Astronomia BRITANNICA, Exhibiting The Doctrine of the Sphere, and Theory of the Planets Decimally by Trigonometry, and by Tables. Fitted for the Meridian of LONDON, according to the Copernican Systeme As it is illustrated by Bullialdus, and the easy way of Calculation, lately published by Doctor WARD. By JOHN NEWTON, M: A: bookseller's logo LONDON, Printed for the Author, by R. and W. Leybourn, and are to be sold by Thomas Pierrepoint, at the Sun in St. Paul's Churchyard, 1657. To the Right Honourable ROBERT Earl of WARWICK, Baron of LEES, etc. RIGHT HONOURABLE, AS it were presumption in me, to think, that I have any thing in myself, that is worthy the presenting to your Honour: so it were injustice to keep from you, that which is your own; He that is once an Admiral, hath so great an interest in the Sea, that of necessity he must have some ●n the Stars also, because Navigation without Astronomy is very lame and defective. The compass I know is the Seaman's best direction when the weather is foul, but the Sun is found a better when it is fair, yea, serveth to correct the errors committed by the other; unless his place therefore be rightly known, our Seamen, how otherwise skilful soever, will be many times troubled to steer their course aright: This then (without prejudice to other men's endeavours) is that which I aim at, and do believe I have effected, as with more ease, so also with more exactness, than those who have written before me, and that not only in relation to the Sun, but also to the Moon and other Planets, the truth of which Time only can discover, & must be therefore waited for. And now that these endeavours of mine may in the mean while receive some shelter from the envious, through your Honour's protection, is the humble suit of him that is Your Honours to dispose of JOHN NEWTON. To the Courteous READER. Courteous Reader, AS there is no part of Mathematical learning more excellent, so is there none more difficult than this of Astronomy, it hath for some thousands of years been much studied, and not without great expense of treasure, brought to that perfection, in which we now enjoy it; nor can we expect, that those mistakes, to which this noble Science is yet too often liable, should ever be redressed, without the expense of more, and hard it is to persuade the men of this earthly-minded age, to look higher than the earth they tread upon, and wallow in; they will not look so high as Heaven themselves, nor give encouragement unto those that would; but that our Students should neglect the benefit of that knowledge they might enjoy; that they should be in love with those difficulties they might avoid, in a study that is too intricate and difficult at the best, can never be sufficiently admired. It is therefore our chief and principal aim to show how much of trouble may be avoided in computing the motions of the heavenly bodies; if only the form of our Tables were changed from Sexagenary into decimal, the excellency of Decimal Arithmetic will in part appear, if we but consider the manner of working, in our Sexagenary Canons of natural Sins and Tangents, in which (to avoid the vast trouble, if not almost the impossibity of working with a Canon that should consist of vulgar Fractions) the Sine and Tangent of every minute is nothing else but the decimal of a Unite; and this that famous Mathematician of our age Mr. Henry Brigges did well perceive, when (having perfected that noble invention of Logarithms, first found out by the Right Honourable, John, Lord Neiper, Baron of Merchiston in Scotland) he took the pains to make a new Canon of Sines and Tangents, dividing the degrees into Decimals, as well as the parts of the Radius answering unto those degrees; and according to which Canon, Mr. Henry Gillebrand did since prepare a Treatise of Astronomy for the Press, but his death prevented the publication: To these I may add Mr. William Oughtred, who is the present wonder of our age, for his extraordinary knowledge in this kind of learning, who in his Clavis Mathematica, doth not only wish that this decimal form were observed in all Astronomical Canons, but hath also lately professed, that he ever found so much trouble in the Sexagenary way, that he took the pains to turn the Equations in the Rudolphin Tables into Decimals before he used them; besides the trouble of Reduction this advantage our Decimal Tables have above the Sexagenary, that in finding the part proportional, the half of your work is done before you begin, there being a necessity both of Multiplication and Division, in Sexagenary numbers, but here of Multiplication only, or only of Division. And now that this wonderful ease in calculation, commended to us by these famous men, might not still lie buried in oblivion, & that our Artists might be no longer enforced to use those labyrinthical Tables in the Sexagenary form, we have adventured to publish these, which never should have seen the light, if there had been any hope of those which Mr. Gillebrand did long since compose, or that Mr. Moor could have found encouragement to have published his; or that any other could have been persuaded to this Decimal form. The ease then that is in the form of our Tables, is in truth the reason for which we have undergone this labour, and yet the method of Calculation, which Dr. Ward professor of Astronomy in Oxford hath lately published (in his Book entitled Inquisitio in Bullialdi Astronomiae Philolaicae fundamenta) and which we have used in the composure of our Tables, is so brief, so easy, and so exact, as that a better is not to be expected. I am not ignorant, that some (which have a desire to make others and themselves work) are not therewith satisfied, they will rather take the pains of seven or eight operations, and yet the aequation at last found, is not so legitimate as that which here we find at one; of which there needs no other proof than the Geometry of our Method, our very Enemies being Judges; yet all that we shall promise is the places of the Planets prope rerum, at a cheaper rate; if we do fail of their true Phenomenon, it shall be with less trouble and expense of time. Our Middle-motions, Aphelia, Excentricities, and Dimensions of the several Orbs mentioned in the ensuing Treatise, we have borrowed from Bullialdus, the method by which they are computed is the same in all, and therefore as to the Excentricities & Aphelia, we thought it sufficient to instance in the Sun or Earth: and for the proportions between the Earth's Orb, and the Orbs of the other Planets with their angles of Inclination, we have given an Example in Saturn only, and refer you to Bullialdus for the rest. And although this method of his be not Geometrically true, yet knowing no better; we have contented ourselves with his, until there be a better found; and to make his Middle-motions to us more useful, we have reduced their Epoches to the Meridian of London, the most famous City of this our Island of Great Britain: For which reason, and for the easiness of the calculation which our own Countryman hath invented, and we here used, the Treatise itself doth carry the style of Astronomia Britannica. And whether this method of finding the first inequality will agree with observation, cannot be known; until a Geometrical way of finding the Excentricities & Aphelia of the Planets in an Ellipsis be also propounded to us; and if at last, when all things in this Elliptical Astronomy shall geometrically be demonstrated, the places of the Planets thus found shall not agree with observation, it will be hard to say in what particular the fault doth lie, and therefore we must not then impute it to the first inequality, much less now, when the Geometry of that is demonstrated, & other parts are defective, but a new Hypothesis must be thought of; and until this shall be effected, as there are no Tables extant, by which the places of the Planets can be computed with so much ease, so none can be expected, by which their places may be computed with more probability of truth, then by these which we must now submit to thy censure, and do commend to thy perusal. JOHN NEWTON. The Contents of the several Books or parts of Astronomia Britannica. The first Book. The Preface. Page 1. THe Sun's greatest declination being given, to find his declination in any point of the Ecliptic 9 How to find the declination of a Planet or fixed Star, with latitude 10 How to find the Right Ascension of any point of the Ecliptic 13 How to find the Right Ascension of a Planet or other Star with latitude 15 The elevat. of the Pole, & declin. of the Sun given, to find his amplit. 16 The Meridian altitude, and declination of the Sun, with the Poles elevation given to find his true place in the Zodiac 17 Having the Meridian altitude of an unknown Star, and the distance thereof from a known Star, to find the Right Ascension of the unknown Star Ibid. Having the declin. and Right Ascension of a Star given, to find the longitude and latitude thereof 19 How to find the ascensional difference 20 How to find the Oblique Ascension or Descension of any point of the Ecliptic 21 The Poles elevation and the Sun's declination being given, to find his altitude at any time assigned 22 Having the Sun's greatest declination, with his distance from the next Equinoctional point, to find the Meridian angle, or intersection of the Meridian with the Ecliptic 26 To find the angle of the Meridian, with the Horizon Ibid. The Poles elevation, with the Sun's altitude and declination given, to find his Azimuth Ibid. How to erect a Figure of Heaven 27 To find the angle of the Ecliptic with the horizon, or the altitude of the Nonagesime deg. together with its distance from the mid-heaven 36 To find the Parallactical angle, or angle of the Ecliptic, with the vertical circle ●7 The elevation of the Pole, and declination of the Sun given, to find the time when he will be due East and West 39 The elevation of the Pole, with the Sun's declination and altitude given, to find his distance from the Meridian 40 To find the time of the Suns rising and setting, with the length of the Day and Night Ibid. To find the distance of a Star from the Meridian 41 To find the elevation of the Pole above any circle of Position Ibid. Of the Ark of Direction what it is, and how to find it 45 How to direct the Mid-heaven, and the Imum Coeli 46 How to direct the Ascendent, or Significator posited in the Signs ascending Ibid. How to direct a Significator, posited in the Signs descending 47 How to find the Arch of the Equator, whereby is made the general Table of Positions 48 How by the general Table of Positions to make a particular Table for any latitude there expressed 49 Of the doctrine of the Sphere in Tables 51 The second Book. OF the year Civil and Astronomical 57 Of the Figure which the Planets describe in their Motion 66 Of the lines and method to be used for the finding of a Planets true longitude from the Aphelion in this Figure 72 Of the proportion by which the motion of the Planets do increase from the Aphelion to the Perihelion 74 Of the inequality of the Earth's annual motion, and of the Diameter in which the Aphelion and Perihelion are placed 81 Of stating the Earth's middle motions by sundry observations 90 To calculate the Sun's true place and distance from the Earth 94 Of the Aequation of Civil Days 97 Of the Theory and motion of the Moon 98 To calculate the true motion of the Moon by Tables 109 To find the Moons true latitude and place in the Ecliptic 113 Of the motion of the fixed Stars 115 Of the motion of Saturn 116 Of the motion of Jupiter 121 Of the motion of Mars 124 Of the motion of Venus 128 Of the motion of Mercury 133 Of the Semidiameters of the Sun, Moon, and shadow of the Earth 136 Of the proportion and magnitude of the three great bodies, the Sun, Moon, and the Earth 142 Of the proportion between the Orbs of the superior and inferior Planets, and the Orb of the Earth 144 To find the mean Conjunction and Opposition of the Sun & Moon 151 To find the true Opposition and Conjunction of the Sun and Moon 152 To find whether there will be an Eclipse or not 154 To find the quantity of a Lunar Eclipse Ibid. To find the duration of a Lunar Eclipse, or the continuance of the total darkness, where the Eclipse is total 155 To find the Moon's latitude at the beginning & end of the Eclipse 156 To find the middle of the Eclipse or greatest darkness 157 Of the calculation of the Sun's Eclipse 159 To find the Parallaxes of longitude and latitude 160 To find the visible motion of the Moon from the Sun for any time assigned 162 To find the time of the visible Conjunction of the Sun and Moon Ibid. To find the visible latitude of the Moon, at the time of the visible Conjunction 163 To find the quantity of a Solar Eclipse 164 To find the beginning and ending of the Sun's Eclipse Ibid. To find the visible latitude of the Moon at the beginning and end of the Sun's Eclipse 165 To delineat the Eclipses of the Sun and Moon 166 The use of the Table of Refractions 168 The Index of the Tables. A View of the more notable Epochae 2 A Table showing the Dominical Letter in both accounts 4 A Table showing the Golden number & Epact in both accounts Ibid. The Anticipation of the Gregorian Calendar Ibid. A Table of movable Feasts in both accounts 5 A Table of fixed Feasts 6 A Catalogue of Places, their latitudes and distance in longitude from the Meridian of London 8 A Table to convert Sexagenary minutes, seconds, thirds, fourth's and fifths into decimals, and the contrary 10 A Table to convert the hours, minutes, seconds, thirds, fourth's and fifths of a day into decimals, and the contrary 14 A Table to convert hours & parts into deg. & parts of the Aequator 20 A perpetual Table for the Equation of Time 21 The Suns mean motions 22 The Aequations of the Sun's Excerntrick 26 The Moons mean motions 29 The Aequations of the Moons Eccentric 34 A Table for the finding of the second & third inequalities of the Moon 37 Bullialdus his Table of Evection 40 A compounded Table of the Moon's Evection and Variation 43 A Table of the Aequations of Nodes and Moon's latitude 53 A Table of the Reductions to the Ecliptic 56 The difference of the true ☌ or ☍ from the middle of the obscuration 57 A Table of the mean Lunations 58 The horizontal Parallaxes, Semidiameters, and hourly motions of the Sun and Moon 59 The Declination and Meridian Angles 60 Tychoes Table of Refractions 61 Saturn's mean motions 62 Jupiter's mean motions 66 The mean motions of Mars 70 The mean motions of Venus 74 Mercury's mean motions 78 A Table of Declinations 82 A Table of Right Ascensions 89 A Table of Ascensional Differences 100 A Table of Oblique Ascensions 108 A Table of Positions for the latitude of 51 degrees 53 parts 138 A Table showing the elevation of the Pole upon the several circles of Position of the 11, 12, 2 and 3 houses for 60 degrees of latitude 151 A general Table of Positions 152 A Catalogue of the more notable fixed Stars with their longitude, latitude, and magnitude for the year 1650 complete. 154 The Preface. ALL Propositions Astronomical and Astrological, have some dependence on the Sphere or Globe, for the better understanding therefore of that which follows, it is fit that the Reader be somewhat acquainted with the doctrine thereof; that he know at lest what a Globe is, and what the lines, circles and arches usually drawn thereon do represent. Now a Globe or Sphere, is an Analogical representation either of the Heavens or the Earth. And in this Sphere or Globe there are ten imaginary circles whereof there are six great and four small. A great circle is such a one as divideth the body of the Globe into two equal Hemispheres. And a small circle is that which divideth the same, into two unequal Hemispheres, whereof the one is more, the other less than half the body of the Globe or Sphere. The six great circles are these. 