JARAtLAX. ] 



NAVIGATION NAUTICAL ASTRONOMY. 



1077 



collections : these, however, are computed for the mean 

 state of the atmosphere ; and it must occur to the reader 

 that, as this state is continually varying in certain lati- 

 tudes, it becomes necessary to modify the numbers in 

 the table, when the true altitude of a celestial object is 

 required with the utmost accuracy, by taking note of 

 the actual state of the atmosphere, as indicated by the 

 thermometer and barometer. To the table of mean 

 refractions a table of these corrections is generally 

 annexed. When the latitude only of the ship is 

 required, the correction of the mean refraction is of 

 comparatively little consequence ; but, in determining 

 the longitude by lunar observations, it is deserving of 

 attention. 



When the corrections, now explained, are applied to 

 the observed altitude of a celestial object, the result is 

 the true altitude of it above the sensible horizon of the 

 i,li-rrver ; an<l it now only remains to reduce this to the 

 altitude above the rational horizon of the place, as if the 

 object were observed from the centre of the earth, 

 instead of from the point on its surface immediately 

 above the centre. In the case of a star, the altitude 

 would be the same, whether the observation be made on 

 the surface or at the centre the change of position 

 beini; insensible in reference to objects so remote as the 

 stars ; but, for the sun and moon, especially for the 

 latter, the angle subtended at the body by the radius of 

 the earth, called its parallax in altitude, is of sensible 

 aim unit. 



PARALLAX. Let S (Fig. 25) represent the place of the 

 tial body olwerved from the surface of the earth at 

 K ; tlio observed angle t> E II, when corrected for dip, 



Fig. U. 



Eelni-diametcr, and 

 refraction, will be the 

 true altitude of the 

 centre of S above the 

 sesniblc horizon EH; 

 and the angle S C K, 

 will be the true alti- 

 tude of the centre 

 above the rational 

 horizon C 11. It is 

 the dilference of these 

 angles that in called 

 the parallax in alti- 

 tude. If -the body be 

 in the sensible horizon, 

 as at H, then the dif- 

 ference spoken of will 

 be the whole angle H C R : this is called the horizontal 

 parallax. For any other position of the body the 

 parallax is leas diminishing as the object approaches 

 the zenith, and vanishing at that elevation. Since 

 parallax in altitude = SE'H SEH = ESC, the 

 parallax is always the angle subtended by the semi- 

 diameter of the earth at the object ; and since the true 

 altitude above the rational horizon is 



the correction for parallax in altitude must be applied 

 atiditirrhj to the true altitude above the sensible horizon, 

 to obtain the true altitude above the rational horizon. 

 The gun's horizontal parallax is always about IT; tlie 

 moon's horizontal parallax varies considerably, and is 

 given, together with her semi-diameter, for every noon 

 ad midnight, at page 3 .f the Nautical Almanac. 

 And from tlio horizontal parallax Iwing known, the 

 parallax in altitude is easily found thus. Referring to 

 the trijinglu S E C, we have tlie proportion 



S C : E C : : sin. S E C : E S C 



EC 



j, ,, sin. SEC; 



bntsin. SF,C = fiin. SEZ = cos. S EH ; and as E C, SC 

 are constant, it follow* that the sine of the parallax in 

 altitude varies as the cosine of the altitude ; that is, 



1 : cos. alt. : : sin. hor. par. : sin. par. in alt. 

 Tlie parallax being always a very small angle, it is 

 UHiial to substitute the seconds in the arc for tlie sine, so 

 that we have, as above, 



par. in alt. in seconds = hor. par. in seconds X cos. alt. 

 And in this way the table for parallax in altitude is con- 

 structed. 



We have now explained the necessary corrections for 

 reducing the observed altitude of a celestial object to its 

 true altitude, as seen from the centre of the earth. When 

 the object is the sun or moon, these corrections are four 

 in number namely, for dip, semi-diameter, refraction, 

 and parallax in altitude ; when it is a star, there are only 

 two corrections namely, those for dip and refraction. 

 The Nautical Almanac furnishes the necessary particulars 

 for the other two corrections when either the sun or 

 moon is observed : the semi- diameter of the moon, as 

 seen from the centre of the earth, is given for intervals 

 of twelve hours throughout the year ; its value for any 

 intermediate time is to be found in proportion, and it is 

 the same for the horizontal parallax. In the " Explana- 

 tion" which accompanies the Nautical Almanac, every 

 needful information is given as to how values which 

 vary continuously, may be determined for any proposed 

 time, from the recorded values at stated intervals : 

 thus 



To find the moon's semi-diameter and horizontal 

 parallax at Ch. A.M. (that is, before noon) on February 

 23rd, 1846, at a place 16, or In., to the east of Green- 

 wich. 



The civil time at the place, expressed in mean astro- 

 nomical time, is February 22nd, 18h., from which, sub- 

 tracting Hi., because the place is to the east of Green- 

 wich, we have, February 22nd, 17h. for the corresponding 

 time at Greenwich, or 5h. after midnight. Proceeding 

 from the semi-diameter given for midnight of the 22nd, 

 we must compute the proportional part of the variation 

 in 32 hours, due to the time elapsed, viz., 5h. ; thus, the 

 semi-diameter for midnight, or 12h. of the 22nd, is 

 10' 31*-6, and for the 23rd, at noon, or 24h., it is 

 10' 34" -7; the difference, 3*'l, is the variation in 12 

 hours. Therefore, 



12h. : 5h. : : 3" 1 : l-3, 



which added (because the quantities are increasing) to 

 1C' 31" -0, gives 10' 32* -9 for the moon's semi-diameter 

 at the time proposed. Similarly, the horizontal paral- 

 lax at midnight of the 22nd, is GO' 39", and at noon of 

 the 23rd, it is CO' 50" -4 ; the difference 11"'4 is the 

 variation in the 12 hours, which include the given time : 

 therefore, 



12h. : 5h. : : 11" -4 : 4"'75 or 4" -8, 



which added (because the quantities are increasing) to 

 00' 39", gives OO' 43 "8 for the horizontal parallax required. 

 And if with this horizontal parallax, and the apparent 

 altitude of the moon, we enter the table entitled " Moon's 

 Parallax in Altitude," we shall obtain the parallax in 

 altitude. But in most nautical tables, the two correc- 

 tions for refraction in altitude and parallax in altitude 

 are combined, and the results tabulated under the head 

 of "Correction of the Moon's Apparent Altitude," and 

 this is the preferable arrangement when the true altitude 

 is to be deduced. 



Besides the foregoing corrections for obtaining the 

 true altitude of a celestial object from the observed 

 altitude, the observed altitude itself generally requires a 

 little correction for the known error of the instrument 

 (quadrant or sextant) employed in taking the altitude. 

 "Human hands, or machines, never formed a circle, 

 drew a straight line, or erected a perpendicular ;' * there 

 are, in consequence, unavoidable departures from strict 

 mathematical accuracy in all mechanical constructions. 

 The shortcomings may be discovered and allowed for, 

 though not remedied just as the gain or loss of a 

 chronometer maybe discovered, though to construct ojn', 

 without gain or loss, be a practical impossibility. The 

 indrx error as it is usually called of the instrument, 

 is to be allowed for before any of the astronomical cor- 

 rections are introduced ; it is not constant, but varies 

 with temperature. The following examples will suffi- 

 ciently show how the several corrections are supplied. 



OF CoKKELTING ALTITUDES AT SKA 1. !Sup- 



Sir Julia IJerscLcl's TrcaCac on Ailionomy. 



