11 >I 



NAVIGATION NAUTICAL ASTRONOMY. 



[LUNAR DIHTA.NCK.I. 



tion. instead of 28*, so thut the correct apparent altitude 



Unless th time at the ship is to be deduced, preci- 

 sion is not necessary in compntm*' the true altitude: 

 sooondi mar always be disregarded, aud the result found 

 to the nearest minute ss above. But seconds should not 

 be neglected in the corrections. 



It is of importance that the practical navigator have a 

 due appreciation of the value of small quantities in the 

 computation of the true lunar distance : it is only in tho 

 apparent altitudes that precision can bo dispensed with. 

 In finding 1-itHuJf. if the result bo brought out to the. 

 nearest minute, the demands of practice will be fully 

 satisfied, as the error cannot exceed half a milo ; but an 

 of only twenty-two seconds in the lunar distance 

 will, on the average, occasion an error of ton minutes of 

 longitude, which, except in high latitudes, is equivalent 

 to seven or eight miles; and within 'M' of latitude the 

 error would range from eight to ten miles. Too much 

 pains and caution cannot therefore be exercised in ob- 

 serving a lunar distance : tho instrument should be of 

 the very best description, and the observer should have 

 n well-disciplined eye ; but the corresponding altitudes 

 may be safely taken by a less skilful person. 



An interesting incident is related by the late Captain 

 Basil Hall, an officer who was highly accomplished in 

 the science of his profession. He once sailed from San 

 Bias, on the west coast of Mexico ; and after a voyage of 

 eight thousand miles, occupying eighty-nine days, he 

 arrived off Rio Janeiro, having in this interval passed 

 through the Pacific Ocean, rounded Cape Horn, and 

 crossed the South Atlantic, without making any land, or 

 seeing a single sail, with the exception of an 

 American whaler off Capo Horn. When within about a 

 week's sail of Rio, he set seriously about determining, 

 by lunar observations, the longitude of his ship, and 

 then steered his course accordingly by those common 

 principles of navigation which may be safely employed for 

 short distances between one known position and another. 



Having arrived to within what he considered, from his 

 computations, to be about fifteen or twenty miles of the 

 coast, he hove to, at four o'clock in the morning, to await 

 the break of day, aud then bore up, proceeding cautiously 

 onward on account of a thick fog which enveloped the 

 ship. As this cleared away, the people on board had 

 the satisfaction of seeing the great Sugar-loaf Rock, 

 which stands on one side of the harbour's mouth, so 

 nearly right a-hcad that they hail not to alter their 

 course above a point, in order to hit the entrance of the 

 liarbour ! This was the first land they had seen for 

 three months, after crossing so many seas, and being set 

 backwards and forwards by innumerable currents and 

 foul winds. The etl'ect on all on board was electric, and 

 the admiration of the sailors was unbounded. 



Something in this remarkable case may have been due 

 to a compensation of small errors ; but it is only fair to 

 conclude, that the accuracy with which the ship's position 

 was ascertained, was almost entirely attributable to the 

 precision with which the lunar distances were taken, and 

 the care with which the computations were executed. 



'!' IlKTKKMtNK TUK LoMHTUUB FROM THE LUNAR 



OBSERVATIONS. In the preceding articles, we have shown 

 at considerable length how the true distance between the 

 moon and the sun, or a fixed star, as seen from the centre 

 of the earth, may be determined from the observed 

 distance taken from the surface. It was also shown, 

 by means of tho altitude of a celestial object whose 

 declination is known, and the latitude of the place 

 where the altitude U taken, how the time at that place 

 may be found. 



