46 MEASUREMENTS 



calibrated, either with words or with the abbreviations TC or TD. Most 

 cahbrations are performed at 20° C. 



Several grades of volumetric glassware are available, differing chiefly 

 in the tolerances of calibration. Class B tolerances are usually about 

 twice as large as Class A tolerances, as indicated in Table 4-2. As ex- 

 pected. Class A glassware costs more. At an even higher cost, the manu- 

 facturers provide pieces tested individually, numbered with a serial 

 number, and accompanied by a certificate from the manufacturer's 

 standards laboratorv. 



Theory of measurement 



Measurement, if you think of it as a process of applying numbers to 

 a sequence of units, is just counting. Some variable quantities are dis- 

 crete; that is, each unit occurs individually with no fractions of units. 

 The number of apples in a bushel or the number of people in a popu- 

 lation illustrates such discrete numbers. The number of cents in a cer- 

 tain number of dollars is also discrete, but the annual interest on one 

 dollar at Wi per cent is a fractional value. The length of a room is a 

 number of meters plus a number of centimeters plus a number of 

 millimeters, etc. Quantities which vary in this way are called continu- 

 ous. Most measurements in the laboratory deal with continuous quan- 

 tities, and the counting consists of applying numbers to units of a chosen 

 size. 



We might suppose that under a given set of conditions (tempera- 

 ture, humidity, etc.) a bench in the laboratory possesses some actual 

 exact value of length. If we measure the bench, we obtain an estimate 

 of this exact value. With a meter stick we find the length to the nearest 

 centimeter, but the true length might be a millimeter or two longer or 

 shorter than our estimate. Using a set of optical instruments, we measure 

 (and calculate) the length to the nearest millimeter. The estimate of the 

 true length is better than before, but still an estimate. If better and 

 better techniques are used, the results approach the true value but never 

 actually reach it. 



Let us now repeat our best measurements several times. Experience 

 teaches us that we should not expect exact duplication of results. Slight 

 human variation, small changes in the instruments, and other fluctua- 

 tions, some of which are too small to be noticed, will combine to affect 

 the final measurement. Our series of several numbers are close to each 



