196 AEROSTATIC MACHINSS. 



facility over a vaft extent of territory, fecure from the attempts, 

 of an enemy. But it is not equally ferviceable in operations 

 which require a rigorous exadnefs, and in which it is requi- 

 fite to connect the angles with the centre of the ftation, and 

 with the plan of the horizon. 



Adaitional ap- The following is the mode in which I have endeavoured to 



rS^r;, fulfi: the various objea,: 



capable of indi- The angles neceffary for conne6ting the pofition of two ob- 



cating fl//there-je£^5 with the centre of the ftation and the plane of the hori* 



<3uir6d an£?lcSt 



zon, are, ift. the angle comprehended between the rays fall- 

 ing on the eye of the obferver from thefe points; 2d. the an- 

 gles formed by each of thefe rays with the perpendicular. — • 

 We have feen, that it is impoffible for the aeroftatic obferver 

 to mark thefe three angles by taking them after each other; 

 but if their meafure were inflantaneous, the difficulty would 

 be overcome. This would therefore be the cafe if an inftru- 

 ment could be devifed, which would give thefe three angles 

 at once by a fingle obfervation; and as the fextant already 

 ihows the angle comprehended between the rays, the obje6l 

 in view is to add the neceflTary parts to that inftrument for ob- 

 taining the other two at the fame time. 



PreKminary ob- Let B AC (Plate X.) be the angle formed by the vifual rays 



fcrvations. A B, AC ; falling on the mirror A of the fextant from theob- 



je6lsB and C; if the index A D be moved until the image 

 of the objeft C refleded by the mirror A placed on the index 

 coincides by double reflection on the mirror L, with the point 

 where the object B is feen; and if they be both perceived at 

 the fame time by the obferver looking through the telefcope P, 

 it is known, (by the Theory and Ufe of the Sextant) Ifl, That the 

 angle DAE, comprifed between the index A D and the fixed 

 radius or line of zero A E of the inftrument, is always equal 

 half the angle BAC, the meafure of which is required: 

 2d, That the line R B, which is fuppofed to pafs through the 

 axis of the telefcope and the centre of the mirror L, is always 

 direfted to the point B, and is ufually taken for the fide A B{ 

 the error arifing from the fmall diftance A R being confidered 

 as nothing in pradice: hence, if we fuppofe a vifual ray pafT- 

 ing from the point R to the obje6l C, the angles B R C and 

 BAC may be reputed equal, and be taken indifcrimiuately 

 for each other. 



This 



