NAVIGATION N'VUTICAL ASTRONOMY. [DIP. KKFRACTIOX, KTO. 



pUlod by the real inn which twenty-four hours is ft 

 variable interval U the apparent solar day. The twenty- 

 four hour* completed in one revolution of a star i* a 

 1 and invariable period ; and, it* already remarked, 

 U about 3m. fife., mean time, less than a mean solar 

 day. The tidereal day commence* when the first poin 

 of Aria U on the meridian, and continue* till it* return 



< IN Tll CoRRrCTIONS TO BK APPLIED TO THE OUSKRVEI 



ALTirroB* OF CELESTIAL OBJECTS. The tnie altitude 

 of a celestial object is the angular distance of it abov 

 the horizon of the place of observation. It is of course 

 measured (by a quadrant or sextant) in degrees am 

 minutes, the altitude of the zenith being 90. 



The ;iltitu.le in estimated, not from the visible, but 

 from the sensible horizon of the observer ; and in the 

 case of the sun or moon it U measured up to the centre 

 nf the body. The observed altitude U the angular dis 

 Unoe of the visible horizon from the lower or upper 

 limb of the body, so that a correction has to be in,-el. 

 for the dip or depression of the horizon, and for the 

 diameter of the body. If the object bo a star, then 

 there is no correction for semi-diameter. These correc- 

 tions licing made, the result is called the apparent alti- 

 tude of the body. 



Some other corrections are necessary to obtain the (rue 

 altitude from the apparent ; these we shall speak ol 

 presently. 



DIP OP THE HORIZON. As the eye is always elevated 

 above the surface of the sea, the visible horizon dips 

 below the sensible horizon, and forms an angle with it. 

 It is the amount of this angle which must bo subtr 

 from the observed altitude. Let (Fig. 24) be the 



place of the observer's 

 eye, and S the j>osition 

 of the celestial object 

 whose altitude is to be 

 found. The visible 

 horizontal line is 11 II', 

 the true horizontal 

 line H ; the altitude 

 of S, as shown by the 

 instrument, is the 

 angle S E H', instead 

 of the angle SEH ; 

 the angle H E H', by 

 which the latter angle 

 is increased, is the diji 

 which must be sub- 

 tracted from the observed altitude to give the apparent 

 altitude SEH. 



The angle HEH' is equal to the angle C, since the 



angle C E B is the complement of each. The height, 



of the eye being known, as also the radius CA of 



the ciirth, K ii becomes known for E B 2 = E D X E A 



1'rop. 36, Book III.), so that the amount of 



the angle of depression can always be found when the 



'it of the eye above the surface is given. 

 Tims, let r bo put for the radius of the earth, and h 

 for the height of the eye above its surface ; then, as just 

 shown, 



EB' - (2r + h) h - 2rA, very nearly, 

 the quantity h 1 Wing omitted as insignificant in relation 

 to 2rA. Hence, because by right-angled triangles, sin. 



EB 

 j,- Q. and since C being always very small only a 



few minute* the arc may bo taken for its sine, we 



I. .11 . 



r+h (very nearly) - ^/ ~. 



which ii the length of tho arc (to radius 1) that measures 

 the dip du.. to the height A. This length, 

 for diilorent value* of A, is converted into minutes, and 

 in this way the correction for dip U calculate*! for dif- 

 ferent altitudes of the eye, aud the results arranged in a 

 Wblt, 

 SiMi-DiAMETnt. The foregoing correction for the dip 



' ' ' ' .-.- ...,., ... ' . ;. f : ..,.,,,,.;y 



U4 la awttel ubln, ud, therefore, often neglected at em. 



of the horizon having been applied to the altitude of the 

 point observed, if this point bo the uppermost or lower- 

 most point of the disc of the sun or moon, a corr< 

 for the semi diameter of the Itody must lie applied iu 

 order to obtain the apparent altitude of the centre. As 

 the measurements in the present subject are all aiuttilar 

 measurements, the correction here ad\ the 



angle subtended at the eye, by the semi-diameter of tho 

 observed body. This angle, both for tho sun and n. 

