1835.] 



Distance of objects at sea» 



339 



a = the observed elevation less the true dip for the 

 height h 



h = the height of the eye above the sea„ 

 H = the height of the motintain. 



which is equal to the cosine of the true dip for the 

 height H. 



The value of the sin 0 will therefore be 



== cos true dip for H x cos a 

 which is Lt. Raper's formula ; it is however slightly in- 

 correct, from the elevation of the horizon by refraction, 

 being supposed equal to the elevation of the top of the 

 mountain from the same cause, which is not the case, 

 the mountain being more distant and the refraction there- 

 fore greater. The correct value of « then is = (e — 

 apparent dip — dist.) e being the observed elevation. 

 For an example suppose 



H = 3000 feet 



h = 20 feet 



6 = 20 4' 25" 



True dip for H = 58^ 16'^ 



True dip for h = 4^ 45" 



App\ dip do. = 4' 25": thenbyLt. Raper's formula 

 6 = 2° 4' 25'' 

 True dip = 4' 45'^ 9.9999376=cosine 5816" 



lo59'40" cosine=9.9997369 



87° 46' 54" sine = 9.9996745 



890 46' 34" 



r 21" To 0" 13^26" the approximate distance, 



the quantity 



li 4- H 



may be taken equal to 



R -f H 



