Instrumental Error of his Horizon-Secior. 103 



wires were not then distinctly seen through the round tele^- 

 scope on account of the smallness of its object-glass. In ex- 

 planation of the decrement of 2"-5 in the value of the error 

 (= 19"- 7), it is to be remarked that the reversing points were 

 obtained at 42°-5 Fahr,, and the measurements at 57= Fahr. 

 Besides which, the reversing point of the right-hand level had 

 diminished 2"-7, which would affect the constant error by half 

 that quantity minus. 



March 22nd, 1831. Temp. 57° Fahr. 



On Board. 



^ . On Plank. 



Depression of the round telescope ,, 



by right-hand level 21-2 



by left 26-1 



Depression of the square telescope 



by right-hand level 13'5 



by left 20.0 



Instrumental error 20*2 I 19-2 



% the Fourth Method. 



II 

 20-2 



24-5 



13-1 

 19-2 



Theory/.— When two telescopes have been pointed in suc- 

 cession from precisely the same place at the same distant ob- 

 ject, the position of the bubble of the level, with which each 

 telescope is furnished, being marked, we may ascertain the 

 exact horizontal inclination of the object bv placing the two 

 telescopes in a line with their object-glasses opposite each 

 other, and the bubbles of their levels stationary at their marks 

 Supposing the object to have been exactly on a level with the 

 telescopes, it is evident that on looking through either of 

 them, their lines of collimation would be found parallel to 

 each other. Admitting the object to have been inclined to 

 the horizon, the deviation of parallelism would be equal to 

 twice that inclination, or to the angular equivalent of the 

 displacement ot the bubble of either telescope, produced by 

 varying the inclination of tiie latter, until its line^of collima- 

 tion became parallel to that of the other {undisturbed) tele- 

 scope It is now clear that when the bubble in question is 

 brought, by a movement of its telescope, to a point of its scale 

 equidistant from its present and original positions, the line of 

 collimation of that telescope will be parallel to the horizon 



Demonstration.— l.et E O be the elevation of the line of 

 collimation of one telescope, and eo the ecjual elevation of 

 tfiat of the other. To make the former parallel to the latter, 

 we must depress EO below the horizontal line Ec by an 

 angle equal to its present elevation above it; its direction beinff 

 now LO , and the angle OEO' the equivalent of the run of 

 the bubble. I hen, as this latter angle is bisected by the ho- 



