As the Radius Is to the Co-tangent of Od, 51°.32′, To the Sine of O d, 19°.46′, io. 9.900087 9.629255 9.529342 This being converted into Time, by allowing an Hour for every 15°, and four Minutes of Time for each Degree, gives one Hour and fixteen Minutes for the 19°, and three Minutes and four Seconds for the 46', which makes one Hour, nineteen Minutes, and four Seconds. Now, as the Sun rifes at y, where the Parallel of Declination cuts the Horizon, in his Afcent to his Meridian Altitude, he will be on the Axis POS at Six o'Clock in the Morning; therefore it will be paft that Time one Hour, nineteen Minutes, and four Seconds, when he is due Eaft, or at O, that is, it will be nineteen Minutes and four Seconds paft Seven o'clock in the Morning: And, when he hath paffed the Meridian, and is going towards the Horizon, to fet at y, when he is at O, or due Weft, it will want one Hour, nineteen Minutes, and four Seconds of Six o'Clock, that is, it will be forty Minutes and fifty-fix Seconds paft Four in the Afternoon. Hence, the Degrees and Minutes, being converted into Time, and added to Six o'Clock, give the Time he is due Eaft; and, being taken from Six, give the Time he is due Weft in the Afternoon. But, if the Latitude of the Place and Declination be not both North, or both South, the Sun will be fet before he is due Weft, and will not rife 'till after he is past the East Point of the Horizon. Prob. 98. The Latitude of the Place 51°. 32′ North, and the Sun's prefent Declination 23°. 4 North, given, to find the Altitude of the Sun at Noon. When the Latitude of the Place and the Declination of the Sun are both North, or both South, add the Declination to the Complement of the Latitude, and the Sum will be his Meridian Altitude; but, if the Declination and Latitude are, one North, the other South, fubtract the Declination from the Complement of the Latitude, and the Remainder will be the Sun's Meridian Altitude: From In the fame Latitude, if the Declination had been South 23°.4', fubtracting that from 38°. 28′, leaves 15°.24 ́ for the Meridian Altitude of the Sun. Prob. 99. The Latitude of the Place 51°. 32′ North, and the Sun's Declination 18°.7 North, to find the Sun's Altitude and Azimuth at Six o'Clock. Conftruction. With the Chord of 60°, draw HZ RN the Meridian of the Place; then draw HOR the Horizon, and ZON the Prime Vertical at right Angles to it; fet the FI Latitude, 51°. 32', from H B to P, and from R to S; then draw the Axis POS, and at right Angles to it draw EOQ the Equinoctial; lay 18°.7', the Sun's Declination, from P Z N R E to b, and from Q to a, alfo the Half-Tangent of 18°.7 from O to x; by Prob. 17, draw the Parallel of the Sun's Declination, a xb, interfecting the Axis POS in x, the Place of the Sun at Six o'Clock; thro' x, and the Poles of the Horizon Z and N, by Prob. 17, draw the AzimuthCircle Zx N, interfecting the Horizon in e, and forming the right-angled Triangle ex O, right-angled at ; in which is given the Angle at O 51°.32, and the Hypothenuse Ox 18.7, to find the Perpendicular ex, the Sun's Altitude at Six o'clock; this is an Extreme disjunct, and the required Perpendicular is the middle Part; whence, by Lord Nepier's third Rule, and its Note, Page 266, As As the Radius x Is to the Sine of Oe, 51°. 32, So is the Sine of Ox, 18°.7' 10. 9.893745 9.492695 To the Sine of ex, 14.5, the Altitude of the } 9.386440 Sun above the Horizon, For the Sun's Azimuth: The fame Things being given, to find the Bafe e O, the Sun's Azimuth from the Eaft, Northward, is an Extreme conjunct, and the Bafe is one of the Extremes; whence, by Lord Nepier's fecond Rule, and its Note, Page 266, As the Co-tangent of Qx, 18.7', Is to the Radius, So is the Co-fine of x O e, 51°. 32', To the Tangent of Oe, 11°. 3', 10.485223 10. 9.793832 9.308609 Hence the Sun's Azimuth from the Eaft or Weft, at Six o'Clock, is 11°. 3'; and this, being added to 90°, or OR, gives e R 101.3, the Sun's Azimuth from the Meridian towards the North Point of the Horizon. P Z a Prob. 100. The Latitude of the Place 51°. 32 North, and the Sun's prefent Declination 15°.46' North, given, to find the Sun's Amplitude, and the afcenfional Difference; the Time of the Suns Rifing and Setting, with the Length of the Day and Night; alfo the oblique Afcenfion and Defcenfion of the Sun. Draw the Meridian HZRN, with the Chord of 60°; draw the Horizon HOR, and the Prime Vertical ZON at right Angles to it; take the Latitude, 51° 32', and fet it from H to P, and from R to S; draw the Axis POS, and EO Q the Æquinoctial at right Angles to the Axis; take 15°. 