The determination of a lunar distance necessitates tho 

 determination of the altitudes of tho objects whoso dis 

 Unco is observed, so that the data for finding the true 

 lunar distance, involves likewise the data for finding the 

 time when that distance had place. But, as already 

 remarked, if these two objects be sought to be accom- 

 plished, the altitude employed for the purpose of aacer- 

 t*in>i>- i ,e.-inp. must be taken with a degree 



of precision which is nut indispensable in " working tho 



lunar:" much more care and accuracy U r>.|'. in 

 observations of altii . i'..r either latitude 



or lunar distance ; aud on this account tho time at ship 

 i, in general, determined independently by one or 

 of the methods explained at page IDIH, et Kq., either 

 hhortly before or shortly after the distance is taken, liy 

 means of the chronometer or watch, the interval bet 

 the time thus found, and the instant of taking the dis- 

 tance, is known, and the proper correction for change of 

 longitude in that interval being made, we get the time 

 corresponding to the distance. 



We have just said that the altitude or rather the set 

 of altitudes for determining tho time, are taken sli 

 before or after the observations for the. distance, when- 

 ever these observations are not themselves sutlieiently 

 accurate for the purpose. It is desirable that the interval 

 should not be large, because the difference of longitude 

 in that interval may be large too, and our estimation of 

 its amount is, therefore, liable to a larger error. Itut as 

 it is important to get the altitude as precise as possible, 

 the situation of the object should be as near the prime 

 vertical ; that is, as nearly due east or duo west as possible 

 (page 1093). There is thus room for the exercise of 

 some judgment : tho object selected for the determina- 

 tion of the time at ship should be near the prime vertieal, 

 and it should reach this position shortly before or shortly 

 after the observation for the lunar distance. Whenever 

 the weather is so favourable as to render all risk of losing 

 the anticipated observation but very small, it is prudent 

 to wait till these conditions are fulfilled, provided other 

 circumstances are such as to allow of the delay. In 

 general, the object best suited to the determination of 

 the time at sea is the sun, as its declination, though 

 varying with the time, changes so slowly, as to bo 

 deducible accurately enough for the purpose from tho 

 e-timated time, or time by account, as sufficiently shown 

 at page 1095. A fixed star, however, is very .suitable for 

 the purpose, whenever it is nearly due east or we>t. and 

 the horizon clearly enough defined to admit of an. 

 accurate observation of its altitude. 



The object of the lunar distance is to find the time at 

 Greenwich at the instant that distance has place : and 

 tho object of the other, or extra observation, is to find 

 tho time at the same instant at the ship. Tim difference 

 of the two times gives the longitude in time. The 

 Greenwich time is obtained by comparing the true 

 distance, deduced from the observation, with the nearest 

 predicted distance, supplied by tho Nautical Almanac, 

 in the way that will be explained presently. It may bo 

 well, however, first to show what will be the average 

 effect on the inferred longitude of a given error, in tho 

 determination of the lunar distance. 



EFFECT ON THE LONGITUDE OF AN ERROR IN THB 

 LUNAR DISTANCE. The mean diurnal motion of tho 

 moon in her orbit is 13'1764: at certain times it is 

 about 2 slower, and at other times 2 quicker ; but this 

 is her average rate of motion ; so that, on the average, 

 360 of longitude (or 24h. of time) correspond to 13 1 TH I 

 of the moon's progress. Hence, to find the error in 

 longitude produced by an error of a seconds in the dis- 

 tance between the moon and a fixed star in her path, we 

 have the proportion 



13-17G4 :360 



which show that the error in tho longitude is 27 

 times tho error in tho distance. Thus an error of lo" in 

 i lie lunar distance, causes, on tho average, an error of 

 _;:; l'-J in the resulting longitude, or 4' 33 '22 ; and an 

 error of V in the distance, causes, on tho average, an 

 error of 27' 19" '3 in the longitude. 



Tho more rapidly the moon moves, the less is the effect 

 upon the longitude of a given error in the lunar distance : 

 the most rapid change in throe hours is very nearly 

 1 48', orl'8; so that for any error in the distance, 

 the corresponding error in longitude, in the most favour- 

 able cose is -, - 25a. Hence in the most favourable 



