CHAP. XI.] HEIGHTS 261 



The problem can be solved in two ways — either by finding 

 H D independently, or by adding the angle H A D to H A B to 

 get the angle BAD, when a right-angled triangle gives us B D. 

 The latter method is the shorter, and is now employed, and 

 the former is therefore not described ; but a table giving H D, 

 the dip, or the height of the part of the object observed 

 obscured by the horizon, is given in Appendix, Table 0, as it 

 may be sometimes useful to know how much of a mountain 

 is below the horizon. 



In the method now used, the angle H A D is found as 

 follows : 



Angle H A B is the elevation, corrected for refraction, and 

 the angle HAD (between the chord and tangent) is equal to 

 half the angle at the centre — i.e., half the distance in arc. 

 Suppose A B to be 60 miles, 



Then H A D = +30' 

 Correction for refraction (J^ of the distance = - 5' 



— to elevation, + to depression). 



Whole correction = + 25' 

 Consequently, as 60' : 25' 



or I' : 25" is a constant proportion for all 

 angles. 



Therefore, the total correction, for dip and refraction, in 

 seconds of arc, to the observed angle of elevation or depres- 

 sion is : — 



Distance in sea miles X 100 



This correction is to be added to angles of elevation, and 

 subtracted from angles of depression. 



A ruled form is supplied by the Hydrographic Oflfice, wliich ^eight 

 much facilitates the calculation of heights. This form, bownd bound 

 into a book, constitutes the Height Book. A specimen is ^^^° ^°°^- 

 given on p. 262, which nearly speaks for itself. 



The angle observed to the object is entered under the head Entering 

 of either elevations or depressions, as the case may be — as cuiating 

 observed, in the case of theodolite ; minus the correction for Eieva- 

 height of eye, if with the sextant ; and the distance in miles 

 and decimals is entered under its head. 



