.^} 



and of the Altitude and Azimuth Inst rumen f. 109 



Since writing the above, I liave put my hand uj^on another 

 experiment of the same kind, which was made to determine 

 the angailar distance between two land objects. It was made 

 at Glasgow b}' a gentleman whose science is universally ac- 

 knowledged, and who was eminently qualified to do justice to 

 the subject. The diameter of the uistrument was 12 inches. 



Double Obs. Angle by Angle by 



repetition. successive pairs. 



O I II II 



1 = 63 33 52,5 52,5 



2 = 51,0 49,5 



3 = 50,0 48,0 



4 = 48,7 45,0 



, * 5 = 49,3 50,0 



6 = 49,1 50,0 



7 = 48,6 45,0 



8 = 48,5 45,0 



48,8 51,5 



The two series of observations with R, inserted above, are 

 all I can find where the collimated angles have been read off. 

 They serve to show, in such instruments as were used, the 

 amount of the errors of observation, division and reading off, 

 that one collimated result leaves to be corrected by repetition 

 or taking means. Thus, in the first example, the greatest 

 differences from the general mean are +3",4 and —3", 7, and 

 in the second, +3",7 and — 3"',8. The examples also exhibit 

 the irregular manner in which the successive pairs differ from 

 each other; while the columns of repetition with more regu- 

 larity approximate towards a constant quantity, as the diA'isor 

 of the total arc becomes greater. It may be useful sometimes, 

 to exhibit a series of observations in this manner, for it shows 

 what may be expected from an instrument after n certain num- 

 ber of repetitions. It is curious that, in both of the examples, 

 the same rcsiih is obtained at the fourth pair as was gained at 

 last, a circumstance, no doubt, purely accidental, and which 

 could not have been known, liad the ordinary means of reduc- 

 tion been employed. 



With respect to the accuracy of the angles obtained in the 

 two series of observations, it might be presumed, that in neither 

 case, could lliey differ irom the truth by a quantity much 

 greater than l)alfa second: but this presumption depends en- 

 tirely upon the instrument being perfect, or free from fixed 

 error; a thing, for the detection of which, an observer is not 

 furnished with any direct means. 



The instrument R ha-, been equally praised by those who 



liave 



