1096 



NAVIGATION NAUTICAL ASTRONOMY. 



[LONOITUDB. 



declination at the time of observation, 22 9' 17" N. The 

 chronometer on the 20th of May preceding wa 45*. slow 

 .reenwich time : iU daily rate was 2.'l losing. Re- 

 qoired the longitude of the ship. 



1. Apparent Time at Greenwich from Chronometer. 



h. m. a. 



Time by chronometer . . 610 



+ 46 

 Loss from May 20 to June 2 . + 25-2 



Mean time at Greenwich . . 6 2 10-2 

 Corresponding equation of time . + 2 31 ~4 



A pp. time at Greenwich . 6 4 41' 6 

 2. Apparent Time at Sliip from Triangle P ZS, Fig. 29 

 HereZS-6958', PS=67604S', PZ= 49 55', to find P. 



Z S, 69 68' 0* Arith. Comp. -0333098 

 in. P S, 67 60 43 Arith. Couip. 11 027 08 

 sin. PZ, 49 66 



2)177 43 43 



sin. s, 88 61 61 

 sin. (s ZS), 28 63 51 



eos. J P, 3420' 17 6" 

 2 



99999140 

 9-G8410CO 



2)19-833GC78 



9-9108339 



P = G8 40 35-2 

 2 



3)13,6 8,0 7,0-4 

 4 



32 

 2 



40 

 2-3 



(See page 1079). 



App. time from noon 

 at ship 



App. time at Green- 

 wich (by chrou.) 



Longitude W. in time 29 69" 3 



41i. 34' 42-3* 

 5 4 41-C 



29m.- 7 

 69s. -3 = 



16' 



14 49 5 



(See page 1088). 



LoieoiTUDE W. 7 29 49-5 



2. On the 28th of May, 1823, in latitude 5V N., 

 the mean of several observed altitudes of the star A n tares, 

 when eastward of the meridian, was 30 s 42^ and the cor- 

 responding time by the chronometer was 9h 35m. 43s. 

 The chronometer was too fast 1m, 6s. on April 20, at 

 noon, at Greenwich, and its daily gain was 5s. -4. The 

 height of the eye was 16 feet. Required the longitude of 

 the ship. 



Apparent Time at Oreenicich from Chronometer. 



b. m. . 



Time by chronometer . . 9 35 43 



Fast, April 20 . . 1' 5" 



Gain, from Apr. 20 to May 283 27-5 



= - 4 32-5 



Meantime at Greenwich . . 93110-5 



Corresponding equation of time . + 3 9 '2 



App. time at Greenwich . 9 34 19 7 



2. Apparent Time at Ship from Triangle P Z S. 



Mean of observed altitudes . 30 42" 0* 

 Dip . - 3 60 



Star's apparent altitudes . . 30 38 10 



Refraction . . 1 39 



Bur's true altitude . . . 303631 



ZS, 59 23' 29" 



sin. PS, 116 1 37 Arith. Comp. -Ol 

 sin. P Z, 89 10 Arith. Gump. -0000459 



I 35 6 



sin. s, 132 17 33 

 sin.(s-ZS), 72 54 4 , 



27 29 32 

 2 



9-S090<?G9 



2)19 K 



9 -9479594 



64 69 



4 

 I 



3)10,8 11,8 ,8 



3 30 



3 56-3 



(See page 1079). 



Polar angle in ) 

 sid. time . j 

 Star's R.A. . . 



R.A. of merid. . 



Sun's R. A May ) 

 28, at (U: 34ni. [ 

 20s. app time ) 



3h.39' 50 -3* 



16 18 31-2 



12 38 34-9 



4 19 17 



App.timeatship 8 18 179 



Long. W. in time 1 16 1-8 Long. W. = 19 0' 28'. 

 triples for Exer- 



1. On September 23rd, 1845, in the afternoon, and in 

 latitude SO^SO'N., the <>. .'titudo of the sun's 

 lower limb was 11 ff 50', the index corrertion being 

 3' 20", and the height of the eye 20 feet. The chronometer 

 showed llh. 59m 30s. ; it was fast on Greenwich mean 

 time 45s. -5 on August 21st, and its daily rate was 

 losing ; the sun's declination at the time of observation 

 being 18' 41" S., and the equation of time 7m. f>2s. -3 ; 

 also the sun's semi-diameter was 15' 58'. l!o|iiin-d the 

 longitude. Ans. Long. 110 18' 10 \V. 



2. In the afternoon of October 18th, 1841, in latitude 

 15 46' N., the observed altitude of the sun's lower limb 

 was 12 40' : the chronometer showed llh. 12m. 42s. 

 Greenwich time of October 17th : its error August 

 12th, at noon, was 5m. 20s. slow, and its daily rate was 

 12s. -5 gaining. Etequind the longitude, the index cor- 

 rection being + 2' 30", the height of the eye 16 feet, and 

 the following particulars being furnished by the Nautical 

 Almanac, namely 



Sun's dec. October 17th, 9 18' 8" S. Hourly diff. + 

 54" -81. Eq. of time 14m. 34s. -3. Hourly dill'. + 0"-483. 

 Sun's diameter 10' .V. Long. 83 61' -I 



3. On September 10th, 1844, in latitude 48 J 20' N., 

 an afternoon altitude of Arcturus was observed to be 

 31 6' 40", the star west of the meridian: the chrono- 

 meter showed 6h. 1m. 28s. : its rate August 25th, was 

 4s. -3 gaining, and it was 2m. 40s. slow on Greenwich 

 mean time. The index correction was 4' 10", and the 

 height of the eye 20 feet : also the sun's R. A. at the time 

 of observation was llh. I'.lm. 18s. ; the star's K. A. llh. 

 8m. 34s -05, and its declination 14 59' 44' N. Required 

 the longitude. Long. 32 8' 20 K. 



ON FINDING THE LONGITUDE AT SEA BY LUNAR 

 OBSERVATIONS. The reader has sufficiently seen that 

 the difference of longitude between two places on the 

 surface of the earth, is virtually the samu as the dif- 

 ference of time between those two places at the same 

 absolute instant. Suppose, for example, that a rocket 

 could bo projected so high, and give out li'_;'it of such 

 intensity, as to be seen at the instant of explosion 

 by two observers thirty or forty miles apart : the ex- 

 plosion takes place, of course, at a certain instant of 



