ASTRONOMY. 39 



If L be the length of the horizontal line in English 



2L* 

 miles, the correction for curvature in feet is 



o 



2L* 

 and for refraction TTT- 



and this last is to be subtracted from the former, 

 which gives - or for the quantity to be 



added to the height as calculated trigonometrically, 

 including both the corrections for curvature, and, 

 in the mean state of the atmosphere, for refraction. 



When a height is calculated trigonometrically from 

 the angle of apparent elevation observed at a gi- 

 ven distance, both the preceding corrections maybe 

 made on the angle itself, which on some occasions 

 is more convenient. Divide the horizontal dis- 

 tance in feet by 6075, the feet in a geographical 

 mile or a minute of a great circle of the earth. 

 Let the quotient = H, and let the observed angle 

 of elevation = E, then the true angle corrected 

 both for curvature and refraction is E -f- 0.428 H. 



SECT. III. 



FIGURE OF THE EARTH. 



53. THE figure of the earth is understood to be 

 determined by a surface at every point perpen- 

 dicular 