1 The Horizon. 2 The Meridian. 3 The Equinoctial. 4 The Zodiac. The fifft and sixth are the two colours. The four lesser circles are, 1 The Tropic of Cancer. 2 The Tropic of Capricorn. 3 The circle Arctic. 4 The circle Antarctick. And are all expressed in this annexed Diagram. 1 The Horizon which is also called the Finitor, is a circle which divideth the visible part of the Heavens from the not visible, that is the lower Hemisphere from the higher, in the figure noted with A B. 2 The Meridian is a circle which passeth by the Poles of the World, and through the Zenith and Nadir, and is marked with A Z B N. 3 The Equinoctial is a Circle which divideth the whole Sphere into two equal parts, and is therefore equally distant from both the Poles, to which when the Sun cometh (which is twice in the Year) the Days and Nights are of equal length all the World over, this circle is noted with E F. 4 The Zodiac is a great circle which containeth the 12 Signs, cutting in the very middle the Equinoctial in two points, which are the beginning of Aries and Libra, whereof the one half. viz. six Signs decline from the Aequator to the North Pole, and are therefore called the Northern Signs, as Aries ♈, Taurus ♉, Gemini ♊, Cancer ♋, Leo ♌; Virgo ♍. The other six decline towards the South Pole and are therefore called the Southern Signs, as Libra ♎, Scorpio ♏, Sagittarius ♐, Capricornus ♑, Aquarius ♒, Pisces ♓. 5 The one of the Colours which dividing the Sphere into two parts passeth by the Poles of the World and the two Equinoctial points, called the Equinoctial Colour, and marked with C D. 6 The other Colour which dividing the Sphere also into two equal parts, passeth by the beginning of Cancer and Capricorn, and the Poles of the World, called the Solstitial Colour, and is the same with the Meridian as the Sphere is here projected. 7 The Tropic of Cancer is one of the lesser circles distant from the Equinoctial towards the North Pole 23 deg. 31 min. 30 seconds, or in Decimal Numbers, 23 deg. 525, to which when the Sun cometh he causeth the longest day, and shortest night to all Northern, the shortest day and longest night to all Southern inhabitants, and is noted with G ♋. 8 The Tropic of Capricorn is a circle distant from the Equinoctial towards the South Pole: 23 deg. 31 min. 30 seconds, or in Decimal numbers, 23 deg. 525 parts, to which when the Sun cometh, he maketh the longest day and shortest night, to all Southern the shortest day & longest night to all Northern Inhabitants, and is noted, with H ♑. These two circles are called of the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 à convertendo, because when the Sun toucheth any of these circles, he is at his greatest distance from the Aequator, and returneth thither again. 9 The Arctic circle is distant from the North pole of the world as much as the Tropic of Cancer is distant from the Equinoctial, and is noted with K L. 10 The Antarctic circle is distant from the South Pole as much as the Tropic of Capricorn is distant from the Aequator, and is noted with O M. Besides these circles expressed upon the Globe, there are other circles not expressed, that are also in familiar use; but these being sufficient for our intended matter, omitting the rest, we will now speak of the several affections of the Sphere or Globe, and so proceed to practice. According to the divers habitude of the Aequator to the Horizon (which is either Parallel to it, or else cutteth it, and that either in right or oblique angles) there is a threefold position or Situation of Spheres. The first is of those that have either Pole for there Zenith or vertical point, with these the Aequator and Horizon are Parallel to each other, or rather indeed do make but one circle between them; and this is called a Parallel Sphere, and they which there inhabit (if any such be) see not the Sun or other Star either rising or setting, or higher or lower, in their diurnal revolution. The third position of the Sphere agreeth to all other places else, and is called an oblique Sphere, in which the days are sometimes longer than the nights, sometimes shorter, and sometimes of equal length: when the Sun is placed in the Equinoctial point, the days and nights are equal, but when he declineth from the Aequator, the days are observed to increase, and when he declineth towards the opposite Pole the day's decrease, as it is manifest in the first figure. And thus having briefly showed, what a Globe is, the lines thereon described, with the several affections belonging thereunto, what remaineth but that we now proceed to practice, & show there use as to the matter in hand; which is to find the Declinations and Asceusions of the Sun and other Stars whether right or oblique, and divers other things depending on, or belonging to the Doctrine of the Sphere, the which we will show first by Trigonometrical Calculation, and then by Tables. Astronomia BRITANNICA: The first Book. CHAP. 1. To find the Sun's greatest Declination, and the Poles Elevation. THe Declination of a Planet, or other Star is his distance from the Aequator, and as he declines from thence either Northward or Southward, so is his declination nominated North or South. And because that all the Planets (the Sun only excepted) do move sometimes in and sometimes out of the Ecliptic besides there declination North or South from the Aequator, they have also latitude North or South from the Ecliptic, while the Planets keep in the ecliptic, one rule will serve to find their Declination, as well as the Declination, of the Sun, but if they have either North or South latitude, there must another rule be given, in both which rules the greatest Declination of the Sun is supposed to be known; and first therefore we will show how, that may be found instrumentally, and then compute the Declination of a Planet or other Star, with latitude or without. For the finding the Sun's greatest Declination, you must by a Quadrant or other Instrument, take his greatest and his least Meridian altitude; the difference between which altitudes is the distance of the Tropiques, and half the distance of the Tropiques, is the quantity of the Sun's great Declination, as by the following Figure it doth appear. In which A Z B N represents the Meridian, E F the Equinoctial, ♋ ♑ the Zodiac, the North pole D the South A B the Horizon Z the Zenith, N the Nadir, ♋ G a parallel of the Sun's Diurnal motion at ♋, or the Sun's greatest Declination from the Equator towards the North Pole. From whence it is apparent that from A to ♋ is the Sun's greatest Meridian altitude from A to H his least, if therefore you deduct A H the least Meridian altitude from A ♋ the greatest, the difference H ♋ is the distance of the Tropiques, and because the angles ♋ centre F and ♑ centre E are equal, therefore the Sun's greatest Declination towards the South Pole is equal to his greatest Declination towards the North, and consequently half the distance of the Tropiques, or the arch that is the arch ♋ F is the quantity of the Sun's greatest declination. And then if you deduct the Sun's greatest declination or the arch A ♋ F from the Sun's greatest Meridian altitude or the arch A ♋ the difference will be A F or the height of the Aequator above the Horizon, the compliment whereof to a quadrant is the arch A D equal to C B the height of the Pole. Example. The Sun's greatest Meridian altitude taken, June 11 at London 61, 99167 The Suns lest Meridian altitude, December the 10th. 14, 94167 Their difference is the distance of the Tropiques 47, 05000 Half that difference is the Sun's greatest Declination whose difference from the greatest altitude is 23, 52500 The elevation of the Equator and the compliment thereof to 90 is the Elevation of the Pole 38, 46667 51, 53333 CHAP. 2. The Sun's greatest Declination being given, to find his Declination in any point of the Ecliptic. LEt DFHG represent the Solstitial Colour, D BAG the Equator, F A H the Ecliptic, I the Pole of the Ecliptic, E the pole of the Equator, E C B a meridian line passing from E, through the Sun at C, and falling upon the Equator D A G with right angles at the point B. Therefore in the Rectangle spherical Triangle A B C we have known. 1 The Hypothenuse A C the Sun's distance from the next Equinoctial Point, whether Aries or Libra and may be supposed to be in 10 degrees of Cancer, and that being nearer unto Libra then Aries, I take his distance from Libra which is two signs and 20 degrees, or 80 degrees. 2. We have known the angle B A C the Sun's greatest declination, which by the accurate Observation of Tycho is found to be 23 deg. 31 minutes and 30 seconds. And in decimal numbers 23. 525. Hence to find the present declination the proportion is. As the Radius is to the sine of the Sun's geatest declination. So is the sine of the planets distance from the next Aeqninoctiall point, To the sine of the declination required. And by this proportion, together with the help of the Canon of artificial sins and tangents, I find the declination of the Sun at the time proposed thus. First, I seek for the sine of Radius or 90 degrees, the measure of the right angle at B, and I find the sine thereof 10, 000000, next I seek the sine of 80 degrees, and likewise the sine of 23. 5250, these two I add together and from their aggregate, I subtract the Radius and what remaineth is the sine of the declination sought, as in the following work you may perceive. As Radius To the sine of B A C 23. 525 9, 6011352 So sine of A C 70. 9, 9729858 To the sine of B C 22. 02910 9, 5741210 CHAP. 3. How to find the Declination of a planet or fixed Star with Latitude. What the Declination of a planet is, and how to find the same in any point of the Ecliptic hath been already showed, we will now show how to find the same with latitude either north or south, and for demonstration sake. Let G F I H represent the Solstitial Colour, H A F the Aequator, I A E the Ecliptic, K M N a circle of latitude, G M C a circle of declination, A N the longitude of the star, M C the declination. Then in the Oblique angled spheical▪ Triangle M G K we have limited. 1 The side K G the Sun's greatest declination. 2 The side K M the compliment of latitude. 3 The angle M K G the compliment of longit. From hence the declination M C may be found at two operations, for first to find K O the proportion is, As the Radius to the Cousin of the compliment of Longitude, so is the tangent of the Sun's greatest declination, To the tangent of the first arch: K O, which being added to or substracted from the compliment of Latitude K M, according to the direction ollowing their aggregate or difference will be the arch O M. If the Declination sought be in the Northern Signs and North Latitude, subtract the arch found from the compliment of latitude and what remaineth is the second Arch O M. South Latitude add the arch found to the compliment of latitude and their aggregate is the second arch if less than a quadrant, but if more the compliment thereof to a semicircle. Southern Signs and North Latitude, add the arch found to the compliment of Latitude, and their aggregate is the second arch. South latitude subtract the arch found from the compliment of latitude, and what remaineth is the second arch. And then the second proportion is, As the Consine of the first arch found, Is to the cousin of the Sun's greatest declination, So is the Cousin of the second arch found, to the Cousin of an arch, whose compliment is the declination sought: To make it plain we will in each case add an example. In the first Quadrant. We will suppose a star to be in 10 deg. of Gemini, with 4 deg. of north latitude. The longitude of a star so posited is 70 deg. the compliment thereof M K G is 20 deg. The latitude 4 deg. north, the compliment thereof 86 M K. And the Sun's greatest declination K G 23 deg. 5250. Then according to the former analogy, first I say, As the Radius 90. 10, 000000 To the Cousin of M K G 20. 9, 9729858 So is the tangent of K G 23. 5250 9, 6388198 To the tangent of K O 22. 25 9, 6118056 The compliment of latitude 00 s. 86 d. 00 The arch K O 22 25 Their aggregate 108 25 Their difference 63 75 Because the latitude is North I take their difference and say, As the Cousin of K O: 22. ●5 9, 9663954 To the Cousin of K G 23. 5250 9, 9623154 So is the Cousin of O M: 6●. 75 9, 6457058 To the Cousin of G M: 64. 01 9, 6416258 The compliment thereof 25. 99 is the declination sought. To find the declination of the same point with 4 degrees of South latitude: I take the compliment of 108. 25. viz. 71. 75. And say as the Cousin of K O 22. 25. 9, 9663954 To the Cousin of K G 23. 5250 9, 9623154 So the Cousin of O M 71. 75 9, 4957715 To the Cousin of G M 71. 93 9, 4916915 whose compliment is the declination sought, viz. 18. 7. The point of the Ecliptic answering hereunto in the 2 quadrant, is the 20 of Cancer, and hath the same declination North and South. In the third and fourth quadrant the 10 of Sagittary, and the 20 of Capricorn, have the same declination, but with contrary latitude. In the second Quadrant. We will suppose a star in 10 deg. of Leo whose longitude is 130. The latitude 4 deg. north. The compliment of longitude M K G is 50, but because the longitude is more than a quadrant, I take the compliment of 50, viz. 40 deg. The compliment of latitude M K is 86 as before. And the Sun's declination fixed, first then I faith, As the Radius 90 10, 0000000 To the Cousin of M K G 40 9, 8842539 So the tangent of K G 23. 5250 9, 6388198 To the tangent of K O. 18. 44 9, 5230737 The compliment of latitude 86. 00 The arch K O 18. 44 Their aggregate 104. 44 Their difference 67. 56 For the north latitude I take their difference and say, As the Cousin of K O 18. 44 9, 9771084 To the Cousin of K G 23. 5250 9, 9623154 So the Cousin of O M 67. 56 9, 5817400 To the Cousin of G M 68 35 9, 5669470 whose compliment 21. 65 is the declination sought. For the declination of the same point with South latitude, I take the compliment of 104. 44: viz. 75. 56. And say, As the Cousin of K O 18. 44 9, 9771084 To the Cousin of K G 23. 52. 50 9, 9623154 So the Cousin of O M 75. 56 9, 3968372 To the Cousin of G M 76. 05 9, 3820442 whose compliment 13. 95 is the declination with South latitude The point of the Ecliptic answering hereunto in the first quadrant is the 20 of Taurus, and hath the same declination North latitude North and South. In the third and fourth Quadrants the points answering thereunto are the 20 of Scorpio and the 10 of Aquarius, and have the same declination but with contrary latitude. CHAP. 4. How to find the Right Ascension of any point of the Ecliptic. THe Ascension of the Sun or Stars is the degree of the Aequator that riseth with the same above the Horizno. And the Descension of it is the degree of the Aequator that goeth under the Horizon with the same, both these are either Right or Oblique. The Right Ascension or Descension is the degree of the Aequator that Ascendeth or Descendeth with the Sun or other star in a Right Sphere, and the Oblique Ascension is the degree of the Aequator, that ascendeth or descendeth with the same in an oblique sphere. The former of these is simple, and of one kind only; because there can be but one position of a Right sphere, but the later is various and manifold according to the divers inclination of the same. To find the Right Ascension of a planet in the Eclptique, There must be given as in the first Chapter, the planet's longitude or distance from the next Equinoctial point: and the Sun's greatest declination. Then in the Rectangle spherical Triangle of the first chapter A B C, we have limited. 1 The angle B A C, the Sun's greatest declination 23. 31. 30. 