4- 



4- 



-9 



r 



scale without going to the extremity of subdividing the limb into 

 microscopic spaces. 



The principle of the vernier depends upon the simple 

 proposal to take // number of divisions on the limb and of dividing 

 a space of equal length into n + 1 equal parts. Practical consider- 

 ations as to the space available and the legibility of reading, as well 

 as the least count desired, are the influences which determine the 

 value of . 



The least count is the quotient of the value of the smallest 

 division on the limb (/), divided by the total number of divisions 

 on the vernier (n + 1), representnd by the formula: x -/-- (n + 1). 

 In the inserted example, the space equal to nine subdivisions on 

 the scale is redivided into ten equal parts. One space on the vernier is 

 therefore equal to "ioof a space on the limb, or one-tenth shorter; hence 



the distance ab is Mo of the value 

 of the smallest division on the limb, 

 and cd would be 710, etc. If the ver- 

 nier scale is raised until a coincides 

 with A, the index line will be \ i. 

 of a division above the figure 3, 

 and the reading will be 3.01. In 

 the second drawing, in the same 

 way, we have 3.02, but in the third 

 drawing the index has been moved 

 above the second tenth-mark on 

 the scale and the sixth line of the 

 vernier is in coincidence. The 

 reading is therefore 3.26. 



The value of the least count 

 in this example will be determined 

 by dividing the value of one 

 subdivision on the scale, Vio, by 

 the number of subdivisions on the vernier, 10, or Moo. The zero 

 of the vernier is the index line which indicates the position on the 

 main scale of which the linear or angular value is desired. 

 The reading begins by first counting the number of whole divisions 

 on the main scale then running the eye along the vernier scale until 

 a coincidence is found. 



The width of line is not 'necessarily dependant upon the 

 width of marginal space occupied by the least count on the per- 

 iphery. Accuracy depends more upon the ability to judge when 

 two lines are in coincidence than the attempt to deal with actual 

 relative values. If the width of the graduation line and the spaces 

 between them are absolute and uniform, then legibility is more 

 important than any other consideration. 



A Direct Vernier is one in which the numbering of the scale 

 increases in the same general direction with the numbering 

 of the limb. The direct verniers, as used with transits, are 



3- 



-7 



--'I 

 -35 



-4 



-3 

 -2 



-1 

 -0 



53 



(Prom Johnson-Smith) 





