally estab- 

 lished with the coulometer. I can now extend the application of that 

 concept to systems in which the charges are too large, too small, or 

 too abruptly delivered to be measured with the silver coulometer. 



All colligative relations somewhere fail of reliability. With the ac- 

 commodation of the relations in theories, we may acquire some help- 

 ful indications. We may thus be warned not to extend "equivalent" 

 denotations in circumstances demanding extrapolations that would 

 run counter to approximations used in the theoretical derivation of 

 the relations of equivalence (see p. 59). Our theories may encourage 

 us to risk certain other extrapolations, but some element of risk per- 

 sistently remains. We accept that risk to make this notable gain: im- 

 portant concepts may thus be made available for use far beyond the 

 domains of their original applications. 



Consider the case of "temperature." Today our scale of tempera- 

 tures is pinned to certain fixed points established with the aid of gas 

 thermometers. Applying certain corrections, suggested by theoretical 

 (thermodynamic) considerations, we use such thermometers through- 

 out the range from ca. — 265°C to ca. +1200°C. For the sake of con- 

 venience, we accept also many alternate denotations established 

 with such devices as liquid-in-glass thermometers, resistance ther- 