2 The Hypothenuse A C, the Sun's distance from the next Equinoctial point, whose place we will suppose to be in 10 degrees of Gemini, and consequently his distance from Aries is 70 degrees. Hence to find the base A B, the right Right Ascension the point sought, the proportion is. As the Radius is to the tangent of the planets distance from the next Aequinoctial point: So is the Cousin of the Sun's greatest declination▪ to the tangent of the Right Ascension of the point sought, Example. As the Radius 90 10, 0000000 To tangent of A C 70. 10, 4389341 So is the Cousin of B A C 23. 5250 9, 9623154 To the tangent of A B 68 34874 10, 4012495 which is the Right Ascension of the Sun or any other planet without latitude, when they be in the the 10 degree of Gemini. Note that if the Right Ascension of the point sought be in the second quadrant (is in Cancer, Leo, Virgo.) you must take the compliment of the arch found to a semicircle: if in the third Quadrant (as in Libra, Scorpio, Sagitarius) you must add a semicircle to the arch found: if in the last quadrant (as in Capricorn, Aquarius, Pisces) you must subtract the arch found from a whole circle or 360, and so shall you have the Right Ascension of any point of the Ecliptic, to make it plain we will in each case add an Example. In the second Quadrant. Let the Right Ascension of the point sought be 10 degrees of Virgo, the distance thereof from Libra, which is the next Equinoctial point is 20 degrees, according therefore to the former Analogy, I say. As the Radius 90. 10. 0000000 To the tangent of A C 20. 9 5610658 So is the cousin of B A C 23. 5250 9 9623154 To the tangent of A B 18. 45 9 5233813 whose compliment to a semicircle 161. 55 is the Right Ascension thereof. In the third Quadrant. Let the Right Ascension of the point sought be in 14 degrees of Scorpio, the distance thereof from Libra, the next Equinoctial point is 44 degrees. Therefore I say. As the Radius 90. 10. 0000000 To the tangent of A C 44. deg. 9 9848371 So is the Cousin of 23. 5250 9 9623154 To the tangent of A B 4152 9 9471525 to which if you add a semicircle or 180 degrees the Right Ascension of of the point sought will be 221. 52. In the last Quadrant. Let the Right Ascension of the point sought, be 22 degrees of Aquarius; the distance thereof from Aries, which is the next Equinoctial point ●s 38 degrees. Therefore I say. As the Raduis 90. 10. 000000 To the Tangent of A C 38. 9 8928098 So is the Cousin of 23. 5250 9 9623154 To the tangent of A B 35. 62 9 8551252 which being subtracted from 360 there rests▪ 324. 38 for the Right Ascension of the point sought. CHAP. 5. How to find the Right Ascension of a Planet or other Star with Latitude. THe Declination being found by the 3 Chapter, we have in the oblique angled Spherical Triangle of that Diagram G K M all the sides given with the angle M K G, therefore to find the angle K G M, say. As the Cousins of the declination, is to the Cousin of the Planets distance from the next Equinoctial point. So is the Cousin of its latitude to the Cousin of its Right Ascension. For Example. The Declination of 10 degrees of Gemini, was found to be 25. 99 with 4 degrees North Latitude. Whose compliment is G M. 64. 01 the compliment of Longitude is the angle M K G 20, the compliment of Latitude is M K 86, hence to find the Right Ascension, the Analogy is. As the Sine of G M 64. ●01. co. arith. 0. 0463059 To the sine of M K G 20. 9 5340516 So is the sine of K M 86. 9 9984407 To the sine of K G M. 22. 28 9 5787982 whose compliment 67. 72 is the right Ascension of a Star in 10 degrees of Gemini, with 4 degrees of North Latitude. CHAP. 6. The Elevation of the Pole and Declination of the Sun given, to find his Amplitude. THe Amplitude of the Suns rising or setting is an arch of the Horizon intercepted betwixt the Aequator and the place of the rising and setting of the Sun. And it is either Northern or Southward, the Northern Amplitude is when he sets and riseth on this side of the Equator, toward he North Pole: and the Southern when he sets or riseth on the contrary side. Now when the Sun is in the Aequator, he hath no Amplitude at all: but when he is in the Solstitial points, he hath then the greatest Amplitude. That we may find then the Sun's amplitude or distance from the East or West points at the time of his rising or setting; let D P L G F represent the Meridian, F A I the Horizon, D A L the Equinoctial. P the Pole of the Aequator. Then in the Rectangle Spherical Triangle A B C, let there be given the angle B A C or compliment of the Poles elevation, 38. 47 and B C the Sun's Declination 23. 15. To find A B the Sun's Amplitude, The Analogy is. As the sine of B A C. 38. 47. co. are. 0. 2061365 To Radius. 90. 10. 0000000 So is the sine of B C. 23. 15. 9 5945468 To the sine A B 39 19 9 8006833 CHAP. 7. The Meridian Altitude and Declination of the Sun with the Poles Elevation given to find his true place in the Zodiac. IF the Meridian Altitude of the Sun be less than the compliment of the Poles elevation, subtract the meridian altitude from the height of the Aequator, and what remaineth is the Sun's Declination towards the South Pole; But if the Meridian altitude of the Sun be more than the height of the Aequator, subtract the height of the Aequator from the Meridian altitude and what remaineth is the Sun's Declination towards the South Pole. Then in the Diagram of the second Chapter, in the right angle Spherical Triangle A B C, we have known, the angle B A C the Sun's greatest Declination, and the perpendicular B C the present Declination to find the Hypothenuse A C, the Sun's distance from the next Equinoctial point, or true place in the Zodiac, for which the Analogy is. As the sine of B A C. 23. 5250 co. are. 0. 3988648 To the sine of B C. 23. 15 9 5945468 So is the Radius or whole sine. 90. 10. 0000000 To the sine of A C 80. 04 9 9934116 That is in 20 degrees of Gemini, and 4 Centesmes, if the Meridian altitude were taken in Summer: But in 20 degrees 04 Centesmes of Capricorn, if the Meridian altitude was taken in Winter. CHAP. 8. Having the Meridian Altitude of an unknown Star and the distance thereof from a known Star, to find the Right Ascension of the unknown Star. ABout the end of the year 1577 Tycho observed the distance of the little Star in the breast of Pegasus from the bright Star of the Vulture to be exactly 45 deg. 31 min. or in decimal numbers 45. 51667. And by the Meridian altitude thereof, he found the Declination to be 22 deg. 26 min. North that is 22. 43333. Which given the Right ascension of the said Star is to be enquired. For the finding whereof in the oblique angled Spherical Triangle (of the annexed Diagram) F O L, there is known First, F L the compliment of the Declinat. of the bright Star of the Vulture 82. 13333. Secondly F O the compliment of the Declination of the Star in the breast of Pegasus, 67. 56667. Thirdly O L the distance of them, 45. 51667, to find the angle at F or difference of their Right ascension. The side L O. 45. 51667. The side F L. 82. 13333. The side F O. 67. 56667. Sum of the sides. 195. 21667. The half Sum. 97. 60833. Sine of F L. 82. 13333. co. are. 0. 0041064 Sine of F O. 67. 56667. co. are. 0. 0341757 Dif. of F L ½ sum. 15. 47500. 9 4262148 Dif. of F O ½ sum. 30. 04167. 9 6995164 Quadrat of the sine of half the angle. 19 1640133 Half is the sine of 22. 45453. 9 5820066 Double is the angle L F O. 44. 90906. Equal to the arch D E the difference of their Right ascensions, which being added to the Right ascension of the bright Star of the Vulture. 292. 58333. The sum 337. 49239 is the Right ascension of the little Star in the breast of Pegasus. CHAP. 9 Having the Declination and Right ascension of a star given, to find the longitude and latitude thereof. IN the Diagram of the 3 Chapter, having the Right ascension of the little Star in the breast of Pegasus A C. 337. 49239. And the declination C M. 22. 43333. with the greatest obliquity of the Ecliptic B A C. 23. 5250. we are to inquire its Longitude A N. and Latitude M N. wherefore in the Triangle A B C. we have the angle B A C. 23. 5250. and the side A C 22. 50761 the compliment of the Right ascension: then I say. As Radius. To Tangent of B A C 23. 5250 9▪ 63●●198 So sine of A C. 22. 50761 9 ●8●●787 To Tangent of B C. 6. 46125 9 2217985 Add C M. 22. 43333 The Declination Sum is M B. 31. 89458 when the Declination is South the arch found must be subtracted from it, and their difference shall be M B. 2. To find the angle A B C. As the sine of B C 9 46125 co. are. 0. 7841497 To the sine B A C 23. 5250 9 6011352 So the sine of A C 22. 50761 9 5829787 To the sine of A B C 68 36843 9 9682836 3. To find the side A B. As the sine of B A C. 23. 52520. co. are. 0. 3988648 To the sine of B C. 9 46125. 9 2158503 So is Radius. 10. 0000000 To the sine of A B. 24. 31967 9 6147151 4. The angle A B C is equal to the angle M B N, therefore to find the latitude M N. As the sine M N B 90. To the sine of M B 31. 89458. 9 722928● So the sine of M B N. 68 36843. 9 9682836 To the sine of M N. 29. 41602. 9 6912118 Lastly, to find the arch B N. As Radins. To Cotangent of. M B N. 68 36843. 9 5983151 So Tangent of M N. 29. 41602. 9 7511554 To the sine of B N. 12. 92052. 9 3494705 Which is to be added to A B if the Right ascension be less than a semicircle, but if the Right ascension exceed 180, as in our example, the Compliment of B N. 357▪ 07948, is the longitude desired. CHAP. 10. How to find the ascensional Difference. Then in the Right angled spherical Triangle B M C we have limited. 1. The angle C M B the compliment of the Pole 38. 46667. Secondly, the side B C 19 deg. the Sun's Declination, hence to find, the ascensional difference M C the Analogy is. As the Cotangent of the poles Elevation, is to Radius. So is the tangent of the planets Declination, to the sine of the ascensional difference. As the tangent of C M B 38. 46667. co. are. 0. 09991●6 Is to Radius 10. 000000 So is tangent of B C 22. 0291 9 6070441 To the sine of M C 30. 61613 9 7069577 which is the ascensional Difference sought. CHAP. 11. How to find the Oblique Ascension or Descension of any point in the Ecliptic. OBlique ascension is when a less arch or portion of the Aequator●iseth ●iseth, then doth of the Zodiac, or else of that Star may be said to rise obliquely with whom a less portion of the Aequator ascendeth above the Horizon, & so the oblike Descension or setting of a Star, is when a less proportion of the Aequator descendeth with it, then doth in a right Sphere. In the former Diagram, D C represents the right Ascension, M C the Ascensional Difference, D M the oblique Ascension, D B an arch of the Ecliptic above the Horizon, which being greater than D M, a Star in this position of the Sphere, is said to rise obliquely. The quantity whereof is found, by deducting the Ascensional difference C M from the right ascension D C, according to the direction following. If the Declination be North Subt. The Ascensional Difference from the right Ascension, and it giveth the oblique Ascension. Add The Ascensional Difference to the Right Ascension, and it giveth the oblique Descension. South Add The Ascensional Difference to the Right Ascension, and it giveth the oblique Ascension. Subt. The Ascensional Difference from the Right Ascension, it giveth the oblique Descension. Right Ascension of ten degrees of Gemini, 68 348●● Ascensional Difference 30. 61613 Oblique Ascension of ten degrees of Gemini, 37. 73261 Oblique Descension of ten degrees of Gemini, 99 08137 CHAP. 12. The Poles Elevation and the Sun's Declination being given, to find his Altitude at any time assigned. IN this proposition there are three varieties, first, when the Sun is in the Aequator, that is the beginning of Aries and Libra, in which case supposing in this Diagram the Sun to be at H two hours or 30 degrees distant from the Meridian A, and the poles Elevation R F equal to A C 51. 53333, the angle at A being right, I say. As the Radius. To the Cousin of A H 30 9 9375●06 So the Cousin of A C 51. 53333 9 793831● To the Cousin of C H 57 40351 9 7313624 whose compliment 32. 59649 is the side L H or altitude sought. The second variety is when the Sun is in the Northern signs Aries, Taurus, Gemini, Cancer, Leo, Virgo. For the solving of the Problem in this variety, let A E C represent the Equinoctial. F the pole thereof, L E R the Horizon, G the pole thereof. B D a parallel of the Sun's declination. F O the Meridian of the Sun. B H the distance of the Sun from the Meridian. H O the Sun's declination North, R F the poles elevation, F G the compliment. First, the side F G 38. 46667. Secondly, the side F H. 67. 97090. and the included angle F G H. 45 degrees to find G H. As the Radius To the Tangent of F G 38. 46667 9 9000864 So the Cousin of F G H 45. 9 8494850 To the Tangent of F K 29. 32669 9 7495714 Then from F H 67. 97090 Deduct F K 29. 32669 There rests H K 38. 64421 2. As the Cousin of F K 29. 32669. co. are. 0. 0595626 To the Cousin of F G 38. 46667 9 8937451 So Cousin of K H 38. 64421 9 8926710 To the Cousin of G H 44. 54111 9 8459787 The compliment whereof N H 45. 45889. is the altitude of the Sun above the Horizon. The third variety is when the Sun is in the southern signs Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces. And in this case supposing the Sun to be in 10 deg. of Sagittarius, and having South declination 22. 02910, and also 45 deg. distant from the Meridian as before in the oblique angled triangle F G H of the annexed Diagram we have given 1. The side F G. 38. 46667. 2. The side F H 112. 02910 and the angle G F H 45 deg. Then as before, I say As Radius To the tangent of G F 38. 46667 9, 9000864 So Cousin of G F H 45. 9, 8494850 To the tangent of F K 29. 32669 9, 7495714 From F H 112. 02910 Deduct F K 29. 32669 Rest K H 82. 70241 As the Cousin of F K 29. 32669 co. are. 0, 05956●6 To the Cousin of F G 38. 46667 9, 8937451 So the Cousin of K H 82. 70341 9, 1038818 To the Cousin of G H 83. 43974 9, 0571895 whose compl. H N. 6. 56026 is the Sun's altitude required. The like is to be observed of the Moon with the other planets and fixed Stars. CHAP. 13. Having the Sun's greatest Declination, with his distance from the next Equinoctial point, to find the Meridian angle or intersection of the Meridian with the Ecliptic. IN the Diagram of the 10 chapter, we have in the triangle D C B. 1. The angle B D C 23. 5250 the Sun's greatest Declination. 2 The Hypothenusal D B 70 the distance of the Sun from Aries. 3 The angle B C D 90, to find the angle D B C. The Analogy is, As the Radius To the tangent of B D C. 23. 525 9 6388198 So the cousin of D B 70 9 5340516 To the Cotang. of D B C 81. 53133 9 1728714 or the angle of the Ecliptic with the Meridian. CHAP. 14. To find the angle of the Meridian with the Horizon. IN the Diagram of the 5 chapter, we have in the triangle B C M, first, the angle B M C 38. 46667 the elevation of the Equator. 2 B C 22. 02910 the Declination of the point given, to find M B C. As the Cousin of B C 22. 02910 co are. 0. 0329234 Is to Radius 10. 000000 So is Cousin of B M C 38. 46667 9 8937451 To the Sine of M B C 57 63275 9 9266685 CHAP. 15. The Poles elevation, with the Sun's Altitude and Declination given, to find his Azimnth. IN the oblique angled spherical triangle G H F, in the second Diagram of the 12 Chapter, we have known H F the compliment of the Sun's Declination. 2 The side G F the compliment of the poles elevation. 3 The side H G the compliment of the Sun's altitude, to find H G F. ●. The side F H 67. 97090 2. The side G F 38. 46667 3. The side H G 44. 54111 Sum 150. 97868 Half sum 75. 48934 Sine of G F 38. 46667 co. are. 0. 2061682 Sine of H G 44. 54111 co. are. 0. 1540214 Diff. G F ½ sum 37. 02267 9 7796909 Diff. H G ½ sum 30. 94823 9 7111855 Quadrat of the Sine of ½ the angle 19 8510560 Half is the Sine of 57 39644 9 9255280 whose double 104. 79288 is the Sun's Azimuth from the North, and the compliment thereof 75. 