LATITUDE AND LONGITUDE. 197 



observed at sea, are measured from the apparent horizon, 

 which is evidently below the sensible by the quantity 

 depending on the height of the eye; those altitudes 

 are sometimes greater and sometimes less than they 

 should be, by this quantity, for let S be an object whose 

 altitude is to be determined by bringing its image in 

 contact with the horizon, the apparent horizon EH ; 

 then is the angle GEH the observed altitude, which is 

 greater than the angle GEF or the altitude from the 

 sensible horizon by the angle FEH : by another method 

 of observing with a Quadrant called the back obser- 

 vation, the observed altitude is only GEL which is less 

 than GEF by the angle LEF=GEK=FEH. 



In this case therefore the angle FEH must be added 

 to obtain the altitude above the sensible horizon FE ; 

 so that the altitudes are greater when taken by a fore 

 observation, and less when taken by a back observation, 

 by a quantity equal to the angle contained between the 

 two horizons, (those methods of observing will be ex- 

 plained under the theory of the Quadrant.) 



The dip of the horizon is also effected by terrestial 

 refraction, but astronomers differ respecting the quan- 

 tity, usually estimated at one tenth of the whole angle. 

 The corrections for the dip are usually calculated at 

 different heights of the eye, and collected in tables for 

 convenience of calculation. 



PARALLAX, or the effect which the position of an ob- 

 server on the surface of the earth produces on the 

 apparent position of the stars. Since the daily motion 

 of the earth is made about one of its diameters, the 

 apparent daily motion of the stars is also made about a 

 diameter, and consequently round the centre of the 

 earth ; but since our observations are all taken on the 

 surface, it is evident that unless the heavenly bodies 

 are considered at an infinite distance, we do not see 

 their motions and situations such as they really are. 

 This assumption of infinite distance does not lead us 

 into much error as concerns the stars, but in obser- 

 vations respecting the sun and moon, this error becomes 

 sensible, and we are obliged to take the earth's semi- 



