190 Mr. Nixon on the Measurement by Trigonometry of the 



have varied on the route ; and the thermometer would rarely 

 indicate the precise temperature of the levels, necessarily ex- 

 posed on bright days during a pair of observations alternately 

 to the sun and the shade of the instrument. Some time ago 

 the original levels were replaced by two superior ones (by 

 Dollond), with tubes so nearly cylindrical as to require little 

 or no correction for temperature*. To avoid the other source 

 of error, when the instrument had acquired at the station 

 the temperature of the air, the telescope was placed with- 

 in its Ys at a slight angle of elevation f. The left index being 

 then levelled and the angle of elevation read off, the telescope 

 was inverted, and the right index similarly levelled and read off. 

 The telescope was subsequently taken out of the Ys, and re- 

 versed in position, when the indices were once more levelled 

 and read off. With the levels correctly adjusted, the angle of 

 inclination would be the same by the four readings ; or if the 

 sum of the two angles read off before the telescope was reversed, 

 equalled that of the two succeeding measurements, a compen- 

 sation of error would exist ; otherwise one-fourth of their dif- 

 ference would give the mean error of the levels, additive to, 

 or subtractive from angles of elevation, according as the second 

 pair of readings exceeded or fell short of the first pair. Thus 

 at Dod Fell the readings were : 



Left index and level ... 3' 30"; reversed ... 4' 15" 

 Right 3 45 3 50 



Sums 7 15 8 5 



Difference 50 



Hence 12"\5 (= -^-) is the mean error of the levels additive 

 to the elevations. The inclination of the telescope, as given 

 by the left level, is 3' 52"-5; by the right one, 3' 47"*5 ; of 

 which the minute difference may arise from errors of division 

 and reading off. When the temperature had varied consi- 

 derably in the course of the observations, the verification of 

 the adjustment was repeated on their termination, and the mean 

 of the two values registered as the proper correction. 



In addition to this variable error is the constant one arising 

 from an inequality in the size of the cylindrical rings ; the one 

 at the object end of the telescope exceeding the other by a 

 quantity which affects the elevations with an error of at least 



* The bubbles are displaced one-eighth of an inch for a change of incli- 

 nation of 5", the angle to which the graduations (having a radius of about 

 15 inches) are read off. 



f Had there been no risk of mistaking an elevation for a depression in 

 the readings with the telescope reversed, it might have been preferable to 

 have placed the telescope in a horizontal position. 



