56 INTRODUCTIOX. 



of a degree and tenth parts. An example will 

 sufficiently explain this : 



On the 1st of July, 1805, the height of the 

 Pico, in the island of Matana, was measured off 

 the Kurile islands, in latitude 18° & north, 

 and longitude 206° 50' west from Greenwich. 

 The angle of elevation, after deducting the index 

 correction, and the dip of the marine horizon, was 

 3° Q6\ The horizontal distance of the ship from 

 the middle of the mountain =: e was on the chart 

 that was made = 12', 4 minutes. We have then 

 ^c= 1.0 min. and hence e' = (3° 26' - l' 0) = 

 3° 25'j (e' + i c) = 3° 31', 2, and (e' + c) = 3° 

 37', 4 ; the distance of tlie mountain in toises = 

 951, 6 X 12 toises, 4 min. = 11800 toises = D. 

 The calculation is, therefore, according to the first 

 formula, 



log. D = 4,07188 



log. tg e' = 8,77600 



log. h = 2,84788 



therefore h = 704,5 toises. 



According to the second formula, we have, 



log. D = 4,07188 



log. sin. (e + i c) = 8,78815 



2,86003 

 log. cos. (e + c) = 9,99913 



log. h' = 2,86090 



therefore h = 725,9 or 726 toises ; 



SO that the neglecting of the convexity of the earth 



has here made the height too small by twenty-two 



toises. 



