1826.] ■ fielding the Longitude at Sea. 29 



At the head of each page stands a value of Z M, which com'* 

 mences at5°, and increases by 1° in each page to 75°; the hopi» 

 zontal column contains values of S M, beginning at 15', next 20', 

 next 30', as far as 2°; the lateral column contains values of 

 Z S ; the tiist is Z M — 2°, the last = Z M + 2° ; the intervals 

 are 10': in the spaces where the values of S M and Z S meet, 

 will be inserted the correction of the apparent distance, with ita 

 proper sign ; thus required the correction, when 



Z M = 5° 0' 

 S M = 20 

 ZS = 3 10 



In the space where the correction will be inserted, is found 

 — d. 



If the numbers be between those inserted in the tables, the 

 correction is found by a simple proportion : suppose Z M = 6°, 

 Z S = 8°, S M = 17'; 5' : 2' :: l—m : the proportional part to 

 be applied to I. Beyond two or three such proportions, there 

 will be no computation required. The tables will not give so 

 very minutely accurate results as the direct solution of every 

 case; but their deviation will never exceed 30'; I may safely 

 say, 15' of longitude. The parallax used in finding the tabulated 

 corrections will be the mean ; when, therefore, the proper 

 correction is found, say mean parallax : true parallax :: tabu-, 

 lated correction : true correction. 



A short subsidiary table may be constructed to make the 

 correction for variations in the parallax more accurately, or it 

 may be joined to the larger table, insertedbetween its columns. 



The tables will contain only 70 pages ; viz. from 5° of zenith 

 distance to 75°: in each horizontal line will be 12 spaces, or 

 values of S M ; and in each vertical column 25 values of Z S. 



There are about 54 zodiacal stars sufficiently bright for the 

 purpose ; in this list are only nine of the 3.4 and 4.3 magnitude; 

 all the rest, viz. 45, are 1.2, or 3. Stars of 3.4, 4.3, and even 

 lower magnitude, may be readily observed. When close to the 

 moon, by a telescope of moderate aperture and power; the 

 common refracting telescope, not achromatic, is the best instru- 

 ment. With an aerial of 18 feet focal length, varying the aper- 

 ture from 1-3 to 2-5 inches, and without eye-hole, or any other 

 addition, to exclude foreign light, I have observed many occul- 

 tations of stars of the 3.4 and"4.3 magnitude, and even smaller. 

 With small instruments of the same sort, I see small stars close 

 to the moon better than with an achromatic of greater aperture. 

 The telescope of my quadrant is a simple refractor, of 3t» inches 

 focal length, and one inch aperture ; that of my transit instru- 

 ment is an achromatic, 22 inches focus, and 1-5 aperture. With 

 the former I see small stars better than with the other; indeed 

 many can be seen through it, which the other does not render 