 is given in the, N Almanac. In the case of tin? 



moon, the diameter is seen under a greater angle as she 

 approaches towards the zenith ; for at the zenith she is 

 nearer to the observer than when she is in tho horizon, 

 by a semi-diameter of the earth ; and sueh is the e,,m- 

 parative nearness of tho moon that this difference in her 

 distance makes a sensible difference in her apparent mag- 

 nitude. The semi-diameter given in the Xniitiral Al- 

 manac is the horizontal semi-diameter, or that under 

 wliieh she would be seen when in the horizon ; or, which 

 is the same thing, it is tho angle subtended by the semi- 

 diameter at tho centre of the earth. As this semi-diam- 

 eter increases with her altitude, the increase being so 

 much as one-sixtieth part of the whole when the m< 

 in tho zenith for she is about sixty semi-diameters of 

 the earth off tho amount of increase for any altitude is 

 found by multiplying one-sixtieth of tho moon's linear 

 semi-diameter by the sine of the altitude ; and in this 

 way the table entitled Augmentation of Hie Moon's 

 Semi-diameter, and given in some collections of Nautical 

 Tables, is constructed : it supplies the proper correction, 

 to be applied additively to tho horizonal semi-diameter, 

 to obtain the semi-diameter at tho given altitude.* 



On account of the great distance of the sun, tho varia- 

 tion of his semi-diameter, as ho increases in altiti:<i 

 too minute to give any correction : it is practically 

 insensible. 



Tho corrections for dip and semi-diameter being thus 

 applied, the result is the apparent altitude of the centre. 

 As to the stars, the only correction of the observed alti- 

 tude of a star, to reduce it to the apparent altitude, is 

 the correction for dip. It remains to Ixj shown how tho 

 true altitude is obtained from the apparent altitude : this 

 requires two additional corrections one for refraction, 

 and the other for parallax. 



REFRACTION. Tho atmosphere which surrounds tho 

 earth is of variable density, the lower parts being com- 

 pressed by the weight of the upper. A ray of light, 

 therefore, from a celestial object passe* through a 

 medium, which opposes some obstruction to its free 

 passage, the density of the medium increasing as the ray 

 advances from the upper to the lower regions of tho 

 atmosphere, where it meets the eye of the observer. 

 This disturbance causes the ray to be deflected or bent, 

 the deflection being greater as the density of the medium 

 through which it passes increases. Instead, therefore, 

 of reaching the eye in a direct lino from the object, it 

 begins to curve as soon as it enters the atmosphere, and 

 the curvature increases as it reaches the earth : tho 

 direction of the object from which it proceeds which 

 direction is judged of by tho last direction the ray takes, 

 and in which it enters the eye thus appears to be dif- 

 ferent from its true direction : the object always, except 

 when in the zenith, seems higher than it really is. Con- 

 sequently, tho correction for this refraction, as it is i 

 called, of tho rays of light, like that for dip, is always ' 

 iil'trtii-tin: At the horizon it is greatest, for the rays 

 >ecome more bent the more obliquely they enter a 

 refracting medium ; when they strike upon it perpen- 

 licularly they are not bent at all. These facts are proved 

 >y many optical experiments f 



Tho refraction takes place entirely in tho vertical 

 'lane ; for contiguous to this piano, to the right aud 

 left, the medium being tho same, there is nothing to 

 divert it from its path either on one side or the oth.-r. 

 Refraction, therefore, like dip, affects altitudes only. 

 Tables for the corresponding correction of the altitude, 

 from tho horizon to the zenith, are given in all nautical 



+ The ntnrlcnt my refrr to the trticlc Refraction, in the lection on 

 Light, for fuller dt-uili on thu lubjcct-- ED. 



