23 Goniometrtc Prohltms. 



three objects were exactly on the same level : otherwise the 

 positions, if put dawn in a map, would be erroneous, as the 

 distances between them would be too great. This reduction 

 is casilv effected by the assistance oF goniometrv. 



When an instrument simihu- to colonel Mudge's is made 

 use oi, having both an altitude and azimuth circle, it is clear 

 all the angles, being rcFerred to one horizon, require no 

 further reduction than what is necessary to be allowed on 

 account of the earth's sphericity. But if, instead of an in- 

 sli;uiTient of this kind, a sextant be used, and some of the 

 objects be elevated or d-r'pressed, then the angles, not being 

 all of them referred to the horizciU, will require the aid of 

 our iheorenjs to reduce iheni lo this plane. 



Before we enter upon our subject we shall premise the 

 following particulars : 



In tlie first place, all geodesic angles of elevation are af- 

 fected by the horizontal refraction ; it is therefore necessary 

 to show how the quantity of it may be found. 



To (leltrniine IIvj hor'tzontul Ecfrac/mi. 



Rays of light which pass through the atmosphere, and 

 which are neither reflected nor absorbed bv it, do not pro- 

 ceed in a straight line, but are contitiuallv bent towards the 

 earth as they go on ; for they change their direction in pass- 

 ilig obliquely from one mediuu) to another of a different 

 density; as for example, when they pass fiom air to water, 

 ftr from glass to air. The atmosj)here being composed of 

 an infinity of layers, whose densities increase as they ap- 

 proach the earth, the rays of light, as they pass through, 

 undergo the same change as if thev had passed successively 

 ihrougli an infinity of different mediums: they must there- 

 fore be inflected towards the earth in proportion as the den- 

 sity increases. But as the density of the air at different al- 

 titudes does not alter suddenly, but slowly, or by insensible 

 degrees, the rays of light do not describe a polygon in pass- 

 it)g through the atmosphere, but a regular curve line that is 

 concave towards the earth's surface. Tho effect of refrac- 

 fion is iherehjre to make objects appear higher above the 

 liorizon than what they really are. 



Ilcnce 



