THE ANGULAR MICROMETER 
399 
In any triangle formed by the intersections on the vernier of the 
radii of the protractor and the vernier, as a-c-h: i8o° — (i8o° — jS) 
— 7 =j^\ hence /3 — 7 = a and 
sin an . n , 
= or sin Q! = — sin 7. 
sin 7 ' R ' 
We may assume that n = o.\ mm. represents the extreme case, 
for it is hardly conceivable that an error as great as this could be made 
by any instrument maker likely to be intrusted with the construction of 
Fig. 2. Construction for errors caused by non-centering of the 
protractor and vernier. 
the micrometer. R will be assumed to be 17.5 cm., which is the radius 
of the instrument now in use. If the degrees are read clockwise from 
the line passing through a and h the following relations will be true: 
I When 7 = 0, sin 7=0, sin a = o, a = o and there is no error. 
When 7 = 90°, sin 7 = 1 and sin a = n/R. 
