Instrumental Error of his Horizon-Sector. 99 



responding depression of the station, both angles being first 

 corrected for curvature and refraction. When the distance 

 is considerable, the uncertainty of the latter element, which 

 sometimes amounts to one minute, and may differ considerably 

 dn value at the two places of observation, renders the observa- 

 tions inapplicable to the determination of the constant error 

 of the instrument. In the event of the proximity of the sta- 

 tions being such as to reduce any probable allowance for the 

 refraction to an insignificant quantity, yet would the extreme 

 accuracy required in pointing the telescope and obtaining the 

 measurements of the height of the eye, &c. render the results 

 iiable to gross errors. Fortunately, the discovery of Professor 

 Gauss enables us to measure to the greatest accuracy the re- 

 ciprocal elevation and depression of a ray of light a few inches 

 in length from observations made at its extremities. 



The method consists in pointing at each other two tele- 

 scopes, each furnished with a spirit-level, and marking, when 

 their lines of collimation are parallel to each other, the exact 

 positions of their respective bubbles. Both lines of collima- 

 tion, it is evident, are now either parallel to the horizon, or are 

 equally inclined to it, — with this difference in the latter case, 

 that one is depressed and the other elevated. On pointing a 

 •perfect telescopic-level first at one and then at the other tele- 

 scope, (their bubbles being stationary at the marks,) their lines 

 of collimation will appear both level, or one will be found de- 

 pressed and the other elevated at the same angle. Admitting 

 the telescopic-level to be imperfect^ half the sum of the ob- 

 served inclinations, when both are depressions or both eleva- 

 tions, or half their difference, when one is a depression and 

 the other an elevation, will be equal to the instrumental error. 

 When both angles are depressions, or the one of depression 

 exceeds that of elevation, the telescopic-level measures eleva- 

 tions (as in the case of the horizon-sector) in defect. 



Apparatus, S)C. — The horizontal plank resting on the iron 

 brackets driven into the eastern wall of the roohi, supported 

 the telescopes, &c. used with the sector in the measurements. 



One of the arcs of the sector being placed in a horizontal 

 position with its zero-line coincident with that of its move- 

 able index, hot diluted glue was applied by a hair-pencil to 

 the edge of the vernier part of the index in order to secure 

 it, in default of a clamp, to the arc. After the lapse of a day 

 or two the other index was attached by a similar process to 

 its corresponding arc. 



The reversing points of the great levels of the sector were 

 most carefully ascertained, immediately subsequent to the 

 completion of a set oi' measurements, by numerous observa- 



02 



