LONGITUDE.] 



NAVIGATION NAUTICAL ASTRONOMY. 



1093 



chronometer on Harrison's principles. The instrument 

 he produced was committed to the care of Mr. Wales, on 

 his voyage round the world with Captain Cook, in the 

 years 1772, 1773, and 1774 ; and it so fully justified 

 Harrison's expectations in this severe trial, that the 

 House of Commons ordered the remaining 10,000 to be 

 paid to him. 



Subsequently to this, chronometers were constructed 

 by various persons, upon independent principles and of 

 equal merit ; those by Mudge, Arnold, and Earnshaw 

 were considered to deserve special distinction, and ac- 

 cordingly 3000 were paid by government to each of 

 these makers ; but no parliamentary reward has since 

 been given for chronometers. 



At the present day, chronometers fully equal to any 

 of those here adverted to are readily to be procured, and 

 from the best makers ; even superior time-keepers may 

 at all times be obtained. The difference of longitude 

 between Greenwich and New York, as recently deter- 

 mined by the chronometers of Mr. Dent, agreed with the 

 results of astronomical observations, to within three- 

 quarters of a mile ! 



Such, then, is the degree of perfection to which this 

 department of mechanical art has been brought ; so that 

 the determination of the time at Greenwich, at any in- 

 stant, in any part of the globe, would be an easy matter, 

 provided only that a chronometer could be insured 

 against all external interference with its action. But at 

 lea, a piece of machinery so delicate is peculiarly exposed 

 lyranging influences changes of climate the jerks 

 and vibrations of the ship local attraction, <kc. , <tc., 

 all have their influence ; and however these ordinary hin- 

 drances to the correct performance of the watch may be 

 provided a',':iinst, yet an unavoidable accident may at 

 any time render the machine useless. The safety of 

 navigation requires, therefore, that valuable as the 

 chronometer is other means of finding the longitude, 

 independent of its aid, should be devised ; and these are 

 furnished by what are called the LUNAR OBSERVATIONS. 



By aid of tables of the moon's motion first supplied 

 to the British Admiralty by Professor Mayer of Gottingen 

 (1755 '62), and subsequently improved by Mason, Brad- 

 ley, and others the angular distances of the moon from 

 the sun, and from the principal stars that lie near her 

 path, are predicted for every three hours of time, and 

 for several years in advance. These "Lunar Distances" 

 are given in the Nautical Almanac. The motion of the 

 in "ii in her orbit is so rapid about 13 in 24 hours 

 that her advance to, or recession from a star in her path, 

 is a measurable quantity even in the lapse of a few 

 seconds of time : by means of the three-hourly distances 

 computed in the Nautical Almanac fur Greenwich time, 

 her dist.-uiee from any one of the selected stars, at any 

 intermediate instant of Greenwich time, can be easily 

 found by simple proportion ; and, conversely, any inter- 

 mediate distance being known, the corresponding Green- 

 wich time can, in a similar manner, be found. 



Like as in all the other angular measurements of Nau- 

 tical Astronomy, the observer is considered to be situated 

 at the centre of the earth : a lunar distance, therefore, 

 I- in:; taken at sea, and reduced to this point, the mari- 

 ner has only to turn to his Almanac, and from the dis- 

 tances there given, to compute, by proportion, the time 

 at Greenwich, wheti the distance of the same objects was 

 wliat he has found it to be. The Greenwich time at the 

 instant of observation is thus discovered, and thence 

 Ins own time being known the longitude of the ship is 

 ascertain'"!. 



The heavens thus supply the navigator with an unerr- 

 ing chronometer a time-piece that needs no winding up 

 that never gets out of repair, nor ever requires re-ad- 

 justment that can neither be deranged by accident, nor 

 be deteriorated by neglect. Placed beyond the reach of 

 sublunary vicissitudes, heat and cold, storm and tempest 

 affect it not : these, indeed, may temporarily cloud and 

 obscure its face, but they can neither disturb its mecha- 

 nism nor alter its rate ; and we know that it will run 

 down only when our concerns with TIME are at an end. 

 From these introductory remarks, the student will 



readily anticipate the business that is now before us. 

 Whether we consult a chronometer, or take a lunar dis- 

 tance, for the purpose of finding the time at Greenwich, 

 the time at the ship is an indispensable element in the 

 determination of the longitude ; the problem first to be 

 solved, therefore, is to find the local time. 



ON FINDING THE TIME AT SKA. At first sight it 

 would appear that the time at the ship, most easily de- 

 termined, is the time of noon, or when the sun comes to 

 the meridian ; but, for a minute or two before and after 

 the sun's transit, the change in altitude is so small, ex- 

 cept in very low latitudes, that it is not possible at sea to 

 detect the instant of the meridian passage ; and the same 

 may of course be said in reference to any other celestial 

 object.* 



In determining the latitude by a meridian observation, 

 the error of a minute or so in the time of apparent noon 

 is of no consequence ; for, as just remarked, the altitude 

 of the object which is all that the latitude is concerned 

 with is pretty nearly constant for a few minutes in tho 

 neighbourhood of the meridian ; but, as respects the 

 lowjitu.de, the error of a single minute in the time would 

 occasion an error of fifteen minutes of longitude. It is 

 obvious, therefore, that when time is to be deduced from 

 altitude, with a view to the determination of the longi- 

 tude, the position of the celestial object to be observed 

 should be so chosen when circumstances are such as to 

 permit of a change of position as that a small error in 

 the altitude may have the least effect possible on tho 

 hour-angle, or time from noon. It is of importance, 

 therefore, to consider the following preliminary prob- 

 lem : 



To determine upon what vertical a Celestial Object must be, 

 in order that a small error in the A Ititude may have the 

 least effect on the Time. 



Let S (Fig. 29) be the place of the celestial object ob- 

 served ; but by a small error in taking the altitude, let it 

 be referred to S'. Draw S' S* parallel to the horizon, 

 and meeting the parallel of declination ss', in the 

 point S*. 



Then, when the object is at S* it will really have tho 

 Fiic. 29. co-altitude Z S" equal 



to its supposed co-alti- 

 tude ZS'i when it was 

 actually not at S , but 

 at S ; so that in the 

 determination of tho 

 hour-angle P from tho 

 co-latitude P Z, the co- 

 declination P S', and 

 the erroneous co-alti- 

 tude Z S', the small 

 angle S P S" will mea- 

 sure the amount of 

 error in the time. 



As the triangle SSS" 

 is of course exceedingly 

 small, since the error of observation is not purposely 

 made, it may be regarded as a rectilinear triangle, right- 

 angled at S' ; therefore S S' = S S" sin. S", and S S" = 

 siii. P S ^ S P S", for S S', the distance passed over by 

 the object, may be compared to the distance sailed on a 

 parallel of latitude by a ship, making the difference 

 of longitude SPS'; and we know that in this case 

 (page 1056), 



cos. lat. : 1 : : dist. : diff. long. .'. dist. = cos. lat. X 

 diff. long., .'. S S' = sin. PS ^ SPS". 



Hence S S' = sin. S" sin. P S ^ S P S" .'. S P S" 



SS' 

 "sin. S" sin. P S ' 



(1) 



Now the angle S", that is, tho angle S'S"S, is equal to 



It may be remarked, moreover, that the altitude of the sun, the 

 moon, or a placet, is not necessarily always the greatest when on the mid- 

 day meridian of the place of observation ; nor necessarily the least, when 

 on the midnight meridian : the body's change of declination may be such 

 u to prevent this. 



