524 



Self- Calculating Sextant. 



correspond with the horizontal line at B ; fix the index 

 and the observation is complete. If you now consult the 

 instrument, as a common sextant, you will learn from it the 

 measure of the angle BAC. If, as a Self-calculating Sex- 

 tant, you will further learn the proportion which BC bears 

 to AB. Referring to the figure, the triangle Abe on the 

 instrument is similar to the triangle ABC in the field, 

 consequently, be to Ab on the one, as BC to AB in the other ; 

 thence, if you know the height you learn the distance, and 

 vice versa: if you know neither, move the index one full 

 division forward on the line of cotangents, and retreat until 

 the top and bottom again become coincident ; you then have 

 the perpendicular projected on the ground, and by actual 

 measurement thereof, obtain the height, and thence the dis- 

 tance. 



It is not pretended that a like result may not be obtained 

 by a common Sextant, but perhaps neither with the same 

 certainty nor equal dispatch. Take, for example, the 

 present most simple of all cases, to ascertain the height of 

 an inaccessible object above the horizontal plane. After 



two observations and one measurement backwards, as be- 

 fore, the trigonometrical calculations wanted in the latter 

 case are as follow : — 



Sin./ ACD : Sin ^ D : : AD : AC ; 



B : Sin ^L CAB : : AC : BC the height ; 



and R : Tan ^l BCA : : BC : AB the distance. 

 Now, the purpose of all this apparatus of tables of Sines, 

 Tangents, and Secants, is learned from our instrument by 