20712 is the Sun's Azimuth from the South. CHAP. 16. How to erect a Figure of Heaven. AMong the several ways for the erecting of a figure, used by the ancient Astronomers, that is held most rational which divideth the Equinoctial into twelve parts by circles meeting at the intersections of the Meridian and Horizon, which is according to the following Scheame, in which the line W Z E represents the East and West Azimuth W ♈ E is that half of the Equinoctial above the eareh, and W ♎ E is that half of the Equator under the earth. The arch 7 ♈ 1, doth represent that half of the ecliptic above the earth. And 7 ♎ 1 that part under the earth. The utmost circle N E S W represents the Horizon, N Z S the meridian, N the north, and S the South end thereof. The Eqninoctiall circle W ♈ E ♎ is divided in to 12 equal parts, by which divisions pass arches, from the North and South intersections of the meridian with the Horizon, which cut the Ecliptic at the cusp of the houses, N 1 S is the cusp of the Ascendant, N 7 S of the 7 house N 2. 12 S of the second and twelfth, N 3. 11 S of the third and eleventh, and so of the rest as you see in the Figure. To find the Mid-heaven or Tenth House. When you would erect a figure you must have the true place and Right Ascension of the Sun for the time proposed, let the given time in the meridian of London where the North pole is elevated above the Horizon 51. 53333 be July the 16. After noon 18 hours, 4564 in the year 1587. For which time according to our Tables the Sun's place is in Virgo 4. 07368 which known the Midheaven or 10 house may thus be found. First, inquire the Right Ascension of the Sun at the time proposed by the 4 Chapter thus As the Radius To the tangent of A C 25. 92632 9 6867627 So confine of B A C 23. 52500 9 9623154 To the tangent of B C 24. 02427 9 6490781 whose compliment 155. 97573 is the Right Ascension sought. To the Right Ascension of the Sun 155. 97573 Add the Right Ascension of time 276. 84600 Right Ascension of the Mid-heaven 432. 82173 Deduct a whole circle 360. Then rests for the Right Ascension 072. 82173 Then in the Rectangle Spherical Triangle ♈ 10 F we have given. 1 ♈ F the Right Ascension of the mid-heaven. 72. 82173 2 The Sun's greatest Declination F ♈ 10. 23. 5250 to find ♈ 10 the point culminating. As the Radius. To the Cotangent of F ♈ 72. 82173 9 4901498 So cousin of 10 ♈ F 23. 5250 9 9623154 To the cotangent of ♈ F O 74. 17501 9 4524652 To find the Cusp of the 11 house. Unto the Right Ascension of the 10 house 72. 82173 Add 30 degrees 30. 00000 And then the oblique Ascension of the 11 house 102. 82173 To this add 30. Oblique Ascension of the 12 house 132. 82173 30. Oblique Ascension of the Ascendant 162. 82173 30. Oblique Ascension of the 2 house 192. 82173 30. Oblique Ascension of the 3 house 222. 82173 The Oblique Ascension of the houses thus found by a continual addition of 30 degrees, we must next find the poles elevation upon their several circles of position thus, In the rectangle spherical Triangles E A B and E C D we have limited. 1. Their common angle at E the latitude of the place. 2. E B and E D 38 and 60 with the right angles A and C to find the angles B and D, being the angles that the circles of position make with the Equator. First, then for the 11 and 3 houses. As the Radius To the Cousin of E D 60. 9 69470●0 So tangent of C E D 51. 53333 10. 0999136 To cotangent of C D E 57 81626 9 7988836 whose compliment 32. 18374 is the height of the pole above those circles of position. For the 12 and 2 houses. As the Radius To the Cousin of E B 30 9 375306 So tangent of A E B 51. 53333 10. 0999236 To cotangent of A B E 42. 53308 10. 0374442 whose compliment 47. 46692 is the height of the pole required. Having thus found the several oblique Ascensions of the several houses together with the elevation of the pole, above their several circles of position, in the oblique angled spherical Triangle ♈ C D we have limited 1. The angle ♈ D C compliment to C D E. 2. The angle C ♈ D the Sun's greatest Declination. 3. Their included side ♈ D the oblique Ascension of each house to find ♈ C the point of the Ecliptic. The Analogies are. For the 1 Operation. As the Sine of the half sum of the angles. To the Sine of half their difference. So the tangent of half the side comprehended. To the tangent of half the difference of the sides For the 2 Operation. As the Cousin of the half sum of the angles To the Cousin of their half difference. So the Tangent of half the side comprehended. To the Tangent of half the Sum of the sides. The Sum of these two arches, shall give you the point of the Ecliptic desired. For the Cusp of the 11 house. The oblique Ascension or arch ♈ D is 102. 82173 The half thereof is 51. 41086 The compliment of C D E 57 81626 is the angle ♈ D C. 122. 18374. C ♈ D. 23. 52500. Or the Sun's greatest Declination Sum 145. 70874 Half Sum 72. 85437 Differ. 98. 65874 ½ Differ. 49. 32937 Sine ½ Sum 72. 85437 co. are. 0. 0197429 Sine ½ Differ. 49. 32937 9 8799374 Tang. ½ ♈ D 51. 41086 10. 0980083 Tangle ½ Differ. 44. 84740 9 9976886 For the 2 Operation. Cousin ½ Sum 72. 85437 co. are. 0, 5304705 Cousin ½ Differ. 49. ●2937 9 8140541 Tangent ½ ♈ D 51. 41086 10. 0980083 Tangent ½ Sum 70. 15211 10. 44●5329 1 Arch add 44. 84740 Sum 114. 99951 or ♋ 24. 99951 is the point of the Ecliptic for the 11 house. For the 12 house. The Oblique Ascension or arch ♈ D is 132. 82173 The half thereof is 66. 41086 The compliment of C D E 42. 53308 is the angle ♈ D C 137. 46692 C ♈ D 23. 52500 Sum 160. 99192 ½ Sum 80. 49596 Differ. 113. 94192 ½ Differ. 56. 97096 Sine ½ Sum 80. 49596 co. are. 0. 0060025 Sine ½ Differ. 56. 97096 9 9234483 Tang. ½ ♈ D 66. 41086 10. 3598529 Tang. ½ Differ. 62. 81111 10. 2893037 For the 2 Operation. Cousin ½ Sum 80. 49596 co. are. 0. 7822080 Cousin ½ Differ. 56. 97096 9 7364475 Tangent ½ ♈ D 66. 41086 10. 3598529 Tangent ½ Sum 82. 46470 10. 8785084 1 arch add 62. 81111 Sum 145. 27581 or ♌ 25. 27581 is the point of the Ecliptic for the 12 house. For the Cusp of the Ascendant. The Oblique Ascension or ♈ D is 162. 82173 The half thereof is 81. 41086 The angle C D E is the same with the height of the Equator 38. 46667 whose compliment to a semicircle is the angle. ♈ D C 141. 53333 C ♈ D 23. 52500 Sum 165. 05833 ½ Sum 82. 51916 Differ. 118. 00833 ½ Differ. 59 00416 Sine ½ Sum 82. 52916 co. are. 0. 0037026 Sine ½ Differ. 59 00416 9 9330844 Tangent ½ ♈ D 81. 41086 10. 8209024 Tangent ½ Dif. 80. 09004 10. 7576894 For the 2 Operation. Cousin ½ Sum 82. 52916 co. are. 0. 8859846 Cousin ½ Differ. 59 00416 9 7117867 Tang. ½ ♈ D 81. 41086 10. 8209024 Tang. ½ Sum 87. 81606 11. 4186737 1 Arch add 80. 09004 11. 4186737 Sum 167. 90610. Or ♍ 17. 90610 is the point of the Ecliptic for the Ascendant For the Cusp of the 2 house. The Oblique Ascension is 192. 82173 whose compliment is the Arch ♈ D 167. 17827. The half whereof is 83. 58913. The sum and Difference of the angles are the same with those for the 12 house. Therefore I say first, Sine ½ Sum 80. 49596 co. are. 0. 0060025 Sine ½ Differ. 56. 97096 9 9234483 Tangent ½ ♈ D 83. 58913 10. 9493879 Tangent ½ Diff. 82. 47036 10. 8788387 For the 2 Operation. Cousin ½ Sum 80. 49596 co. are. 0. 7822080 Cousin ½ Differ. 56. 97096 0. 7364475 Tangent ½ ♈ D 83. 58913 10. 9493879 Tangent ½ Sum 88 05055 11. 4680434 1 Arch add 82. 47036 Sum 170. 52091 whose compliment 189. 47909 or ♎ 9 47909, is the Cusp of the 2 house. For the Cusp of the 3 house. The Oblique Ascension is 222. 82173, whose compliment is the arch ♈ D 137. 17827. The half whereof is 68 58913. The sum and difference of the angles are the same with these for the 11 house. Therefore I say first, Sine ½ Sum 72. 85437 co. are. 0. 0297429 Sine ½ Differ. 49. 32937 9 8799374 Tangent ½ ♈ D 68 58913 10. 4065869 Tangent ½ Diff. 63. 71032 10. 3062672 For the 2 Operation. Cousin ½ Sum 72. 85437 co. are. 0. 5304705 Cousin ½ Differ. 49. 32937 9 8140541 Tangent ½ ♈ D 68 58913 10. 4065869 Tangent ½ Sum 79. 94186 10. 7511115 1 Arch add 63. 71032 Sum 143. 65218 whose complem. 216. 34782 or ♏ 6. 34782 is the point of the Ecliptic for the Cusp of the third house. The six Oriental houses being thus found, the other 6 are also found, by consequence, being the same degrees and parts of the opposite signs. And thus we have not only erected a figure for the time given, but composed a Table, for the general erecting a figure in this latitude, for by adding together the first and second numbers, in every of these proportions, there is composed 2 numbers for every house, to each of which the Artificial tangent of half the oblique Ascension being added, their aggregates are the tangents of two arches, which added together is the distance of the Cusp of the house from the first point of Aries. Only note that if the oblique Ascension be more than 180 deg. you must take the tangent of half the compliment to a whole circle; And to find the Cusp of the house, you must also take the compliment of the added arches, as shall be cleared by example. A New Table of Houses for the Latitude of London. 11 & 3 house. Ascendent 12 & 2 house. 1 Oper. 9 8996803 9 9367870 9 9294508 2 Oper. 10. 3445246 10. 5977713 10. 5186555 Having found the oblique Ascensions of the houses as before was showed, take out the tangent of half thereof from a Table of Tangents, whose Radius is 10. 0000000, and set them down twice on your paper as you see in the following example, then seek in the top of the Table, the house whose cusp you would find; and under the same you have two numbers, the first of which being added to one of the tangents in the paper, and the second to the other, will give you the tangents of two arches, whose aggregate is the Cusp desired. Example. The Oblique Ascension of the 11 house was before found to be 102. 82173. And the tangent of the half thereof 51. 41086 is 10. 0980083 the first number in the Table under the 11 house is 9 8996803 their same rejecting Radius 9 9976886, is the tangent of 44. 84740. The second number in the Table. Tangent 51. 41086 10. 0980083 1 Number 9 8996803 Tangent 44. 84740 9 9976886 is ●0. 3445246, which being added to the same tangent, there sum 10. 4425329 is the tangent of 70. 25211 and the aggregate of these two arches. Tangent 51. 41086 10. 0980083 2 Number 10. 3445246 Tangent 70. 15211 10. 4425329 1 Arch 44. 84740 Sum 114. 99951 gives the point of the Ecliptic in Cancer 24. 999 2 Example. The Oblique Ascension of the 2 house was before found to be 192. 82173 The tangent of half the compliment 83. 58913 is 10. 9493879 Tangent 83. 58913 10. 9493879 1 Number 9 9294508 Tangent 82. 47036 10. 8788387 Tangent 83. 58913 10. 9493879 2 Number 10. 5186555 Tangent 88 05055 11. 4680434 1 Arch. 82. 47036 Sum 170. 52091 whose compliment ●●●●47909▪ is the Cusp desired. The Cusp of your houses being thus found, draw your figure after this manner, and then place the Signs and Degrees on the Cusps of their proper houses, beginning with the 10 house. A Figure of the 12 Houses of Heaven. 10 house ♊ 14. 17. The opposite houses are in the opposite Signs. 4 house ♐ 14. 17. 11 house ♋ 24. 99 The opposite houses are in the opposite Signs. 5 house ♑ 24. 99 12 house ♌ 25. 27. The opposite houses are in the opposite Signs. 6 house ♒ 25. 27. Ascendent ♍ 17. 90. The opposite houses are in the opposite Signs. 7 house ♓ 17 90. 2 house ♎ 09. 47. The opposite houses are in the opposite Signs. 8 house ♈ 9 47. 3 house ♏ 06. 34. The opposite houses are in the opposite Signs. 9 house ♉ 6. 34. The 12 signs being placed in the figure we must next inquire for the true places of the Planets, with the Dragon's head, the which according to the doctrine of the second Book at the time proposed are as followeth. Sun's place ♍ 4. 07. ☊ ♏ 1. 40. ♃ ♌ 5. 19 ♀ ♏ 16. 58. Moon's place ♊ 26. 24. ♄ ♌ ● 5. 19 ♂ ♑ 8. 87. ☿ ♎ 19 81. The places of the Planets being thus found, consider under what sign any of them falleth, which being observed, note which of the houses contain the sign in which the planet is, observing the number of Degrees, and in due order place the planet in that house. Right Ascension of the Mid-heaven, 72. 82. A Scheme of Heaven for July 16, Hour 18, parts 4564, AD. 1587. In the Meridian of London, whose Latitude is 51. 53. And when a Planet contains a lesser number of Degrees than the Cusp of the house, he is to be placed before the house, in the house preceding, but if greater, he is be placed beyond the Cusp, according to the sequel, and consequence of the signs. As in the figure, Sol is in 9 degrees and 7 parts of Virgo, and the sign is placed upon the Cusp of the Ascendent, but because the Culpe thereof containeth more degrees of that sign than the Sun, I place the Sun in the preceding house, that is in the twelfth. CHAP. 17. To find the Angle of the Ecliptic with the Horizon, or the Altitude of the Nonagesime deg. together with its distance from the Mid-heaven. BY the rules delivered in the last Chapter, find the point culminating, whose declination being ended to the altitude of the Equator ●n the Northern signs, or subtracted in the Southern, gives you the altitude of the Mid-heaven, suppose 10 degrees of Gemini were in the Mid-heaven, the declination thereof by the 2 Chapter is 22. 02910. which being added to the altitude of the Equator 38. 46667, because the declination is North, their sum 60. 49577 is the Altitude of the Mid-heaven, and the meridian angle of the same point by the 13 Chapter is 81. 53133, hence in the triangle 7. 10. S of the Diagram in the last Chapter, we have given 10. S. 60. 49577 the altitude of Mid-heaven. The angle 7. 10. S 81. 53133. the Meridian angle to find the angle 10. 7. S. As the Radius To the sine of 7. 10. S. 81. 53133 9 9952385 So Cousin of 10. S 60. 49577 9, 6923956 To Cousin of 10. 7. S 60. 84861 9 6876341 And to find 7. 10 or the distance of Mid-heaven from the Nonagesime degree, the Analogy is As Radius To the Cousin of 7. 10. S 81. 53133 9 6677126 So is the cotangent of 10. S 60. 49577 9 7527167 To the tangent of 7. 10 14. 75047 9 4204293 Mid-heaven add 70. 00000 Sum 84. 75047 is the Nonagesime degree. And note that arch found is to be added to the Mid-heaven from Capricorn to Cancer, to be subtracted from Cancer to Capricorn. CHAP. 18. To find the Parallactical angle, or angle of the Ecliptic with the Vertical circle. THe angle of the Ecliptic with the vertical circle, is an angle made by the oblique cutting of the circle of altitude, with the Ecliptic, which is a right angle, when the said circle passeth through the 90 degree of the Ecliptic, but falling without the same it is oblique; as in the following figure, D denotes the Zenith, D C B the vertical circle, D E H V T the Meridian, T A B H the Horizon, V A E the Ecliptic, C the angle of the intersection of the Ecliptic with the Vertical. In the 16 Chapter is showed how to find the point of the Ecliptic Ascending, and the Sun's altitude at any time in the 12 Chapter, which being obtained we may speedily find the parallactical angle. As the tangent of A C 13, 9061 co. are. 0. 6062707 Is to Radius 10. 0000000 So tangent B C 12. 10189 9 3312569 To Cousin of A C B 30. 00067 9 9375276 CHAP. 19 The elevation of the Pole and Declination of the Sun given, to find the time when he will be due East and West. IN the second variety of the 12 Chapter, the compliment of the Sun's Declination F H i● 67. 97090 and the compliment, of the poles elevation F G 38. 46667, hence the angle G F H equal to the Arch of the Aequator A O is to be sought, therefore I say. As Radius To Cotangent F H 67. 97090 9 6070621 So tangent F G 38. 46667 9 9000864 To Cousin of G F H 71. 24779 9 5071485 whose comple. O F E 18. 