76 POPULAR LECTURES AND ADDRESSES. 



dip of the horizon. Let HC be the vertical through 

 H, meeting the vertical through P in C, then the 

 lines CP and CH being perpendicular to LP and 

 HP respectively, LP and HP must have the 

 angle between them, HCP equal to the angle 

 LPH. Considering the earth as approximately 

 spherical and gravitation approximately always 

 towards its centre, we thus see that the dip of the 

 horizon is the angle subtended at the centre by 

 the distance of the horizon from the point of 

 view. In the case represented in the drawing, PH 

 is 2/9 of the radius HC, and therefore obviously 

 the angle HCP is very approximately 2/9 of the 

 radian, or (2 x S7'3)/9 = I2 7> which therefore is 

 the dip of the horizon for a point of view 85 miles 

 above the sea. 



To find the distance of the horizon generally, 

 multiply the height of the point of view by the 

 sum of the height and the earth's diameter, and 

 take the square root of the product. This rule is 

 applicable to any height however great. When 

 the height is not more than a few miles, it is not 

 worth while to add it to the earth's diameter. 



