228 LECTRICAL MEASUREMENTS 



should, however, be used. If this quantity be represented by 

 SM, then when the length L is expressed in meters and the mass 



M in grams, 



S M L* 



S A and S D are frequently referred to as the " length-section" or 

 " volume" resistivities, and S M as the "length-mass resistivity" 

 or the "mass resistivity." 



The relation of S A to S M involves the density, d; for, expressing 

 SM in ohms, 



RM W,QWRAL cm .d lnnnnQ , 



SM = T 2 72 LU,UUU>Aa. 



+* meters *^ cm. 



A careful study by the Bureau of Standards 12 of all available 

 data gives for the density of commercial copper having a con- 

 ductivity of over 94 per cent., 8.89 at 20C. The limits of varia- 

 tion, neglecting extreme values, were found to be 8.87 and 8.91. 

 The density of annealed and hard-drawn copper is sensibly the 

 same. 



To find S A , S D , or S M , the resistance of the sample, R, must be 

 determined at some standard temperature, and the necessary 

 mechanical measurements made in the units above stated. To 

 determine with accuracy the section of a wire of supposed uniform 

 cross-section from measurements of its diameter is a very difficult 

 matter and laborious of execution, for a great many observations 

 must be taken by means of the micrometer caliper, and even 

 then the result is likely to be seriously in error, since the 

 square of the diameter enters the formula. An error of 1 per 

 cent, in the diameter means 2 per cent, in the area. For this 

 reason diameter measurements should be used only when the wire 

 is large. In case the cross-section of the sample is uniform but 

 irregular in outline, such measurements are of course impossible. 

 If the wire be small, its average area or average diameter is best 

 determined by weighing a known length of it in air and then in 

 water, thus finding the mass of the displaced water and conse- 

 quently the volume of the wire. This, however, requires that 

 all the precautions taken in an exact specific gravity determina- 

 tion be observed. 



The determinatior of S&. or the length -mass resistivity presents 