75221 being converted into time giveth 1 hour 25147 parts of an hour, and so long it is after 6 in the morning when the Sun will be due East, and before 6 at night when he will be due West. CHAP. 20 The Elevation of the Pole, with the Sun's Declination and Altitude given, to find his distance from the Meridian. IN the Oblique angled Spherical triangle G H F in the 2 Diagram of the 12 Chapter, we have known H F the compliment of the Sun's Declination, G F the compliment of the poles elevation, H G the compliment of the Sun's altitude, to find G F H the angle of the Sun's distance from the Meridian. 1 The side H G 44. 54111 2 The side F H 67. 97090 3 The side G F 38. 46667 Sum 150. 97868 ●alf Sum 75. 48934 ●●ne of F H 67. 97090 co. are. 0. 0329234 ●●ne of G F 38. 46667 co. are. 0. 2061682 Differ. G F ½ Sum 37. 02267 9 7796909 Differ. F H ½ Sum 07. 51844 9 1167578 Quadrat of the sine of half the Angle 19 1355403 Which bisected, is sine of 21. 69295 9 5677701 And the double thereof is 43. 38590. The Sun's distance from the Meridian, And converted into time, gives two hours, 89259 parts. CHAP. 21. To find the time of the Suns rising and setting, with the length of the Day and Night. THe Ascensional difference of the Sun being added to the Semidiurnal arch in a Right Sphere, that is to 90 degrees in the Northern signs, or substracted from it in the Southern, there sum or difference will be the Semidiurnal arch, which doubled is the day Arch, and the Compliment to 360 is the night Arch, which bisected is the time of the Suns rising, and the day Arch bisected is the time of his setting. As when the Sun is in ten degrees of Gemini, his Ascensional difference is found to be 30. 61613 The Quadrant Add 90. The Semidiurnal Arch 120. 61613 The diurnal arch 241. 23226 Whose Compliment 118. 76774 Converted into time gives 7 hours 91078 parts, which bisected gives the time of the Suns rising. 3 hours 95539, parts; or a little before 4 of the clock. CHAP. 22. To find the distance of a star from the Meridian. IF a Star be between the Mid-heaven and the Horoscope deduct the Right Ascension of the Mid-heaven from the Right Ascension of the Star, what remaineth is the distance from the Meridian. If a star be between the Mid-heaven and the 7 house, deduct the Right Ascension of the star from the Right Ascension of the Mid-heaven, and what remaineth is the distance as before. IF a star be between the 7 house and the Imum Coeli or fourth house, deduct the Right Ascension of the Imum Coeli from the Right Ascension of the star, and what remaineth is the distance from the Meridan. If a star be between the Ascendant and the Imum Coeli deduct the Right Ascension of the star from the Right Ascension of the Imum Coeli, and what remaineth is the distance from the Meridian as before. For Example. In the preceding figure, the Right Ascension of the Mid-heaven is 072 deg. 82 parts. The Sun is in the 12 house and his Right Ascension 155. 97 From which deduct the Right Ascension of the M. C. 72. 82 The distance of the Sun from the Meridian is 83. 15 CHAP. 23. To find the Elevation of the Pole above any circle of position. A Circle of position, is as it were a certain Horizon (upon which the point or star proposed doth arise) passing by the two intersections of the Horizon with the Meridian, and may be either above or under the Earth, in respect of the place for which the figure is erected. A star posited in the 1, 2, 3, 4, 5, 6, house is Under the earth 7, 8, 9, 10, 11, 12, house is Above the earth Thus in the annexed Diagram A H C is a circle of position passing by the Horizontal point of the Significator at H, and the two intersections of the Horizon of the place at A and C, and L M is the elevation of the pole above this Horizon of the star or circle of position. To find which there must be known. 1. The latitude of the place. 2. The Declination of the star or point proposed. 3. The distance thereof from the Meridian. Hence to find the angle of Inclination of the circle of position with the meridian, the proportions are as followeth. 1. As the Radius, To the tangent of the compliment of the stars declination: so is the Cousin of the stars distance from the meridian, To the tangent of the first-arch. To which the pole of the place being added, or subtractod from it according to the following direction, their sum or difference is the second arch. If the distance of the star from the meridian, be more than 90 and the declination South under the earth or north above it, subtract the first arch from the poles elevation, and what remaineth is the second arch. If the distance of a star from the meridian be less than 90, and the declination south under the earth, or north above it, add the poles elevation, to the first arch, and their agg●gate if less than 90 is the second arch, if more than ●0 the compliment thereof. If the distance of a star from the meridian, be either more or less than 90, and the Declination North under the earth, or South above it. Subtract the elevation of the Pole from the first arch, and what remaine●●●s the second arch. If the distance of a star from the Meridian be a just quadrant, the angle of inclination may be found at one operation, as in the fourth example. 2 As the sine of the first arch found: Is to the cotongent of the Stars distance from the Meridian: So is the sine of the second arch found; To the cotangent of the angle of inclination. Then to find the elevation of the Pole above the circle of position, the analogy is. 3 As the Radius, To the sine of the Pole of the place: So is the sine of the angle of inclination; to the sine of the Pole of the Circle. 1 Example. Let the distance of a Star from the Meridian, be more than 90, viz. 97 deg. And the Declination of the Star 31 deg. North above the earth: the Pole of the place 45. Then in the oblique Spherical Triangle H M C we have limited. 1 The side M C the Poles elevation 45 degrees. 2 The side H M the compliment of the Stars declination 59 degrees. 3 The angle H M C, the Stars distance from the Meridian 97, or instead thereof the acue angle I M H 83, the compliment of the other to a Semicircle. Hence to find I M the proportion is. As the Radius 90 10. 000000● To the tangent of H M 59 10. 2212262 So is the Cousin of I M H 83 9 085894● To the tangent of I M 11. 47 9 3071206 which being substracted from 45 the Poles elevation, there resteth 33. 53 the second arch. 2 As the sine of I M 11. 47 9 2985361 To the Cotangent of I M H 83 9 089143● So is the sine of I C 33. 53 9 742232● To the Cotangent of H C M 71. 17 9 5328404 The angle of inclination. 3 As the Radius 90 10. 0000000 To the sine of C M 45 9 8494850 So is the sine of H C M. 71. 17 9 9761116 To the sine of L M. 42. 01 9 8255966 The height of the Pole above that Circle of position. 2 Example. Let the distance of a Star from the meridian be less than a quadrant, viz. 44. 7. The Declination of the Star, 14. 51. North above the Earth, the Pole of the place 45. then as before. 1 I say, As the Radius 90 10. 0000000 To the tangent of H M. 75. 15. 10. 5765162 So the Cousin of I M H 44. 7. 9 8574210 To the tangent of I M. 69. 74. 10. 4329372 To which add the Pole, 45. 00. There aggregate is 114. 74. whose Compliment 65▪ 26. is the second Arch. 2 As the sine of I M. 69. 74. 9 9722634 To the cotangent of I M H. 44. 7. 10. 0141010 So the sine of I C 65. 26. 9 9581892 To the Cotangent of H C M 45 10. 0000267 The angle of Inclination. 3 As the Radius 90 10. 0000000 To the sine of C M 45 9 8494850 So is the sine of H C M 45 19 8494850 To the sine of L M 30 9 6989700 The height of the Pole above that Circle of position. 3 Example. Let the distance of a Star from the Meridian be 22. 82. the declination 13. 53. South above the Earth: And the Pole 49. 1 Then as the Radius 90 10. 0000000 To the tangent of H M 76. 47 10. 6186455 So is the Cousin of I M H 22. 82 9 9646026 To the tangent of I M 75. 37 10. 5832481 Subtract the Pole 49. 0●. There rests 26. 37. for the 2d arch 2 As the sine of IN 75. 37 9 9856855 To the Cotangent of I M H 22. 82 10. 3759530 So is the sine of I C 26. 37 9 6475454 To the Cotangent of H C M 42. 51 10. 0378229 The angle of Inclination. 3 As the Radius 90. 10. 0000000 To the sine of C M 49. 9 8777798 So is the sine of H C M 42. 51 9 8297661 To the sine of L M 30. 66 9 7075459 The height of the Pole above that Circle of position. 4 Example. If the distance from the Meridian be a just Quadrant, or 90 degrees then omitting the two first proportions, the angle of Inclination may be found at one operation, by this analogy. As the tangent of the Compliment of declination, is to Radius. So is the sine of the Pole, to the cotangent of the angle of inclination. Let then the declination be 23, and the Pole 45. I say, As the tangent of H M 67 10. 372148● Is to Radius or the angle H M C 90 10. 0000000 So is the sine of M C 45. 9 8494850 To the Cotangent of H C M 73. 30 9 4773369 Then as Radius, to the sine of M C 45. 9 8494850 So is the sine of H C M 73. 30 9 9812850 To the sine of L M 42. 63 9 8307700 The height of the Pole above that Circle of position. CHAP. 24. Of the Ark of Direction, what it is, and how to find it. AStrologers use to foretell the general Fortune of any Native by the consideration of the 12 Houses, but the particular time, in which we may expect, what is promised by the position of the Heavens at the time of the Birth, they measure out by the ark of Direction. That is, by the distance of the Significators from there Promittors reckoned in the Aequator, by Significators usually meaning, the Ascendent, Mid-heaven, Sun, Moon, and part of Fortune: And by Promittors, the several Aspects of these Significators to the Planets, or the twelve Houses. For the clearer understanding of what the ark of Direction is, in the Diagram of the last Chapter, Let A D C represent the Meridian D V S E the Aequator, A C the Horizon, M the North-pole, A H C a Circle of position above the Earth, H B and N R two parallels of Declination. H the Significator, D O his right Ascension. H O his Declination. R the Promittor D S his right Ascension, R S his declination. Now when the Promittor at R comes to N, it is in the same Circle of position with the Significator at H, and the Circle of Declination M R S will be changed into the Circle of Declination M N V, and then the arch of the Aequator, D V is the Right Ascension of the Promittor at N, and therefore the arch of the Aequator V S is the ark of Direction sought. And the manner of finding thereof is as various, as the position of the Significator may be in the figure, which is threefold, viz. Either in the Meridian, in the Signs Ascending, or in the Signs Descending. CHAP. 25. How to direct the Mid-heaven, and the Imum Coeli. A Star posited in the meridian, that is, either in the mid-heaven or Imum Coeli, must be directed to his Promittors, by the right Ascensions of the Significator and Promittor. If a Significator posited in the mid-heaven be to be directed. Substact the Right Ascension of the mid-heaven, from the Right Ascension of the Star or Promittor, taken with its latitude if it have any, and what remaineth is the ark of Direction. For Example. Let the mid-heaven of the preceding figure in the 16 Chapter, be directed to the 12 degree of Capricorn. The Right Ascension of the 12 degree of Capricorn is 283. 03 From which subtract the Right Ascension of the mid-heaven 072. 02 There rests for the Ark of Direction 211. 23 In like manner: If the Imum Coeli or fourth House, or a Star posited upon the Cusp thereof be to be directed, you must subtract the Right Ascension of the Imum Coeli, or fourth House, from the Right Ascension of the Promittor, and what remaineth is the ark of Direction. CHAP. 26. How to direct the Ascendent, or Significator posited in the Signs Ascending. THe Horoscope or Ascendent, or a Significator posited in the signs ascending, that is, in the 12, 11, 10, 1, 2, or 3 houses, must be directed to Promittors, by the oblique Ascensions answering to the elevation of the Pole above the Circle of position of the Significator. The elevation of the Pole above the ascendent is the same with that of the place for which the figure is erected. The Poles elevation above the Circle of position of any other Significator must be found as hath been showed in 22 Chapter. Then if you deduct the oblique Ascension of your Significator, from the oblique Ascension of your Promittor, what remaineth is the ark of direction. For example. Let the Ascendent of the preceding figure in the 16 Chapter be to be directed to the 26 deg of Taurus. The elevation of the Pole of the Circle is the same with that of the place. viz. 51. 5●. And therefore the oblique Ascension of 26 deg. of Taurus, 27. 50 To which add a Circle that substraction may be made 360 And then the Oblique Ascension is 387. 50 The Oblique Ascension of the Ascendent subtract 162. 82 There rests for the ark of Direction 224. 68 Another Example. Let us suppose a Significator to be posited in the signs Ascending but not upon the Cusp of the Ascendent, in this case though the Ark of Direction must be found out by the Oblique Ascensions as before; yet the elevation of the Pole above the Circle of position must be first found, because it is not given, as in the last Example. In the Diagram of the 23 Chapter, let the distance of the Significator from the meridian be 44. 07. The declination thereof North above the Earth H O 14. 85. Hence the Pole L M is 30 degrees. Let this Significator be posited in 10 degrees of Taurus, the Right Ascension thereof D O 37. 58. His Ascensional difference under the elevation of 30 degrees F O 8. 80. Let the Promittor be in 25 of Gemini, the Right Ascension thereof D S. 84. 55. And the Ascensional difference when this Promittor comes to N. is represented by the letters F V. 14. 47. Now than if you subtract the Ascensional Difference of the Significator F O, 8. 80. from the Ascensional Difference of the Promittor F V. 14. 47. There will remain O V 5. 67. we call it the Aequation of the Ark of Direction, which being added to the Right Ascension of the Significator D O. 37. 58. There aggregate is the arch D V 43. 25. Then if you deduct the arch D V 43. 25 from the Right Ascension of the Promittor, D S. 84. 55. There difference is V S 41. 30. The Ark of Direction sought. Or thus, the Oblique Ascension of the Promittor is 70. 08. The Oblique Ascension of the Significator is 28. 78. There difference 41. 30, is the Ark● of direction sought, as before. CHAP. 27. How to direct a Significator posited in the Signs Descending. THe Descendent or seventh House or Significator there posited, or in any sign descending, that is, in the 4, 5, 6, 7, 8, or 9 Houses, must be directed to his Promittors, by the oblique Descensions answering to the Elevation of the Pole of the Circle of position of the Significator. As suppose the mid-heaven be in 22. 33 of Gemini. And the Right Ascension thereof, 81. 65. Let the Significator be in 10 degrees of Taur●s. The declination thereof 14. 85. North. His distance from the meridian 44. 07. Hence the Elevation of the Pole above that Circle of position is 30, as before. Let the Promittor be in 25 degrees of Gemini, the declination 23. 40 North: Now the declination of the Significator and Prommittor being the same with the former, and the Pole of the Circle the same, the Ascensional Differences as well of the Significator as of the Promittor, must needs be the same with the former Example, and consequently the same Aequation of the ark of Direction: if then you would find this ark of Direction, by the Right Ascensions, Add this Aequation of the ark of Direction, to the Right Ascension of the opposite point of the Promittor: and from their aggregate, subtract the Right Ascension of the opposite point of the Significator, and what remaineth is the ark of Direction. As the opposite point to this Promittor in the 25 of Gemini, is the 25 of Sagittarius, the Right Ascension whereof is 264. 55 The former Aequation of the ark of Direction 5. 67 Their Aggregate 270. 