94 PHILOSOPHICAL TRANSACTIONS. [ANNO 1797. 



sight, I frequently observed the angular distances of the sun's nearest limb from 

 the horizons, on the meridian both north and south, beginning a few minutes be- 

 fore noon, and taking alternately the observations each way, from the poop, or 

 some convenient part of the ship, where the sun and the horizon both north and 

 south were not intercepted; and having found the greatest and least distances from 

 the respective horizons, which was at the sun's passing the meridian, and corrected 

 both for refraction, by subtracting from the least, and adding to the greatest alti- 

 tude, the quantity given by the table; and also having corrected for the error of 

 the instrument, and the sun's semi-diameter; the sum of these 2 angular distances, 

 reduced as above, — 1 80°, is equal to double the dip, as by the following example. 



The sun's declin. 4° 32' 30" north, and semi-diam. 15' 58", observed as follows : 



South. North. 



The meridian dist. of the sun's nearest limb from the horizon of the sea. 78° 36' 30"= 101° 1' 20" 



Kefraction per table — 11 = 4- 11 



Distances corrected for refraction ; =78 36 19 =101 1 31 



Error of the sextant 4- 1 32 + 1 32 



Sun's semi-diameter , 4- 15 58 4- 15 58 



78 53 49 101 19 l 

 I diff. or the dip found — 6 25 78 53 49 



Altitude reduced =78 47 24 180 12 50 



Zenith distance =11 12 36 180 



Diff. 12 50 



The sun's declination n. = 4 32 30 J = 6 25 



Dip. 



Latitude of the ship v. = 15 45 6 



I regret that I cannot in this paper insert the dip which I have found in my ob- 

 servations; for I only retained the latitude of the ship determined by it, as is usual 

 at sea; I generally rejected the error of the instrument, the dip, and semi-diameter, 

 as they affect both observations with the same signs, and reduced the observation 

 by the following method: 



South. North. 



Sun's dist. as before 78° 36' 30" 101° 1' 20" 



Refraction - O 11 4- 11 



Dis. corr. for refraction 78 36 19 101 1 31 101° l' 31" 



+ 78 36 19 



Sum 179 37 50 

 Sum of s. diam. dip, and refraction = | diff. ....4-11 5 180 4- n 5 



78 47 24 Diff. 22 10 



I 11 5 101 12 36 

 90 90 



The J dist. as before = 11 12 36 J n. = 11 12 36 



It may be observed, that neither the dip, semi-diameter, nor index error, can affect 

 the zenith distance of the sun's centre; and the refraction being small near the 



