Eccentricity of a Graduated Circle with one Vernier. 375 



4 o _ = ]80 — (y — d) = 2esm(y + d) (2) 



If the second set is made with the faces of the glass at right 

 angles to the position they occupied in the first set and if 

 farther the first setting is made when the circle reads ; we 

 have simply 



t*ngO=— (3) 



In case the graduated arc is less than 180° the eccentricity 

 can still be determined by the same method by the use of two 

 mirrors mounted together on a single block as shown in fig. 2. 



The first mirror a is as 

 before a sextant glass sil- 

 vered on one side and 

 the second mirror b is 

 placed behind it and in- 

 clined to it at a small 

 angle, sufficient to allow 

 the surface of a to be 

 seen normally by reflec- 

 tion from b as shown by 

 the dotted lines. The 

 mirror a is first set per- 

 pendicular to the plane of 

 the divided circle and 

 the observing telescope 



perpendicular to it as before. The second mirror is then 

 brought to perpendicularity to the axis of the telescope and 

 to the divided circle. The telescope is set to perpendicu- 

 larity with the first surface, and the reading of the circle 

 taken, then to perpendicularity with the opposite side of the 

 same surface as seen by reflection from b and a second reading 

 taken. 



Using the same notation as before, 

 ra = a + £ sin (a + 6) 

 n = fi + £ sin (/3 + 6) 



Let co denote the angle between the two glasses ; 

 Then m—n = 2oo* = a—/3 + a s\n(cx + d) — sin (a + -2GJ-\-6) 

 2go — J\ = e sin (a+d)— sin (a + 2&) + 0) (5) 



A second and third set of readings taken at different points 

 on the same circle gives the two additional equations necessary 

 for the determination of the three unknown quantities w, s, 

 and 0. 



* If the glass a is wedge-shaped the angle m — n will not be exactly 2w, but 

 2(w ± 1$). The effect however is the same as if the angle u had been changed 



tO 0)' = 0) ± ^<j>. 



T\c^ % 