22 The opposite point to the Significator in the 10 of Taurus is the 10 of Scorpio, whose Right Ascension is 217. 56 Which subtracted from the former aggregate leaveth 52. 64 For the ark of Direction sought. Or if you will by the oblique Ascensions of these opposite points thus: The oblique Ascension of the 25 of Sagittarius is 279. 01 The oblique Ascension of the 10 of Scorpio, is 226. 38 There Difference is 52. 63 The ark of Direction as before. Or lastly, by the oblique Descensions, according to the intention of this Chapter, if you subtract the oblique Descension of the Significator, from the oblique Descension of the Promittor, what remaineth will be the ark of Direction. As in this Example the oblique Descension of the Promittor, under the elevation of 30 degrees is 99 01 The oblique Descension of the Significator, 46. 38 Which being subtracted from the oblique Descension of the Promittor, there resteth 52. 63 The ark of Direction sought as before. CHAP. 28. How to find the Arch of the Aequator, whereby is made the general Table of Positions. FOr finding this arch of the Aequator, there must be given the angle of Inclination of the Circle of position with the Meridian, & the height of the Pole above that Circle, both which may be found by the 9 Chapter: but ●● to our present purpose, we are not tied unto such a ●●dious calculation, because the Pole of the Circle may be supposed, and then the angle of Inclination may be found at one Operation, and this arch of the Aequator at another. And first, the Elevation of the Pole above any Circle of position being given together with the latitude of the place or Country, the angle of Inclination may be found, by this analogy. As the sine of the Pole of the place, is in proportion to Radius: So is the sine of the Pole of the Circle, to the sine of the angle of Inclination. For Example. In the Rectangle Spherical Triangle of the 9th Chapter L M C right angled at L. Let M C the Elevation of the Pole of the place be 45. And the Pole of the circle LM 42, hence to find the angle LCM. I say, As the sine of M C 45. 9 8494850 Is to the Radius 90. 10. 0000000 So is the sine of L M 42. 9 8255108 To the sine of L C M 71. 13 9 9760258 Then to find the arch of the Aequator, the proportion is: As the Radius to the sine of the Compliment of the Pole of the place: So is the tangent of the angle of Inclination, to the tangent of the arch of the Aequator. For Example, In the triangle A D F of the aforesaid Diagram, Let there be given the side A D the Comple. of the Pole of the place 45. The angle of Inclinat. DAF 71. 9 Hence to find the arch of the Aequator. DF, I say, As the Radius 90 10. 0000000 To the sine of AD 45 9 8494850 So is the tangent of D A F 71. 13 10. 4662●85 To the tangent of D F 64. 20 10. 3157275 Which is the arch of the Aequator sought. CHAP. 29. How by the general Table of Positions, to make a particular Table for any Latitude there expressed. IF thou wouldst make a particular table of positions, first, divide your paper or book into as many Columns as the largeness of the page will bear, then in the head of your table write the particular latitude, for which you would have the table, and under this title write in the third Column of your page. 1 In the fourth, 2, and so forward till you have filled the Columns of your first page, do so likewise in the 2d. page, and so forward till you have written twice over the several Elevations of the Pole above the circle of position from one unto that degree for which your table is intended; then in the first Column of your left hand page write, North Declination under the earth and South above it, in the second column thereof write orderly the several degrees of declination, beginning with a cipher or nought, and then 1, 2, 3, and so forwards till you have written 32, and in the two first columns of your right hand page write the contrary, that is, in the first thereof write South Declination under the earth and north above it; and in the second the several degrees of Declination beginning with 32, and so downward 31. 30. 29. until you come to nought: having thus prepared your book according to that Table in this book, enter your general table of positions with one degree of Elevation, and in a strait line directy under the latitude of your place, you shall find the arch of the Aequator answering thereunto, then look for the Ascensional differences answering to every degree of Declination, under one degree of the Poles Elevation, the which being substracted from the arch of the Aequator, write the remainder in a direct line under one degree of Elevation, in that page which must serve for North Declination under the Earth: but for the South Declination under the Earth add the Ascensional difference of every degree of Declination to the former arch of the Aequator, and write their aggregate under one degree of Elevation and right against that degree of Declination, whose Ascensional difference was added thereunto, and so shall you have one Column of your table finished, to make it plain we will add an Example. In the latitude of 51 degrees 33 hundred parts, the arch of the Aequator answering to one degree of the Circle is 0 deg. 79. and the Ascensional difference for one degree of Declination under one degree of Elevation is 0. 1. of which being subtracted from 79, there remaineth 78, which I write against one degree of Declination in that page of the Table serving for North Declination. Again, to the same arch of the Aequator, I add 0. 01. and their aggregate is 80, and this I write against one degree of Declination, and under one degree of Elevation in that page of the Table which serveth for South Declination under the Earth, and thus must you also add or subtract the Ascensional differences of all the other degrees of Declination, according to this Example. And so shall you have a particular Table of positions for your particular latitude. The use of this Table is to find the Elevation of the Pole above any Circle or position in that particular latitude, for which the Table is framed, as shall be showed in his proper place. CHAP. 30. Of the Doctrine of the Sphere in Tables. ALthough in the former book there is plainly showed you, how to find the Declination, Right Ascension, Ascensional Difference, Oblique Ascension, Cusps of the 12 Houses, and the height of Pole above any Circle of position, by Trigonometrical calculation: yet considering that, that way is not altogether so expedite and ready for practice, as some may desire, we will also show you how to find the same by those Tables, that are hereunto annexed. Precept 1. The Declination of the Sun or other Planet is found by the sign in the head or foot, and the degree on the right side, if the sign be in the foot, or on the left side if it be in the head: for the common angle gives the Declination sought, if you have respect, to your Planets proper latitude, and the proper part proportional. For Example: Suppose the Moon were in 19 degrees 56 parts of Leo, and her declination were required, having North latitude 3 degrees. Her Declination in that latitude, in 19 degrees of Leo will be found 18. 02 In 20 degrees it is 17. 70 There difference is 0. 32 Now then if one degree give 0. 32 1. 5051499▪ What shall 0. 56 1. 7481880 They give 18 ferè 1. 2533379 Which being subtracted from 18. 02 because the Declination doth decrease, the Moon's Declination will be found to be 17. 84 Precept 2. The Right Ascension by the Table following is had by the sign in the head and degree in the left side, and in the common angle is the Right Ascension. Example. The Right Ascension of a Planet in Aries 1● 251, and 2 degrees of South latitude be sought. The Right Ascension of 13 Degrees 12. 73 The Right Ascension of 12 Degrees 11. 82 Difference 91 If one Degree give 91 1. 9590413 What shall 25 1. 3979400 They give 22 1. 3569813 Which being added to 11. 82, the R. ascension of the point sought will be 12. 04. But if the R. ascen. of the point sought be in Southern signs, you must add 180 to the arch found in the table, and you have your desire, thus the R. ascens. of 12 deg. 25 parts of Libra, with two degrees of North Latitude by adding 180 to the former arch will be 192. 04. Precept 3. The ascensional difference of any part of the Zodiac is found by the degree of declination in the left side, and the degree of the Poles elevation in the head, the common angle gives the ascensional difference ●ought. Example. Let a planet's Declination be 4. 43. whose ascensional difference is sought under the elevation of 52 deg. The ascensional difference in that Elevation answering to 5 degrees of Declination is 6. 43. to 4 degrees is 5. 13. there difference is 1. 30. If one degree Give 1. 30 2. 1139433 What shall 4● 1. 6334684 They give 56 ferè 1. 7474117 Which being added to ●. 13, the ascensional difference of the point sought will be 5. 69. Precept 4. The oblique ascension of any part of the Zodiac is found by the sign and degree in the first Column in the left hand, and the Poles Elevation on the head of the Table, the common angle will give you the oblique Ascension sought. Example. Let the Oblique Ascension of Virgo 09. 23. in the elevation of 42 degrees be sought. In that elevation. The Oblique Ascension of Virgo 10 degrees is 15●. 87 Virgo 6 degree is 155. 80 Their Difference 4. 07 If 4 degrees 4. 00 9 3979400 Give 4. 07 0. 6095944 What shall 3. 23 0. 50920●5 They give 3. 28 0. 5167369 Which being added to 155. 80. the obli●● Ascension sought will be 159. 08 Precept 5. These things premised, the Right Ascension of M. C, and thereby the Mid-heaven itself will easily be found for the hours from Noon (converted into Aequinoctial degrees, by the table for that purpose) being added to the Sun's Right Ascension, do make the Right Ascension of the Mid heaven, which sought in the Area of the Table of Right Ascensions gives the mid-heaven itself. Example. Let the Sun be in 4 deg. 07 parts of Virgo, as in the 16 Chapter, the time from Noon, Hours 18. 4564 The Suns Right Ascension in 4 degrees of Virgo 1●5. 9● His Right Ascension in 5 deg. of Virgo, 156. 85 Difference ●0. 95 If one degree give 95 0. 9777236 What shall 07 1. 8450980 They give 06 1. 8228216 Which being added to 155. 90. The Sun's Right Ascension is 155. 96. The Aequinoctial degrees answering to 18 hours, viz. 270 degrees. And the degrees answering to 4564 parts of an hour are 06. 84, and therefore the Right Ascension of time is 276. 84, which being added to the Sun's Right Ascension, their aggregate 432. 80. or rejecting 360 degrees, the remainder 72. 80, is the Right Ascension of the Medium Coeli, whereto answers in the Table of R. Ascensions; 74. 75. ●●, the point of the Ecliptic for the Mid-heaven itself. Precept 6. The Oblique Ascensions of the other Houses are found by a continual addition of 30 degrees to the Right Ascension of the Mid-heaven, as hath been also showed in the 16 Chapter, and thus the Oblique Ascension of the 11 House is 102. 80. 12 House is 132. 80. Ascendent is 162. 80. 2 House is 192. 80. 3 House is 222. 80. The Poles of Elevation above the Circle of Position of the Ascendent is always the same with that of the place, for which the figure is erected, the Poles Elevation for the 11, 12, 2 and 3 Houses you may find in the Table for that purpose annexed to the Table of Oblique Ascensions. Example. By that Table under our Elevation of 51. 53. the Poles Elevation above the Circles of position of the 11 and 3 Houses, is 32. 18. And the Poles Elevation above the 12 and 2 Houses is 47. 46. Now then to find the Cusp of the 11 House, look the Oblique Ascension thereof, 102. 80. in the Table of Oblique Ascensions answering to 32. 18, of Elevation, and the point of the Ecliptic answering thereunto is Cancer 24. 98. In like manner, if you look the oblique Ascension of the 12 house, 132. 80 under the elevation of 47. 46. the Cusp thereof will be Leo, 25, 26. If you look the oblique Ascension of the Ascendent 162. 80. under the Elevation of 51. 43 the Cusp thereof will be Virgo 17. 94. If you look the Oblique Ascension of the second House 192. 80. under the Elevation of 47. 46. the Cusp will be Libra 9 44. Lastly, if you look the Oblique Ascension of the third House, 222. 80 under the Elevation of 32. 18. the Cusp thereof will be Scorpio, 6. 35. The other 6 Houses, are in the same Degrees and parts of the opposite signs. Precept 7. The Poles Elevation above the Horizon of a Star is found by the degree of his Declination, in the second Column of the right hand page of your Table, if the Declination thereof be North under the Earth, or South above it; And in the second Column of the left hand page, if the declination be South under the Earth, or North above it, and his distance from the Meridian in a strait line, for in the head of your Table in a direct line (using a double proportional part if need be) you shall have the degree of the Poles Elevation above the Circle of position. Example. In the preceding figure of the 16 Chapter, the Sun is in Virgo, 4. 07 and therefore his Declination is 10. 05. North above the Earth; his distance from the Meridian by the 22 Chapter, was found to be 83. 15. Now then to find the Poles Elevation, I look in that Table for the Sun's declination in the second Column of the left hand page, and his distance from the Meridian in a strait line, and in the last folio of that Table, I find against 10 degrees of Declination, the distance of a Star from the Meridian nearest to my number to be 83. 37. and over the head thereof 50, which is the degree of the Poles Elevation above that Circle of Position. Astronomia BRITANNICA The second Book. OR, The Theory of Planets, according to the Copernican Systeme and Demonstration of the Learned BULLIALDUS. Exhibiting their first Inequalities at one Operation Trigonometrical. Their other Inequalities, and Eclipses of the SUN and MOON with much Ease. bookseller's logo LONDON, Printed 1656. Astronomia BRITANNICA: The second Book. CHAP. 1. Of the year Civil and Astronomical. THe Altitudes of the Planets being given to find their places in the Zodiac, hath been already showed in the Doctrine of the Sphere, & thence their annual or periodical revolutions, together with their middle motions must be sought, but how to state them so exactly as that we may thereby find their true or apparent places for any time required, is that which many have endeavoured, but none have as yet found out, at least not so, as that their places computed by their rules, shall exactly agree with observation, nor was Astronomy brought to that perfection in which it now stands but by degrees, and although there hath been very much done of late towards the perfecting thereof, yet shall it not perhaps come to its full Acme in this our age. That which we intent, is not to show you from what small beginnings it hath been increased, or by whose labours, it hath from time to time been still corrected and amended, but to show you how to compute the places of heavenly Bodies, by the plainest, speediest, and exactest ways that are as yet made public. And in order hereunto we will show you first the usual way of finding out the time in which the Planets make their Annual or Periodical revolutions, and how from thence to compute their middle Motions, that their annual revolutions may be known, the time of their entrance into one and the same point of the Zodiac, taken in divers years by observation must be given, with a considerable interval of time between these Observations. And because the Observations taken in any one Meridian (that are as yet published) are not sufficient for our present purpose we must of necessity, use the observations made in divers places, but the interval of time between those observations cannot be had, unless we can reduce the time of an observation made in one account to the like time in another; Although the periodical