EMPIRICAL TOOLS AND EMPIRICISM 139 



immeasurably superior to that of the more "obvious" {i.e., famiHar) 

 concepts of common sense. The sophisticated concept of X-ray 

 wavelength is invested with a comparatively unequivocal denota- 

 tion, established around such a device as the crystal diflFraction 

 spectrometer, and "nuclear spin" one established around the NMR 

 spectrometer. Of course, the situation is not completely uncompli- 

 cated: beyond the instrument itself we have also to specify the proto- 

 col for its "proper" operation. 



The operating protocol. Need any appreciable procedural specifi- 

 cation be given in the simplest of cases, e.g., an accurate measure- 

 ment of "length" with a meter stick? Yes— at least two considerations 

 demand attention. 



First: If the stick and the object to be measured are not in the 

 same plane, then at oblique angles of view we may read from the 

 meter stick substantially erroneous lengths for the object. Grasping 

 this possibility of (parallactic) error, we easily avoid it— perhaps by 

 bringing into play another instrument. Thus a cathetometer can 

 assure us of a perpendicular line of sight and, by a suitable arrange- 

 ment of lenses, allows us to cast the object and the comparison scale 

 in the same focal plane. But even then we do not attain a purely 

 instrumental denotation: "proper" operation of the cathetometer it- 

 self demands a protocol specifying a considerable variety of pro- 

 cedural details. And so on. 



Second: The meter scale has a length of one meter only at the 

 specified temperature at which it was graduated. Often, however, 

 we seek an accurate result from measurements we must make at 

 some other temperature. Then, using what we regard as a well- 

 established relation between the temperature and the length of the 

 scale, we calculate and report, as the accurate length of the object, 

 a "corrected" value more or less different from what we actually read 

 from the scale. That such corrections must be made, and the colliga- 

 tive relations with which they are to^ be made, we learn from the 

 protocol thus required to fill out the denotation of "length" even 

 after we have agreed to center that denotation on an instrument, the 

 meter stick. 



The need for an auxiliary protocol is perfectly general: "length" is 

 an atypical case only in the comparative simplicity of this prescrip- 

 tion. Consider the multiplication of complexities in an instance only 

 slightly less simple. Suppose that, for some liquid, we wish to meas- 



