1826.] finding the Longitude at Sea. ^ 



having a divided object or eye glass micrometer ; the latter will 

 resemble the " Coming up glass," invented, I think, by Jones. 

 With this instrument I propose to measure the moon's distance 

 from a star, when this distance does not exceed 2°, or 2° 30'. 

 The advantages of this method are, that the distance will be 

 much more correctly measured than by any sextant (Dr. Halley 

 has proved that a telescope of sufficient power maybe used, and 

 instruments of adequate power are daily employed at sea) ; and 

 the limits of the observations are such, that the correction to be 

 applied to the observed, to reduce it to the true distance, may 

 be registered in tables of short compass in every case, which 

 will take out of the hands of the most ignorant master of a ship 

 all the labour and uncertainty of the calculation, and enable him 

 to ascertain his longitude certainly to half a degree ; whereas at 

 present he is uncertain to 3° or 4°, owing to which there is a 

 serious loss of both Hfe and property. The observation will be 

 better taken than by the sextant, because neither the magnify- 

 ing power nor hght of the telescope is limited, and the images 

 are as well defined as in any telescope. 



This method is pecuUarly adapted to the merchant service, 

 because the observation is easily made, and the whole calcula- 

 tion will be limited to two or three common rule-of-three state- 

 ments. The data or principles on which the tables will be con- 

 structed are as follows : — Let Z be the zenith, M the apparent 

 place of the moon, S that of the star. By a sextant, or other 

 proper instrument, measure the altitudes of the two bodies • 

 from the zenitii, and through the moon and star, pass two great 

 circles ; Z M = 90° — ]) 's apparent altitude ; Z S = 90° — * 's 

 apparent altitude ; correct the apparent altitude of the moon for 

 refraction and parallax ; then Z m = 90° — D 's true altitude • 

 correct the stars for refraction, and Z s = 90° — ^'s true alti- 

 tude. S M is the apparent distance, measured by the telescope 

 and micrometer; and s m is the true distance which is required. 

 Therefore in the spherical triangle Z S M, the three sides are 

 known by measurement, and the angle Z is first required ; lof. 



cos. -}r z = i-\ log. cosec. Z S + log. cosec. 



Z M + log. sin. ^ {Z S + Z M + S M} + 



log. sin. J± {S Z + Z M + S M}-SM( \ 



Refraction and parallax take place entirely 

 in vertical circles ; refraction depends upon 

 the apparent altitude only ; and although it 

 requires a correction for the thermometer 

 and barometer, it may be neglected on 

 account of its minuteness ; however, when 

 the observer has ability and leisure, since 

 most large vessels are provided with a 

 ^Tiarine barometer (and none shpuld be luiprovided with cne, 