revolutions therefore of the planets are the only proper years and first in nature; yet since the civil year in every nation is somewhat different from them, we will first show the quantity of that in most nations, and how to reduce the day of the month given in one account, to the correspondent time in another. The Civil year then, though it doth not exactly agree, yet hath it some proportion with the motions of the Sun or Moon in every nation; Twelve Moons or Months is the common measure of the year in Turkey, in every month they have 29 or 30 days, in the whole year 354, and in every third year 355 days. The Persians and Egyptians do also account 12 Months to their year, but their months are proportioned to the time of the Sun's continuance in every of the 12 signs; in their year therefore which is Solar, there are always 365 days. And the Julian year, which is the account of all Christendom doth differ from the other only in this, (that by reason of the Sun's excess in motion above 365 days, which is about 5 hours 49 minutes) it hath a day intercalated once in 4 years, and by reason of this intercalation it is more agreeable with the motion of the Sun than the former, and yet here is a considerable difference between them, which hath occasioned the Church of Rome to make some further amendment of the Solar year, but hath not brought it to that exactness which is desired, nor will (as is to be feared) be over-hastily brought to that exactness which it might; taking these accounts therefore as they now stand, if we will reconcile that discrepancy that is between them, there must be some beginning appointed to every of these accounts, and that beginning must be referred to some one, as to the common measure of the rest. The most natural beginning of all accounts, is the time of the World's Creation, but they who could not attain the World's beginning, have reckoned from their own, as the Romans, ab urbe condita, or from some great name or notable event; so the Greeks account from their Olympics, and the Assyrians from Nabonasser, and all Christians from the birth of Christ, the beginning of which and all other the most notable Epochaes, as others formerly, so we now have also ascertained to their correspondent times in the Julian Period, which Scaliger contrived by the continual multiplication of three circles all in former times of good use, & two of them do yet remain; the Circles yet in use are those of the Sun and Moon, the one to wit the Sun is a Circle of 28 years, in which time the Sunday Letter makes all the varieties that it can have by reason of the Bisextile or Leap-year, and the Circle of the Moon is the revolution of 19 years, in which time, though not precisely, the Lunations do recur; it is called the Golden Number, and was made Christian by the Fathers of the Nicene Council, as being altogether necessaay to the finding out of the Neomenia Paschalis, upon which the Feast of Easter, and the rest of the movable Feasts depend. The third Circle which now serves for no other use, than the constituting of the Julian Period, is the Roman Indiction, or a Circle of 15 years, for if you multiply 28 the Cycle of the Sun, by 19 the Cycle of the Moon, the product will be 532, & this by 15, the product will be 7980 the number of years in the Julian Period; whose admirable condition is to distinguish every year within the whole Circle, by a several certain character, the year of the Sun, Moon, and Indiction, being never the same again until the revolution of 7980 years be gone about: this Period, the Author fixed in the Tohu, or eternal Chaos of the World, 764 Julian years before the most reputed time of Creation; which being, premised, we will now by example show you how to reduce the years of Foreigners to our Julian years, and the contrary. 1 Example. I desire to know at what time in the Turkish account, the 5 of June 1649, falls. The work is this The years complete are 1648, and are thus turned into Days, by the table of Days, and Decimals of Days in Julian Years. 1000 Julian years give days 365250 600 years give 219150 40 years give 14610 8 years give 292● May Complete 151 Days 5 The Sum 602088 Now because the Turkish account began July the 16. Anno Christi 622, convert these years into days also thus 600 Julian years give 219150 20 years give 7305 1 year gives 365 June Complete 181 Days 15 The Sum subtract 227016 From 602088 There rests 375072 900 Turkish years gives 318930 There rests 56142 150 years gives 53155 There rests 2987 8 years give 2835 There rests 152 Giumadi I. gives 148 There rests 4 Therefore the 5th. of June 1649, in our English account, falls in the Turkish account, in the year of Mahomet, or their Hegira, 1058, the 4th. day of Giumadi II. 2 Example. I desire to know upon what day of our Julian year, the 23 day of the month Pharmuthi in the 1912 year currant of the Egyptian account from the death of Alexander's fall. The beginning of this Epoch● is from the beginning of the Julian Period in complete days. 1603397 1000 Egyptian years give 365000 900 years give 328500 10 years give 3650 1 year gives 365 Phamenoth complete 2●0 Days 23 The sum 2301145 6000 Julian years 2191500 There rests 109645 300 years give 109575 There rests 70 April complete 59 There rests 11 It therefore fell out in the year of the julian period 6300 the 11 of March, that is subtracting from that period, 4712 in the year of Christ 1588. He that understands this may by like method convert the year, of other Epochaes into our Julian years and the contrary. Next to the tables which concern the reduction of years in general, we annexed tables for the perpetual finding of the Sunday letter, Golden number and Epact in both the Old Julian, and New Gregorian account, with the fixed and movable Feasts, and a Catalogue of some famous places with their latitude and distance in longitude from the meridian of London, whose use is so obvious that it needs but little explanation; yet to take away all difficulty we have added these directions. The Cycle of Sun, Sunday Letter, Golden Number and the Epact in both accounts are set against the year of our Lord, and when those years are out, they may be renewed again as oft as you please, thus for the year 1656 the Cycle of the Sun 1513, the Sunday letters in the English account are F E, in the Gregorian B A the prime or Golden number in both is 4, the Epact in the English account is 14 in the Gregorian 4. And now to find the movable Feast, seek the English Epact, in the first Column of that Table towards the left hand, and the first F that follows▪ will show you that the 3d. of February is L X X Sunday, the 17 of February▪ L Sunday, & the 20th of February Ash-wednesday, & the first E that follows will show that Easter day is the 6th. of April, Ascension day the 15th. day of May, Whitsunday the 25 of May, Corpus Christi the fifth of June, Advent Sunday, November the 30th. But in the Gregorian, the Epact and Sunday Letters must be sought in the first Column towards the right hand, so shall the Sunday Letters B A show the Feast of Easter to be on the 9th of their April, and the rest as in that line they are set down. The fixed Feasts, together with the Weekday Letters, are set against their proper days in every month of the Julian year, knowing therefore the Sunday Letter, you may easily know upon what day of the Week any Feast or day of the month shall be. The Catalogue of places doth serve to show the height of the Pole in those places, and the Difference of the Meridian's of any place in the Catalogue from that of London. The Letter S notes that the distance is Westward, A that it is Eastward, the figures under the title of Time are Hours and Decimal parts of an hour, the Earth or any Star comes sooner or later to the Meridian of that place than that of London. If the time of a Lunar Eclipse then or other appearance be given at London, afternoon 8 hours, 23 parts, and the time when this happens at Uraniburge be inquired, there is found in the Catalogue for Uraniburge 0 hour 83 parts A, if therefore according to the letter A, 83 parts be added to the time given it makes 9 hours 06 parts for the time at Uraniburge. But if the time of another place be to be reduced to the time at London, the difference is to be applied with the contrary title. And that these Reductions whether in time or motion may be the better compared with those books that are written in the old Sexagenary form, we have added tables for the ready converting of Sexagenary parts into decimal and the contrary, the first of these tables is for the converting of the Minutes and Seconds, etc. of a Degree in motion; and the other of the parts of a day in time, an example in each will be a sufficient explanation. Let it be required to find the decimal answering to 37′ 25″ 16‴ 5 ' ' ' ' 29 ' ' ' ' ' in motion. In the first page of the table I find 37′ 12″ which is the nearest less, and 62 answering thereunto, and in the third column of the second page in the top of the page I find 12″, in which column I find 25 seconds, and in the sixth and last column of that page right against 25″, I find this number 36111111, which being annexed to 62. The decimal of 37 minutes 25 seconds is 6236111111 And the decimal of 16 thuds 0000740741 The decimal of 5 fourth's 0000003858 The decimal of 29 fifths 0000000373 Their sum 6236856083 is the decimal sought 2. Example Again, if it be required to find the decimal of 8 hours, 17 minutes, 8 seconds, 5 thirds, 12 fourth's, 9 fifts. In the first column of the table entitled, A Table to convert the hours and minutes of a day into decimals, I find 7 hours 12 minutes, and in the second column the figure 3, then looking the 12 minutes in the top of the pages, I cast mine eye downward in that column till I come to 8 hours 17 minutes, and in the last column of the page against 8 hours 17 minutes, I find this number 451388889 and therefore, The decimal of 8 hours 17 minutes is 3451388889 The decimal of 8 seconds 925926 The decimal of 5 thirds 009645 The decimal of 12 fourth's 0387 The Decimal of 9 fifths 0005 Their aggregate 3452324852 Is the decimal sought. To find the parts of a degree in motion, or of a day in time answering to any Decimal given, is but the contrary work to the former; Example. As if it were required to find the parts of a degree answering to 6236856083, the 2 first figures of this decimal are 62 which being sought in the first page of the table give me 37′. 12 and 62 being subtract▪ from 6236856083, the remainder will be 36856083 which being sought in the last column, my nearest number is 36111111, and right against that number under 12 in the top of the page I find 25, therefore 37′ 25″ are the parts of a degree answering to the decimal given, but if you would find the thirds, fourth's and fifths, from 36856083 Subtract 36111111 The remainder is 749972 Which being sought amongst the Decimals of the thirds, gives me 16 thirds, and this number to be subtracted from it 740741; and the remainder 004231 being sought amongst the Decimals of the fourth's gives me 5 fourth's, and this number to be subtracted from it 3858, and the remainder 373 sought amongst the Decimals of the fifths gives me 29 fifths, and so the parts of a degree answering to the decimal given are 37 minutes, 25 seconds, 16 thirds, 11 fourth's, and 29 fifths. Thus may you also find the parts of a day in time answering to any decimal given. The next thing to be done towards the finding of the annual revolutions of the planets is to find their entrance into any point of the Zodiac desired, and that may be done thus. Having the place of the planet taken by observation before and after its entrance into the point desired, subtract the observed place next before from the observed place next after, and the remainder shall show you the apparent motion answerable to the time between those observation, subtract also the former place, from the place in the point desired, and note their difference: for as the former remainder, that is the apparent motion between the observations, is to the time between those observations: so is this difference, to the time between the first observation, and the planets entrance into the point desired: thus we are to deal with those observations that we ourselves shall make, but one man's age not being distance enough between the observations from whence the middle motions may be rightly stated, we must take some observations upon trust; and find the middle motions by comparing the observations made in former ages with those of our own, of the Sun or Earth, take this Example following. The vernal Equinox observed by Hypparchus in the year from the death of Alexander 178, was Mechir the 26 day, and 95833333, that is at London 86746111. And the vernal Equinox observed at Uraniburge by Tycho 1588. was March the 9th. 86458333, that is at London 82986111. And that the interval of time between these two vernal equinoctials may be known, the 9 of March 1588. must be reduced to the correspondent time in Egyptian years from the death of Alexander, which according to the former directions is thus. The Christian Aera began in the 4713 complete year of Julian period, to which 1587. being added, it makes 6●00 from the beginning of the Julian period therefore to the 11 of March 1588., there are days as followeth. 6000 Julia● years give 2191500 300 years give 109575 February 59 Days 08 The Sum 2301142 The Aera Alexandri began in the 12 of November in 4390 year of the Julian period in which there are days, 4000 1461000 300 109575 80 29226 9 3287 October 304 Days 11 Which being subtracted 1603397 From 2301142 There rests 697745 1000 Egyptian years give 365000 There rests 332745 900 years give 328500 There rests 4246 10 years give 3650 There rests 596 1 year gives 365 There rests 231 Phamenoth complete 210 There rests 21 Therefore the 11 of March 2588 in our English account, falls in the 1912 year of the Aera Alexandri the ●1 day of Pharmuthi. In which space of time There are days 697746 And from the death of Alexander to the 26 of Mechir 178, there are 64781 There rests 632965 From days 697746. 829●6111 Subtract 64781. 86746111 There rests 632964. 96240000 And in this time the Earth or Sun hath gone 1733 circles, 〈◊〉 623880 degrees. Hence to find the mean motion for a year or 365 days I say▪ If 632964. 9624 d▪ Give 623880 degrees; How many degrees shall 365 days give? And the answer is 359 deg. 7611456036. That is in Sexagenary numbers 359 deg. 45 minutes, 41 seconds, 1 third, 27 fourth's. Again, to find the mean motion for a day I say, If 365 days gives 359 degrees, 7611456036, what shall one day give? And the answer is 0. 9856469743. That is in Sexagenary numbers 0 deg, 59 minutes, 8 seconds, 19 thirds, 44 fourth's. And what is here done for the middle motion of the Earth or Sun, may be done for the other planets. CHAP. 2. Of the figure which the planets describe in their Motion. HAving showed in the former Chapter, by what means the Annual or periodical revolutions of the Planets may be known, with their mean or equal motion, for any part of those revolutions, we should now show you, how by those equal motions to find their true or apparent places. But we can never hope to find the true and exact Phenomenon of the planets, unless we first know the figure in which they move; And this must be collected from such affections, as are by the constant observations of all ages found to be proper and natural to them, or may be rationally collected from them. 1 That the planets have one only motion, in one only line, and that those motions are equal, constant and perpetual, hath been confirmed by the observation of all ages, 2 And therefore they must needs be regular, their motions must be in a circle or some other line returning into itself, or else their motions could not be perpetual. 