TIMJS AT SEA.] 



NAVIGATION NAUTICAL ASTRONOMY. 



1095 



Mean obs. alt. ...... 



Index ..... 3' 20" 



Dip ...... 4' 24" 



Semi-diam ..... 15' 58" 



App. alt 

 Bef. 



and Par. 



11 <y 50" 

 + 8' 14" 



11 9' 4* 

 4' 38* 



True alt 11" 4' 26* 



90 



.'. ZS=78 55' 34 r 



Time nearly 4h. 45m. Os. P.M. 



Long. HOW 7h. 20oi. 



Mean time at Greenwich 12h. 5m. 



Sun's dec. at noon Green- 

 wich time 6' SG'S.v. 



Cor. for 12h. 5m. (58V' x 

 12Jj) 11' 47' 



18' 43" S. 

 90 



PS = 90 18' 43" 



Also since P Z = 39 30', the computation of the hour- 

 angle P, will be as follows, namely : 



Z S, 78 55' 34' 



Sin. P Z, 39 30' 0" Arith. Comp. 

 Sin. P S, 90 18' 43" Arith. Comp. 



2)208 44' 17* 



0000064 



Sin. s, 104 22 1 9* 9-9861908 



Sin. (a ZS), 25 26 35" 9-6330782 



Equation of Time. 



Sep. 23 7m. 42s. var. 0*-858 * 2)19-8157700 



Cor. for!2h., + 10s. 



7m. 52s. 



99078854 



cos. i P, 36 



(T 47' 

 2 



.*. P = 72 1' 34" 



In time = 4h. 48m. 6s. Apparent time 

 Equation of time 7ni. 52s. at ship. 



4h. 40m. 14s. Mean time 

 at ship. 



In this result a quarter of a second has been disre- 

 garded, and we conclude that the watch is about am. 

 font. 



It is of importance in discussing operations of this 

 kind, the results of which are required to be brought 

 out with the utmost attainable accuracy, that the stu- 

 dent's confidence in such results be not shaken by the 

 fact that certain of the data with which ho works are 

 confessedly erroneous, and are never more than approxi- 

 mations to the truth ; the estimated longitude, and the 

 estimated time at the ship are, of course, more or less 

 affected with error. He must take notice that these two 

 elements do not enter directly into the trigonometrical 

 process : they merely affect the preparatory reductions 

 for declination And equation of time ; quantities that 

 vary so little, even in a large interval of time, that a 

 considerable error in the estimation of this interval, occa- 

 sions but an inconsiderable error in the proper correc- 

 tions. Hence, with but ordinary cam in the dead- 

 reckoning, and the proper accuracy in taking the alti- 

 tude, the time at sea, determined as above, may be 

 depended .upon as correct, not only to the nearest 

 minute, but even to the nearest second notwithstanding 



Thin in the rari.ition of the equation of time in one hour, ai given In 

 the Jtoutical Almanac. 



the acknowledged fact that certain of the data are only 

 approximately true. 



To illustrate this, let us modify the foregoing opera- 

 tion by applying the above correction to the watch, or by 

 putting it back 5m. ; then the mean time at Greenwich, 

 when the observed altitude of the sun at the ship was 

 H 0'50", will be!2h. The correction for declination 

 will therefore be 58" | X 12 = 11' 42" ; hence, sub- 

 tracting 5" from the above value of P S, we shall have, 

 for the more correct value, P S = 90 18' 38" ; and the 

 work, modified in accordance with this change in the co- 

 declination of the sun, will stand as follows : 



Z S, 78 55' 34" 



sin.PZ, 39 30' 0' Arith. Comp. -1964895 



sin. P S, 90 18' 38" Arith. Comp. "0000064 



sin. s, 

 sin. (-ZS) 



2)208 44' 12" 



104 22' 6" 

 25 20' 32' 



cos-iP, 



36 O'ol' 

 2 



9-9861985 

 9-6330650 



2)19-8157594 

 9-9078797 



.'. P=72 1'42" 



T i- ,iv. jo c \.'.4h. 40m. 14s. 



In time - 4h. 48m. 6s. J a correct mean 



Equation of time -7m. 52s. j at the ship . 



The time, according to the former result, was 

 4h. 40m. 14s. J ; for, as stated above, the fraction of a 

 second was suppressed : we see, therefore, that the error 

 of 5m. in the estimated time occasions an error of only 

 half a second in the correct time. Suppose now that not 

 only the estimated time, but that the estimated longi- 

 tude is also affected with an error equivalent to 5m. of 

 time that is, an error of 1J in longitude, which is a 

 large error ; and suppose that both errors conspire, 

 making the mean time at Greenwich 12h. 10m. The 

 correction for declination will then be 58J" X 12J- = less 

 than 11' 52" ; then P S will be 90 18' 48", and the 

 modified work will be as follows : 



Z S, 78 55' 34" 



sin. P Z. 39 30' 0" Arith. Comp. -1964895 



sin. P S, 90 18' 48" Arith. Comp. -0000065 



2)208 44 22" 



Bin. s, 104 22- 11' 



sin. (s ZS), 25 2& 37'' 



3C 0'45" 

 2 



9-9801958 

 9-6330871 



2)19-8157789 

 9-9078894 



/. P = 72 1' 30" 

 i time = 4h. 48m. 6s. ) .'. 

 Equation of time 7m. 52s. j mean time at the ship. 



Hence, notwithstanding the above errors in the esti- 

 mated time and longitude, the time at the ship is cor- 

 rectly deduced to within three-quarters of a second of 

 the truth. Whenever there is a very considerable dif- 

 ference between the time per watch, and the calculated 

 time at the ship, it will be prudent to repeat the work 

 with the corrected time, as in the second of the foregoing 

 operations. 



2. Time deduced from a Star. On June 3, 1842, at 

 12h. 9in. P.M., nearly (mean time) in latitude 50 48' N. , 

 and longitude by account 1 6 3" W., the observed 

 altitude (or the mean of a set of altitudes) of a Bootis, 

 west of the meridian, was 89 53' 30", with the artificial 

 horizon : the index correction was 10". Required the 

 mean time at the ship. 



As the artificial horizon was used, there will be no 

 correction for dip (page 1070) : the angle shown by the 



