NA VIGA TION. 77 



Thus, the square root of the number of miles in 

 the earth's diameter being 8 2 '8, we have very 

 approximately the distance of the horizon in 

 miles, equal to 82'8 times the square root of the 

 height in miles, or ro6 times the square root of 

 the height in feet. To find the distance of the 

 horizon in feet, multiply the square root of the 

 height in feet by the square root of the diameter 

 in miles, and divide the result by 78. 



To find the dip in decimal of the radian, divide 

 the distance of the horizon by the earth's radius ; 

 or (as we see by using the preceding rules for 

 distance), divide the square root of the height by 

 the square root of half the radius. Thus the dip 

 in radians is equal to the square root of the height 

 in miles, divided by 41*4, or is equal to the square 

 root of the height in feet divided by 3230. The 

 amount of the dip must be subtracted from the 

 observed altitude to find what it would have been 

 if the observation had been made from a true 

 horizontal plane instead of from the dipping 

 visual cone, along which the observer looks to his 

 horizon. 



