is one-tentli part shorter than a space on the scale. In the present 

 case the spaces on the scale represent inches and tenths; hence the 

 difference between the length of a space on the vernier and one on 

 the scale is ^ of -^=-y^ of an inch. This principle of matching 

 two scales having sj^aces of slightly different magnitude is always 

 followed in the construction of verniers, though, of course, the num- 

 ber of spaces embraced by the vernier is varied to suit the circum- 

 stances and the degree of minuteness desired. Moreover, in some 

 instances, the vernier embraces one more space on the scale, instead 

 of one less, than the number of its own subdivisions; that is, 10 

 spaces on the vernier may be made to correspond to 11 spaces on 

 the scale. 



If, as we have seen, the spaces on the vernier are one-tenth smaller 

 than on the scale, then, in the adjustment shown in Figure 4, the first 

 line above the zero on the vernier is one-tenth part of the space, the 



H~'° 



30.00 



Figure 4 



— b 



next line two-tenths, the next three-tenths, etc., distant from the 

 line next above on the scale. When, therefore, we find the vernier in 

 such a position as shown in Figure 5, where the fifth line on the ver- 

 nier is coincident with a scale line, it is very clear that the zero line 

 of the vernier must be just five-tenths above the scale line next below. 

 Now, since we imagine these scales to represent inches and tenths, 

 then Figure 5 will read 30.15 inches. 



13. Estimation of fractions on a vernier. — In many cases it will 

 happen that no single line on the vernier will be exactly coincident 

 with a scale line, but that one line will be a little above while the 

 next line on the vernier will be a little below the corresponding scale 

 lines. 



In the case shown in Figure 6 the seventh and the eighth lines on 

 the vernier are each nearl}^ in coincidence, but neither one is exactly 

 so. This indicates that the reading is somewhere between 30.27 and 

 30.28. Moreover, we can clearly see that the eighth line is nearer 



