334* Mr. J. Nixon on his Horizon-Sector. 



capable of being adjusted to bisect the same object with the 

 tube direct and inverted, must be inclined, at an angle of ele- 

 vation, to the horizontal axis passing through the centre of the 

 rings. As this deflection evidently increases, or diminishes 

 the error arising from an inequality in the rings, accordingly 

 as the object-glass is fixed nearest to the wider or to the nar- 

 rower ring, its precise amount should be ascertained. 



The error, as measured by the fourth method, being 19"*7, 

 or 5"*7, with the object-glass in the place of the eye-tube, the 

 difference of 14" will be the sum of the two flexures. As the 

 stop is fixed 6*3 inches from the narrower ring, and 10*8 inches 

 from the wider one, 5"'2 will be the deflection of the line of 

 sight in the former, and 8"* 8 its value in the latter case. 

 Hence the measurements by the first method, which requires 

 the tube inflexible, will be in defect by 5" # 2 ; whilst those by 

 the eleventh method, which are not only exclusive of flexure, 

 but also suppose the stop placed equidistant from the rings, 

 must be augmented by half the sum of the two flexures. The 

 peculiar situation of the stop of the eye-tube, made use of in 

 the observations by the sixth method, renders the quantity of 

 deflection uncertain. 



The following list contains the instrumental error, as given 

 by each of the different methods, corrected for flexure. The 

 mean of the whole, 21", cannot possibly deviate from the truth 

 by more than a second or two. 



Method. 



I. Error 16"'5 + 5"'2 Flexure =21"-' 



II 26 



IV 19 



V 21 



VI ll"-5 + 5"'2(?) 16 



Vll 30 



X tt$9t t 21 



XL 13"-7-f7"'0 20 



Arithmetical mean 22£; — rational mean 21^. 



Were the terrestrial refraction unquestionably a constant 

 ratio of the arc of distance, the error of the sector might be 

 ascertained by comparing the observed refraction on short 

 arcs, with its apparent value, for others of greater extent. 

 This method applied to 50 arcs, amounting in the whole to 

 upwards of 8°, and ranging from 3'*0" to 25' 34", determined 



the true refraction to be y^r, and the error in question 1*?"*2. 



Leeds, Feb. 8, 1833. John NlXON. 



