LONGITUDES.] 



ASTRONOMY. 



1023 



M. Strove then proceeds to investigate the differences 

 of determinations of longitude by the moon's 1 L. , and 

 moon's 2 L., and finds it necessary, in order to reconcile 

 the observations made at twelve stations, to increase 

 determinations of longitude by the moon's 1 L. 7s. -2, 

 and to diminish those of the moon's 2 L. by the like 

 quantity. 



The following additional examples of the determination 

 of longitudes by moon culminators, are extracted from 

 Riimker's Lawjen Bestimmung durch den Mond, Ham- 

 burg, 1849. 



The longitude of Hamburg, in three examples, being 

 supposed to be well known, let p be the sidereal time of 

 the earlier, and IT that of the later culmination ; t the 

 mean time of the earlier culmination, and T that of the 

 later, deduced from the known longitude. Then for 

 these times, the moon's right ascensions, declinations, 

 and semi-diameters (viz. , a and a, d and S, r and p re- 

 spectively), are to be interpolated from the ephemeris. 

 There will thus be obtained from the ephemeris, the 

 difference of the moon's right ascension a a, and there 

 will be deduced from the observations the difference 

 r p + (p sec. S r sec. rf) = A, the upper sign apply- 

 ing to the first, and the lower to the second liinb of the 

 moon. Hence there will be this proportion 



a a : A = r t : \ L ; 



/ r \ 



consequently (A (a a) -'i c, the correction of 



the assumed longitude. The westerly place in these 

 examples being the first, the sign of c is to be changed. 



The observations at Port Stephens were made by 

 Captain King, R.N., and have been published in the 

 monthly notices of the Royal Astronomical Society ; 

 those at Hamburg, by M. RUmker, are given in the 

 twenty-second volume of the Astronomische Nachrichten. 



1843, April 12, Hamburg, East 



Moon's 1 L. . 11 43 39-797 



r, Virginia . . . 12 11 55-612 



April 13, Port Stephens, West. 



b. m. B. 



17 Virginia . . . 12 12 21 38 

 Moon's 1 L. . . . 12 19 12-16 



Then, reducing the sidereal clock-times of the star's 

 passage to one standard, as Hamburg, we have the 

 right ascension of the moon's 1 L. at Port Stephens, 

 12h. 18m. 46s. -392. 



Moon's 1 L. p . . 

 Sid. time at mean noon 



Acceleration . . 



Mean Hamburg time 

 Long L 



Mean Greenwich time t. , 

 April 12. 



h. m. 8. 



. 11 43 39-797 

 .- 1 20 2'455 



10 23 37-342 

 - 1 42-165 



. 10 21 55-177 

 .- 39 54-000 



9 42 1-777 ) 



Moon's 1 L. TT . 



Sid. time at mean noon 



Acceleration 



h. m. B. 



. 12 18 46-392 

 .- 1 22 25-662 



10 56 20-730 

 - 1 47-426 



Mean time at Port Stephen 10 54 33-204 

 X -10 8 7-000 



Mean Greenwich time r 

 April 13. 



46 20 204) 



The right ascensions of the moon's limbs, accurately 

 interpolated from the hourly ephemeris in the Nautical 

 Almanac, are 



h. m. . 



-11 44 47-13C9 = a 

 And 12 19 54-1846 = a 



35 7-0477 



2107" -0477. 



The moon's semi-diameters sxccurately interpolated are, 

 respectively, r = 16' 39" "414, p = 16' 41" -8745. The 

 declinations are respectively d = 3 47' 5", 3 = 7 37' 

 34" -5. 



Log. r = 999-414 =. 2-9997454 p = IOOL'8742 log. 3-0008133 



Log. sec. d = 3 47' 6* = OO009482 3=7 37' 3t"-5 log. sec 0-0038585 



30006036 



r sec. d = 1001"-5985 

 r sec. d = 1001-5985" 

 p sec. a = 1010 8150" 



p sec. r sec, d _ 9-2165 

 15 ~~15~ 



h. m. r. 



sr = 12 18 46 392 

 p - 11 43 39 797 



3-0046718 

 p sec. o = 1010"-815 



v p = 35 6595 = 21065950 



A = 2107-2094 

 a o = 2107-0477 



A (a o) h 1617 



r t = 16 4' 25 027 = 54265-027 



Correction = 4-165 

 X = 10 8 7-000 



Ar. co. log. = 6-676326 

 log. = 9-208791 

 log. = 4 734520 

 log. = 0-619637 



Sine longitude = 10 8 2-835 



MERIDIAN OR MORAL CIRCLE. The north polar dis- 

 tance of an object is determined by means of the meridian 

 or mural circle. Previous to the introduction of the 

 circle, the astronomical quadrant was used for this pur- 

 pose ; but it was discovered, about the beginning of the 



present century, that its results had been in a great 

 measure vitiated by the expansion of the instrument, 

 and consequent change of figure. The late Astronomer 

 Royal (Mr. Pond), by aid of a circle only two feet In 

 diameter, was enabled to detect and point out the errors 



