EXAMPLE. How long will light be in moving over 0,784 of the earth's radius? Contains the Nonagesimal Degree of the Ecliptic, and its Altitude, for the Latitude of Greenwich, reduced (173) to the Earth's Center, supposed to be 51°. 14'. 7", for the Obliquity of the Ecliptic 23°. 28'. RULE. Enter with the right ascension of the meridian, and against it you have the nonagesimal degree, and its altitude. If the right ascension be not found in the Table, the required quantities must be found by proportion. EXAMPLE. If the right ascension of the meridian be 37°. 17. 30", what is the nonagesimal degree, and its altitude? Hence, 1°. 17. 30":: 42′ 12′. 15", which added to 1. 22°. 41′. 20′′ gives 1'. 22°. 53′. 35" the nonagesimal degree. : Hence, 1° 17'. 30":: 14. 30": 4. 14", which added to 55°. 35'. O', gives 55°. 39. 14" the altitude of the nonagesimal degree. TABLE XXIV. Contains the Correction to be applied to the last Table, for the Latitude of one. Degree north of Greenwich. RULE. Enter with the right ascension of the mid-heaven, and you have the corrections required. If the right ascension be not in the Table, the corrections must be found by proportion. If the latitude be not one degree from that of Greenwich, change the quantities found in proportion. EXAMPLE. In the last example, what is the nonagesimal degree, and its altitude, for a place 20' north of Greenwich? Hence, 10° : 7°. 17'. 30′′ :: {5} {the correction for the nonagesi S5,41 : mal degree and altitude, for 1° change of latitude; therefore the respective corrections for 20' change of latitude; hence, 31',4-1′,31 = 30′,0930'. 5" the correction for the nonagesimal degree; and 54′,3 +0′,39= 54,6954. 41" the correction for the altitude. Therefore 1. 22°. 53'. 35" + 30′. 5′′ = 1o. 23°. 23'. 40" the nonagesimal degree; and 55°. 39. 14′′ — 54′. 41′′= 54°. 44. 33" its altitude. If the place be to the south of Greenwich, apply the corrections with a contrary sign. کے The calculation of parallaxes by the nonagesimal degree and its altitude, being generally used in computing solar eclipses, and occultations of the fixed stars and planets by the moon, these two Tables will be very useful for that purpose. TABLE XXV. ! Contains the Angle between the Ecliptic and a Parallel to the Equator, to the Obliquity. 23°. 28'; with the Variation for 10" Variation of the Obliquity. TT RULE. Enter with the sun's declination, and you have the required angle. If the declination be not found in the Table, you must find the angle by proportion. EXAMPLE. What is the angle between the ecliptic and a parallel to the equator, when the sun's declination is 17°. 30', and the obliquity 23°. 27'. 55"? 17°. 20' declin. the angle is 16°. 4. 8" 15. 41. 58 20 22. 10 Hence, 20'; 10':: 22′. 10": 11′. 5", which subtracted from 16°. 4. 8′′ leaves 15°. 53′. 3′′ for the angle at an obliquity 23°. 28'. Now the variation at this point for 10" of variation of the obliquity is 15",2; hence, the variation for 5" is 7",6, which subtracted from 15°. 53'. 3" leaves 15°. 52'. 55",4 for the angle required. If the obliquity had been taken greater than 23°. 28', the correction must have been added. TABLE XXVI. Contains the Angle of Position of any Point of the Ecliptic, according to the Obliquity 23°. 28'; with the Variation for the Variation of the Ecliptic by one Minute. RULE. Enter with the longitude of the given point of the ecliptic, and you have the angle required. If the longitude be not found in the Table, the angle must be found by proportion. THE USE OF THE TABLES. EXAMPLE. What is the angle of position of that point of the ecliptic, whose longitude is 23. 10°. So'. 10", for the obliquity 23°. 28'? Long. 2'. 10° 2. 11 ang. of posit. 8°. 26'. 43",7 24. 2,9 Hence, 1° : sơ. 15′ :: 24′. 2′′,9 : 12. 7,5, which subtracted from 8°. 26′. 43′′,7 gives 8°. 14. $6,2 the angle of position. The variation of the angle of position for one minute of variation of obliquity, to this longitude, is 23",2; and the variation for any quantity less than one minute will be proportionably less; and this variation is to be added to, or subtracted from the angle of position found for the obliquity 23°. 28', according as the obliquity is greater or less than that quantity. EXAMPLE. Let every thing be as before, except that the obliquity is 23°. 27'. so. Here the variation being half a minute, the corresponding variation of the angle of position is half 23",2, or 11",6, which subtracted from 12'. 7′′,5 gives 11′ 55′′,9, and this subtracted from 8°. 26'. 43",7 gives 8°. 14′′ 47′′,8 for the angle of position. TABLE XXVII. Is to find the Angle of Position, having given the Right Ascension. The computation from this Table is exactly the same as from the last, only you enter with the right ascension instead of the longitude. TABLE XXVIII. Contains the Augmentation of the Angle of Position of a Point in the Ecliptic for the Latitude of the Zodiacal Stars. RULE. Enter with the star's latitude at already found, at the side, and nd in the Table, the correction must be found xample, suppose the star's longitude to be the same oint of the ecliptic there given, and its latitude 3°. position. and 3°. O' lat. correct. is O'. 39",7 14,5 :: 14",5 9,8 the first part of the correction, to be added to correct. is O'. 39",7 5, 1 4. 47",8 :: 5",1: 1",3 the second part of the correction to be ,7; hence, the angle of position is 8°. 14. 47",8 +0. 39",7 + . 15'. 38",6. last Tables are of use in calculating the parallaxes in solar eclipses, tions of fixed stars and planets by the moon, by the method of the · angle. TABLE XXIX. ins the Epochs of the mean Longitude of the Moon's ascending Node, for the Beginning of each Year. RULE. Enter with the epoch, and against it you have the mean longitude. |