DESCRIPTIVE TECHNIQUES 113 



case of measuring.) The actual operations by which num- 

 bers are applied to events vary according to the kinds of 

 events to be measured, and according to the range within a 

 given kind of events. For example, one measures the length 

 of an object at rest in one way and of an object in motion 

 in another way; one measures ordinary lengths by yard 

 and meter sticks, but he measures great lengths by triangula- 

 tion; one measures the distance of the stars from the earth 

 by parallaxes, but he measures the size of the small particles 

 of matter by micrometer screws. Events which are not 

 readily measurable by direct methods are measured by 

 means of other events with which they vary concomitantly, 

 as in the measurement of heat by the height of a column of 

 mercury. Often the attaching of numbers to events indicates 

 nothing more significant in the event itself than the pos- 

 sibility of placing it at a certain point in a series of events 

 similar to it but differing in the degree of some quantitative 

 manifestation; this is well illustrated in the measurement of 

 hardness. All operations of measurement, whether tech- 

 niques of applying standards to events themselves, or opera- 

 tions of inserting automatic recording instruments at the 

 proper points in the physical media, are methods for in- 

 creasing the manifestations of events. In the broadest 

 sense of the word, the numbers which are obtained through 

 measuring techniques are simply appearances of the end- 

 object when the corresponding modifications are introduced 

 into the environment. 



Three features of measurement may be singled out for 

 brief attention. In the first place, the measuring instrument 

 must be relatively unaffected by the event measured. In 

 general one does not employ a red-hot meter stick to ascer- 

 tain the length of a block of ice. As was pointed out earlier 

 in the chapter, the strict neutrality of the measuring instru- 

 ment cannot always be guaranteed. In quantum phenomena 

 the mere introduction of a light impulse interferes with the 

 particle to be measured; a micrometer screw, however del- 

 icate, exerts a slight pressure upon the object and therefore 



