E N D I X. 



107 



DEMONSTRATION. 



Let G F C (plate I. jfig. i .) reprefent the furface of the 

 earth, E Its center, B C the height of a hill or other objed 

 rifing perpendicular from C; A is the place of the obferver's 

 eye, whofe height above the level of the fea is A G. Draw 

 A H perpendicular to A E, and A F touching the circle 

 G F C in F. Then H A F is the dip, E A F its com- 

 plement, D A B is the apparent altitude of the objed 

 above the fenfible horizon ; to this add E A D, the fum 

 is EAB. In the triangle EAB, the fide E A is the 

 fum of the femidlameter E G and G A the height of the 

 obferver*s eye ; E B the fum of the femidlameter E C and 

 C B the height of the objed ; the angle A E B is mea- 

 fured by G C the horizontal diftance between the ob- 

 ferver and objed. Now in the firft cafe there are given 

 in the triangle EAB, the fides E A, E B, and the angle 

 B A E, to find the angle A E B ; and in the fecond there 

 are given the angles B A E, A E B and the fide E A, to 

 find the fide E B and confequently B C. The trigonome- 

 trical folutions of thefe cafes are the above pradical rules. 



S 2 Obseryatioms 



