340 



Distance of objects at sea. 



Again 2« 4' 25^' 



4' 25" = the apparent dip. 



2° 0' 0" 



r2r' = dist. 9.9999376 



lo58'39" cosine == 9.9997413 



870 47' 49" sine = 9.9996789 

 89° 46' 28" 



Qo 13' 32" the true distance. 



In the computation by this formula, it is absolutely 

 necessary to use logarithms to 7 places of decimals, in 

 consequence of the cosines of small arcs and the sines 

 of arcs little less than 9C being made use of, and the 

 smallest error in the computation will cause a formidable 

 error in the result. But a more accurate and conveni- 

 ent formula may be found, for in the well known for- 

 mula for finding the height of a hill from its apparent 

 elevation and distance, i»n which 



. ? (l-2r) 



Height = Tang E X dist. + dist. X 2 Ft 



E being = the corrected elevation, 

 r = the co-efficient of the terrestrial refraction = t« 

 nearly. 



R = the Radius of the earth. 

 By transposition we get 



2 I — R 



Dist. = cotang. E X (Height — Dist. 2 it ' 



Here as in the former example. 

 6 = 2M' 25" 3000. 

 4' 25"=apparent dip 141. 



cotang 20 0' 0" ^ 11.45692 2859 =3,45621 



