1826.] 



finding the "Longitude at Sea. 



31 



the moon's semidiameter, and since this is most correctly known, 

 the distance of the moon's centre from the star will be ascer- 

 tained with greater precision than by any measure : the time, 

 which is a most important element, will be marked to half a 

 second. Now apply the corrections ; s s', the effect of refraction 

 upon the star; M m, the effect of parallax— refraction upon the 

 moon ; from which s' m, the true distance, results. Those who 

 have leisure and skill will find this hitherto neglected method 

 the most correct possible ; and since an occultation may always 

 be observed every two or three days, it will be sufficient for 

 every purpose ; or if taken less frequently, it will serve to rate 

 the chronometer. For others, tables will be constructed, hke 

 those which have been already proposed. The values of S M 

 will always be between the greatest and least semidianieters of 

 the moon, increasing by intervals of 10'' or 12"; the maximum 

 of Z S = Z M + ]) 's semidiameter ; its minimum Z M — D 's 

 semidiameter for every 3' or 5' ; Z M will increase by intervals 

 of 3° or 5°, except near the zenith, when they will be 1° each. 



The best time for taking the observations will be when the 

 moon is not very near the full ; for then the occultations may be 

 observed on the dark limb. 



Since it is difficult to measure 

 the altitude of a star, on account 

 of the excessive darkness of the 

 field of view of the telescope 

 apphed to the sextant, I shall 

 here propose a sextant, to which 

 a telescope of any magnitude 

 may be applied, and with which 

 stars of even the sixth magni- 

 tude may be observed ; and with 

 which the horizon will be dis- 

 tinctly seen, when the night is 

 too dark to allow the common 

 sextant to be used. A B is a 

 telescope attached to one of the 

 radii of an octant or sextant; FC 

 the index, which is mounted in 

 the common way. G H is a plain speculum, 

 fixed perpendicularly to the index ; another 

 plain speculum, I K, is supported by a strong 

 arm to the frame of the sextant, and perpendi- 

 cular to its plane. The disposition of the mirrors 

 is shown in fig. 2. First, set the mirrors per- 

 pendicular to the frame, inclining the fixed 

 mirror I K to the axis of the telescope, so that 

 it may reflect down it a ray L M, the angle 

 LMB being about 100° or 110°. Bring the 



- 3r 



G^ I 



D 



^ 



£ 



