the Trigonometrical Station on Rumbles Moor, Yorkshire. 139 
drical rings of the telescope are not alike, and the one near the 
object glass proves to be of the largest diameter, the zenith di- 
stances will be all in excess, and the mean refraction (granting 
+t to be one twelfth) will appear negative until the are becomes 
of such extent that one-twelfth thereof equals the error of the 
instrument. Still with numerous observations on ares of various 
lengths the refraction (and of course the error of the instrument) 
may be discovered by ascertaining what constant correction must 
be applied to best reconcile the discordancies, and give the most 
uniform. result. 
When corresponding observations are made at both stations, 
the error of the instrument, although it vitiates the true value of 
the refraction, does not prevent the determination of the proper 
angle for calculation as accurately as could have been done witha 
perfect instrument. The refraction will come out too small, but 
then it will be applied to angles of elevation as much in defect*. 
From the following statement it would appear that the Sector 
gave the elevations too little by 23". ; 
, Are j, Corrected 
Jack Hill and Great Almias .. .. 3 li + neg. ay 
Beamsley rock and Rumbles Moor 4 3. yy neg. ar 
Beamsley rock and Symon hut .. 4 Dog BES.) Ur 
Rumbles Moor and Chevin .. -- 4 36. fy Neg. rar 
Beamsley rock and Jack Hill .. 6 4 xe neg: qs 
Rumbles Moor and Jack Hill .. 6 18. ay pos- ws 
Beamsley rock and Chevin .- «+ 6 58 gs — 105 
Rumbles Moor and Symon Seat... 8 6 wo — Te 
Rumbles Moor and Great Almias 8 30 ser — ae 
Symon Seat and Jack ey ye ene a. ao ee rhs 
Symon Seat and Great Whernside 8 40 35 — st 
Great Almias and Beamsley rock 9 8 sr a0 
Rumbles Moor and Observatory .. 11 la— «3s 
Symon Seat and Great Almias .. Il 44 2 —™ is 
Great Whernside and Beamsleyrock 12 40 345 — 5 
Great Whernside and Rumbles Moor NG VO. oy ne a> 
Pendle and Rumbles Moor .. .«- 16° 40. 25 °— aly 
= 
Pendle and Symon Seat... «- 17 48° gs 
Pendle and Great Whernside .. 20 26 xe — 135 
By placing a delicate spirit level upon the cylindrical rings of 
the telescope, the Sector being well adjusted, and supposed to 
be level, it was found that the one near the object glass was 
higher by 35”, With this datum, together with the angular 
opening of the Ys and the diameter of the rings, the error of the 
instrument was calculated to be 28”. . 
* When the power of the telescope is but small, will not the depressions 
be observed in excess? 
$2 A spirit 
