CHAP. XI.] HEIGHTS 267 



approximate results, and a simple multiplication of the decimal 

 of inches by the value of a tenth, as obtained above, is quite 

 sufficient for the purposes for which we use the instrument, 

 the differences being taken from the barometer as observed 

 on board. 



To obtain distance from an angle of elevation of a known Obtaining 

 height is like using a lever with the ends reversed, and is fronT-E^ie 

 seldom had recourse to in surveying, as not being correct vation of 



1 known 



enough. Height. 



As it may be, however, sometimes useful, we give a formula. 



Distance in | _ ^4^ 

 nautical miles j E 



When h is height of mountain in feet 



E is the angle of elevation in seconds, 

 reduced to water-level, and corrected by 

 the addition of the dip, as explained in 

 the rules for obtaining heights. 



The same formula in rougher terms is — 



Distance in ' ) _ 100^ 

 nautical miles J ^ E 



If the estimated distance should differ much from that given 

 by the calculation, it should be recalculated with the correct 

 allowance for dip and refraction. 



An example is appended. 



Given height of mountain observed = 2384 feet. 



Elevation .. ,, 0° 36' 26" 



Height of eye .. .. 16 ft. 



Estimated distance .. 30 miles. 

 Obs. elevation 0° 36' 26" 2384 ,. 3-377306 



Height of eye 3 56 34 .. 1-531479 



32 30 4 



or 1950" 2700 .. 3 



908785 

 431364 



Corr. for Dip for 30' 1-477421 



^, 100 X 30 „rr^ 1^- . 



or .. 750 Distance = 30 miles. 



E = 2700 

 The rougher formula will give the distance as 29-4 miles. 



