1106 



NAVIGATION NAUTICAL ASTRONOMY. [IXAJCFIM at LONGITUDE. 



Prop. log. 28804 

 Prop. log. 67464 



defect. In Dr. Inman'i \anliral Tablet, the proportional 

 logarithms are givon to five placet of figures, to that the, 

 logarithms of consecutive quantities are not confounded. 

 . .-figure proportional logarithms are used in finding 

 the Greenwich mean time, corresponding to a lunar dis- 

 tance, then the proportional logarithm of the difference 

 between the consecutive lunar distances in the Almanac 

 must be sought for in the table, as the Almanac gives it 

 to only four places of figures. Thus, taking the example 

 justg: 



Given distance . 77" 52 45' 

 -2, at 3h Dist 77 14 40 ) 

 6h. 78 47 24 ) 



Diff. of dist. in Aim. 1 32 44 

 Diff. of given dist ) ia K 

 and that at 3h. ] 



Time after 3 hours, Ih. 13m. 66s. . Prop. log. 38650 

 Hence the Greenwich mean time was Ih. 13m. 65s. 



Example* of Determining the Longitude from Lunar 

 Observations. 



The foregoing articles contain all that is necessary for 

 the determination of the time at the ship, and the time 

 at Greenwich, at the same absolute instant ; and it has 

 boen sufficiently explained how these two determinations 

 lead immediately to the discovery of the longitude, as in 

 the following examples : 



K sample 1. On the 1st of September, 1846, the true 

 distance of the star Autares from the moon's centre was 

 39 4flr 20*, the mean time at the ship being 8h. 14m. 12s. 

 Required the longitude. 



The time at the ship at the instant the 'lunar distance 

 was taken being known, we have merely to find the 

 Greenwich time corresponding to that distance. We 

 seek, therefore, among the predicted lunar distances in 

 the Nautical Almanac, for that one preceding it in order 

 of time, which is the nearest to it, and take the dif- 

 ference between the two. The proportional logarithm, 

 annexed to the distance extracted from the Nautical 

 Almanac, subtracted from the proportional logarithm of 

 this difference, will give the proportional logarithm cor- 

 responding to a portion of time, to be added to the time 

 at which the distance taken from the Almanac had 

 place. The result will be the time at Greenwich cor- 

 responding to the given time at the ship. Thus : 



Sept 1, at6h., dist. (tfaue. ^m. ) 38 50' 28" P.L. 2287- 

 Given distance . . . 39 48 20 



Difference . 

 Time after Cli. 



57 52 P.L. 4928 



Ih. 37m. 59s. P.L. 2041 



/.Time at Greenwich 7h. 37m. 59s. 

 Time at ship . . 8h. 14m. 12s. 



Long. E. in time Oh. 36m. 13s. 



Then, page 1104, 36' in time- 9 0' O'Un Longi- 

 13' - 3 15 j tude. 



.'. Longitude . . . . 3 15 East. 



In this example the moan time at the ship is sup- 

 posed to have been determined by one or other of the 

 methods already explained, and the true lunar distance 

 to have been deduced from the observed, at shown in 

 thu preceding pages. But it will be instructive to 

 ' tin 1 it, in a connected form, the operations necessary 

 for anccrtaiuiiii; tin; longitude from the ship's account, in 

 combination with the astronomical observations : we 

 hull, therefore, proceed to an illustration or two of this 

 kind, conducting the process by the following steps : 



first object will be to get, from the ship's 

 account, the approximate time at Greenwich when the 

 observations are made. 



By help of this approximate Greenwich date, wo shall 



find rrmi diameter, horizontal parallax, ' 

 at the instant of observation, milliciently m-.-ir the tint! 

 for our ultimate purpose ; because, as already seen, these 

 1 1< ments vary so slowly, that even a Urge error in the 

 can never affect their values, except in a very 

 trilling degree. 



2. The next thing will bo to apply the necessary cor- 

 ; ructions to the observed, in order to obtain tl>< 

 and true altitudes, and the apparent distance. Siillicicnl 

 data will thus be obtained for deducing both thu time ;i( 

 Khi|i and the time at Greenwich ; and it is mat- 

 iii'litleroncc which of thrse requisites is determined first, 

 when the time at the ship is deduced from cither the 

 sun or a star. 



An error in the ship's account will bnt very slightly 

 affect the time at ship when the observation is niruli-, un- 

 less this time bu determined from the moon (page 1 l<i.">) ; 

 but the altitude employed must be taken with care. 



An error in the ship's account will, in like manner, 

 but very slightly affect the lunar distance, and thence 

 the time at Greenwich ; for the moon's somi-dian 

 though dependent on the time, varies too slowly to cause 

 its approximate value, deduced from the estimated 

 Greenwich time, to differ from its true value, at the 

 instant of taking the distance, by any appreciable 

 amount ; and as far as the altitude is concerned, it has 

 been seen that this difference is of no moment. 



Example 2. On February 12, 1848, at 2h. 35m. P.* , 

 mean time by estimation, in latitude 53 30' S., and lon- 

 gitude by account 15 30* R, the following lunar obser- 

 vation was taken : 



Obs. alt. sun's L. L. 



29 17' 26' 

 Index cor. 2 10 



Obs. alt. moon's L. L. 

 10' 20* 

 Ind. cor. 1 10 



29 15 16 



Obs. dist nearest limbs. 

 99 27' 30* 

 Ind. cor. 60 



25 39 10 



99 26 40 



The height of the eye above the sea was 20 feet. Re- 

 quired the longitude. 



Ship time, Fob. 12 . . . 2h. 36m. 

 Longitude E. in time . . . Ih. 3m. 



Approximate Greenwich time . Ih. 33m. 



Referring now to the Nautical Almanac, wo take out 

 the two semi-diameters for noon of Feb. 12 : the ap- 

 proximate Greenwich time differs too little from noon to 

 render any correction necessary ; the sun's declination 

 and the moon's horizontal parallax are taken out at the 

 same time : we thus have 



From the Nautical Almanac. 



Sun's semi-diam. 

 Mo, m's at noon 



par. noon 58' 30* var. in IL'h., 

 Var. in Ijh. l'"6 



Hi' HI- 

 IS 58 

 13 



Hor. par. atest. 

 time ... 58 34 



Sun's dec. noon 

 Cor. for Ih. 33m. . 



Dec. at estimated time 



13 52* 18" S. 

 1 17 



13 51 1 S. 



90 



Polar dist. P S - 76 8 59 



Hourly diff. of sun's dec. 

 30m. I 

 3 I* 



- 49' -87 



- 24 111 



- 2 I'.P 



- 77 