46', and fet it from A to b, and from Q to a; fet the Half H N S R Tangent of 15°.46′ from O to c, and draw, by Prob, 17, the the Parallel of Declination b c a, interfecting the Horizon in d; thro' P, d, and S, by Prob. 17, draw the oblique Circle Pd S, interfecting EOQ in x, and forming the right-angled Triangle Odx, right-angled at x; in which is given the Angle at O 38°. 28', the Complement of the Latitude, and d x. 15°.46', to find the Hypothenufe Od, the Sun's Amplitude, or Diftance of rifing from the Eaft Point of the Horizon, Northward; which is an Extreme disjunct, and the Hypothenufe is one of the Extremes; wherefore, by Lord Nepier's fourth Rule, and its Note, Page 266, As the Sine of d Ox, 38°. 28′, Is to the Radius, So is the Sine of d x, 15°.46′, Co. At. 0.206168 10. 9.434122 To the Sine of d O, 25°. 54's 9.640290 The Hypothenufe Od may be measured by Prob. 43. If the Sun's Declination had been South 15°. 46', the Parallel gbf being drawn, would interfect the Horizon in i, and an oblique Circle, PiS, would interfect A OQ in z, forming the right-angled Triangle Oiz, right-angled at z equal to the Triangle Odx; in which the Hypothenuse O i, equal to Od, is the Sun's Amplitude, or the Distance of the Rifing and Setting from the Eaft and Weft Points of the Horizon, the fame as before; only, in the former Cafe, the Amplitude is from the Eaft or Weft, Northward, and, in the latter, Southward; that is, in North Latitude, when the Sun's Declination is North, he rifes to the North of the Eaft, and fets to the North of the Weft; but, when the Latitude is North and Declination South, he rifes to the South of the Eaft, and fets to the South of the Weft. Then, for the afcenfional Difference, the fame Parts 'being given, to find the Side Ox, is an Extreme conjunct, and Ox is the middle Part; whence, by Lord Nepier's first Rule, and its Note, Page 265, As the Radius. Is to the Co-tangent of d Ox, 38°.28', To the Sine of Ox, 20°.4′, The Side Ox may be measured by Prob. 43. 10. 10.099914 9.450777 9.550691 The The afcenfional Difference 20°.4', being converted into Time, by allowing 15° for an Hour, four Minutes of Time for a Degree, and four Seconds of Time for each Minute, gives one Hour, twenty Minutes, and fixteen Seconds; and fo much the Sun rifes before Six in the Morning, and sets after Six at Night; that is, the Sun rifes thirty nine Minutes and forty-four Seconds after Four o'Clock in the Morning, and fets twenty Minutes and fixteen Seconds after Seven at Night. But, if the Declination had been different, the one North, the other South, the one Hour, twenty Minutes, and fixteen Seconds, being added to the Hour of Six, gives the Sun's Rifing twenty Minutes and fixteen Seconds after Seven in the Morning; and, being fubtracted from Six, gives thirty-nine Minutes and forty-four Seconds after Four at Night for the Time of his Setting. If the Time of the Sun's Setting, feven Hours, twenty Minutes, and fixteen Seconds, be doubled, it gives the Length of the Day, fourteen Hours, forty Minutes, and thirty-two Seconds; and thirty-nine Minutes and forty-four Seconds after Four, the Time of the Sun's Rifing, being doubled, gives nine Hours, nineteen Minutes, and twenty-eight Seconds for the Length of the Night. To find the Oblique Defcenfion. When the Latitude and Declination are the fame, add the afcenfional Difference to the right Afcenfion, and the Sum is the oblique Defcenfion: But, when the Latitude and Declination are not the fame, then fubtract the afcenfional Dif ference from the right Afcenfion, and the Remainder is the oblique Defcenfion; and, if you cannot fubtract the afcenfional Difference from the right Afcenfion, add 90° to it, then subtract, and the Remainder is the oblique Defcenfion. To find the Oblique Afcenfion. When the Latitude and Declination are the fame, fubtract the afcenfional Difference from the right Afcenfion, and the Remainder is the oblique Afcenfion; and, if the afcenfional Difference cannot be taken from the right Afcenfion, add 90° to it, then fubtract, and the Remainder is the oblique Afcenfion: But, when the Latitude and Declination are not the fame, then the afcenfional Difference and right Afcenfion, being added together, is the oblique Afcenfion, |