3 Their equal motions must have some place assigned (which the planets naturally behold) to be the beginning of this equal motion. 4 And because the apparent place of a planet taken by observation, is generally different from the place reckoned in its middle motion, the inequality of this middle and apparent motion must be referred to the centre of the Zodiac, ●s to the point of that inequality. 5 And because the centre of the Zodiac and of the world is to out appearance the same, the point of this inequality must be referred to the centre of the world. 6 And because of this difference between the middle and apparent motion, the centre of the world cannot be the true and exact centre of the planets, but the centre of that figure which the planets describe in their motion, must be some other point then the centre of the Zodiac. 7 And though the planets to our appearance are observed to be sometimes swifter in motion, then at other some, yet the cause of this inequality of motion must not be such as shall alter the natural and equal motion of the planet, it must be such as shall make the planet to be slower in its furthest distance from the centre of the world, and swifter at his nearest, without transposing the equal motion into any other than the first place assigned, whether superficies or circle. 8 And further the apparent motions of the planets in their nearest and furthest distances from the centre of the world being the same with their middle, the way of the planets must be such, that when they have gone 90 degrees from their farthest distance in their middle motions, their apparent motions must be less than 90 by the quantity of that whole inequality between the middle and apparent motion; And when the planets have gone a quadrant in their apparent motions, their difference between their motions shall be that whole inequality also, and therefore the centre of that figure which the planets describe in their motions must be in the middle between the points of their equal and apparent motions. 9 And because the mean motion from the point of a planets farthest distance from the centre of the world, to the first quadrant is greater than the apparent, therefore the apparent motion must be greater than the mean, from the first quadrant to the point of the planets nearest distance, and consequently a greater portion of the line in which the planets move, must be allowed to the apparent from the first quadrant to the point of nearest distance, then from the point of farthest distance to the first quadrant. 10 And because the equal motion must not change and that the apparent motion doth increase from the point of the planets farthest distance from the centre of the world, the angles of the middle motion must be reckoned, in the arches of many parallel circles, which shall also increase from the points of farthest to the point of their nearest distance to the centre of the world, and the line of the apparent motion, must contain those circles in one and the same superficies, and therefore that line must be excentrical from those circles of apparent motion, and so placed that all the parts of apparent motion may proportionably answer to all the parts of equal, yet so as that the least circles of equal motion, shall agree with the point of the planets farthest distance, and the greatest circles with the point of the planets nearest distance from the centre of the world. Seeing now that these circles of middle motion must be parallel, succeeding one another in a continued series, and are not one within another, and that the apparent motion must in the farthest distance answer to the least circles, & in the nearest distance from the centre of the world to the greatest, there is none but a solid Superficies that can be capable of those greater and lesser circles: And that an unequal sided Cone may be so cut, as that the figure upon the plain of that Section shall truly represent these affections of the planets, the learned Bullialldus doth Demonstrate, and for a preparation thereunto he showeth first, How two equal right lines may be so drawn in an unequal sided Triangle, as that the one shall bisect the other. An unequal sided Cone being cut through the Axis by a plain perpendicular to the plain of the base, shall make an unequal sided Triangle, and let A B C be such a Triangle, whose base B C let be bisected in I, and parallel thereunto draw the line P S, which being within the triangle shall be also bisected in the point R, and from a point taken in this line at pleasure, suppose at H, to the Axis of the Cone A I, draw the line H M so, as that the angles H M R and M R H may be equal; then shall H M and H R be equal also, and let the line H M being continued to the sides of the Triangle A B and A C be bisected in the point X, and by the point of bisection at X, draw the line V X T parallel to the base B C, then are the right lines E K and V T equal, and E K is bisected by V T in the point X. And now if this unequal sided Cone be cut through the bisected line E K, the figure made on that plane by such section shall be an Ellipsis one of whose umbilique points shall fall in the Axis of the Cone. For V T being equal to E K, and E K being bisected in X, the right line X O in the circle V O T shall be the conjugate diameter in the Ellipsis E K, because it is perpendicular to the line E K in the point X, and reacheth to the extremity of the plain V O T, and it is also a mean proportional between V X and X T, because it cuts the line V T at right angles in the point X. And therefore the square of X O is equal to the rectangle V X T more by the square of Z X but the rectangle V X T more by the square of Z X shall be equal to the square of Z V, and the square of Z V shall be equal to the square of E X, because Z V and E X are equal, and therefore the squares of X O and Z X, shall be equal to the square of E X, but E X is the greatest semidiameter, X O the lesser, and the square of Z X or M X the difference between the squares of E X and X O, and therefore M X shall be the distance of the umbilique point from the centre X, and M the umbilique which by construction is placed in the Axis of the Cone A B C, as was to be proved. And because the centre of the Ellipsis at X is distant from the Axis A I, by the quantity of X Z equal to M X, the plane which bisects the Ellipsis by the conjugate Diameter O X N shall not bisect the circles, but shall cut off V X a greater part towards E, and X T a lesser part towards K. Let the equal motion of the planet therefore be about the Axis of the Cone A I, and through all the circles which are intercepted between E D and P K, and let the centres of those circles be in the Axis of the Cone, and upon those centres let the planets be conceived to make equal angles in equal portions of time, but the term of apparent motion to which it is referred, let be the other umbilique at H, the place of the Sun (if we suppose him according to our new Astronomy to be the centre of the World.). Then is the Aphelion or part remotest from the Sun at E, the Perihelion or nearest part at K. And now while the planets describing the Ellipsis shall be equally moved about the Axis of the Cone, in their equal or middle motions, they shall have gone a quadrant about the Cone, when yet they shall want of a quadrant in the Ellipsis by the quantity of the right line M X, and shall be in the point Y, which point is in the circle F M G, and in the Ellipsis, and the right line M Y which is drawn from the centre of the circle F G, is set at right angles, upon the Diameters both of its own circle F G and of the Ellipsis E K, and consequently the angle F M Y is a right angle, and therefore the planets shall move 90 deg. of middle motion about the axis of the Cone when they come to Y, but in the Ellipsis they shall not move so much by the arch Y O, or the right line M X. That this is the true and natural Hypothesis may thus appear, because 1 The planets thus describe one only line about the axis of the Cone, in their equal constant and perpetual motions. 2 Their motions thus are regular, though not in a perfect circle, yet in a line returning into itself. 3 Their equal motions have their beginning always in one place, ●●at is, in the Axis of the Cone. 4, 5 The apparent motion of the planets is referred to the Sun at H, as to the centre of the Zodiac. 6 And the whole inequality between the middle and apprent motion, is between the umbilique points M and H. 7 The motion of the Planets are thus made to be flower in the Aphelion, then in the Perihelion, and yet the equal motion is not reckoned any where but in the first place assigned the axis of the Cone. 8 The Planets in their middle motions will thus go 90 degrees about the axis, being come to Y, when yet they want of a quadrant in the Ellipsis, the arch Y O, or M X, and so the centre of the Ellipsis is in X, the middle of the whole Inequality. 9 There equal motions from the Aphelion at E to the first quadrant are greater than the apparent, but from the first quadrant to the Perihelion at K, the apparent motions are greater than the mean, and therefore a smaller portion of the line which the Planets describe is allowed to the apparent motion from the Aphelion to the first quadrant, to wit, F Y, and a greater part from the first quadrant to the Perihelion, to wit, Y O R. 10 And lastly, because the circles of middle motion, F G, V T, etc. do increase from the Aphelion to the Perihelion, & that the Planets notwithstanding make equal angles in equal portions of time about the axis of the cone, their motions in the Ellipsis do increase also from the Aphelion to the Perihelion, because these greater angles are subtended by greater lines in greater circles, by lesser lines in lesser circles, & because the lesser circles are placed towards the top of the Cone at A, & Aphelion at E, the greater towards the base and Perihelion at K, the motion in the Ellipsis is slower about the Aphelion and swister towards the Perihelion; And thus the middle motions are not reckoned in one only circle, but in many parallel circle's comprehended between E D and P K, these circles are contained in one plain Superficies, and by these circle's the planets describing an Ellipsis do continually pass, and yet they are all of them excentrical in respect of the figure which the planets describe, as was before required. Thus then there is an admirable Harmony between the motions of the planets in this figure, and their motions in the heavens found by observation; probably therefore we may conclude that the figure which the planets describe in their motions is an Ellipsis. CHAP. 3. Of the Lines and Method to be used for the finding of a Planets true longitude from the Aphelion in this figure. HAving resolved upon the figure which the Planets describe in their motions, we come now to show you what lines must be drawn, and method used for the finding a planets true longitude from the Aphelion in this figure; and in order thereunto, we will show you first the order of the spheres in which the planets move, and how mechanically to draw this Ellipticall figure of their motions upon a plane. As to the Spheres, 1 We suppose that the Sun is placed in the middle of the world in or about the centre of the Sphere of the fixed Stars, and hath no circular motion but central only. 2 That the Earth is one of the planets, and with her annual motion about the Sun describeth her Orb between the Orbs of Mars and Venus. 3 That the Moon is moved about the Earth, as her centre, and so in her annual motion hath respect both to the Earth, and to the centre of the Earth's orb the Sun. 4 That the Orb of Venus is next under the Orb of the earth, and the Orb of Mercury between the Sun & the Orb of Venus. Next above the Orb of the earth we suppose the orb of Mars, the Orb of Jupiter next above Mars, and the Orb of Saturn next to the Orb of the fixed Stars. According to these supposed principles, we would have immediately showed the method of calculation, but that the Mechanical way of drawing an Ellpsis, doth if not demostrate, yet at least illustrate that method. An Ellipsis by the help of a thread may be mechanically made thus, first draw a right line to that length which you would have the greatest Diameter to be, which let be A P, and from the middle of this line at X, set off with your Compasses the equal distances X M and X H. Then take a piece of third of the same length with the diameter AP, & fasten one end of the third in the point M, and the other at H, & with your pen extending the thread thus fastened to A, & from thence towards P, keeping the third stiff upon your pen, draw a line from P by B to A, the line so drawn shall be an Ellipsis, in which because the whole thread is equal to the Diameter A P therefore the two lines made by the thread in drawing of the Ellipsis must in every point of the Ellipsis be also equal to the fame diameter A P, they that desire a demonstration thereof Geometrically may consult with Apollonius Pergaeus, Claudius Mydorgius, o● others, in their treatises of conical sections; for our present purpose this is sufficient, and from the equality of those two lines, with the Diameter, a brief Method of Calculation, is thus demonstrated by Dr. Warde. Let the line M E be equal to A P, and draw the lines H B and H E, then in the plain triangle M H E, having the sides M E equal to the Diameter, and M H the distance of the umbilique points, with the angle H M E, the angles M E H and M H E shall be given also, but the angles B E H and B H E are equal, because the sides B H and B E are equal by construction, and therefore if you subtract the angle B E H from the angle M H E, there will remain the angle at the Sun M H B, which is a planets true longitude from the Aphelion or the equated Anomaly. And of these three things propounded to be given, the side M E is by construction made equal to the Diameter A P, how the angle H M E and the side M H must be had shall plainly appear by that which follows. CHAP. 4. Of the proportion by which the motion of the Planets do increase from the Aphelion to the Perihelion. THough the equal motions of the planets are to be reckoned (as hath been said) in divers parallel circles about the Axis of the Cone, whose diameters must still increase from the top of the Cone at A, to the base B C, that the motions of the planets in the Ellipsis may increase also; yet in the calculation we cannot conveniently reckon the middle motion in any more circles than one, and therefore it must be proved, that the angle comprehended between the lines drawn from E to that point in the diameter of the Ellipsis which is made the common Centre of the Circles of middle motion, and fr●● that Centre to the planet in the Ellipsis, is always equal to the a●gle of middle motion, comprehended between the semidiameter of the planets proper circle of middle motion and the line d●●wn from the centre of that circle to the planet in the Ellipsis, this Bull●aldus takes for granted, and Dr. Ward doth thus demonstrate. F M G is a circle of middle motion whose centre is in the Axis of the Cone, and in the umbilique point of the Ellipsis M, but a planet being in the Ellipsis at R the proper circle of its middle motion is L β Q and the angle comprehended by the Radius of that circle Lβ, and the line drawn from β the centre thereof to R the place of the planet is equal to the angle comprehended between the line E M and the line drawn from M to R in the Ellipsis, for thus there are made two right angled triangles M H R and β H R, in which the side H R is common to both, for it is set at right angles in the Ellipsis and in the circle equant, and the sides M H and β H are equal by what hath been already said in the 2 Chapter, therefore the angle R M H is equal to the angle R β H, and by consequence R β L and R M E are equal also, but the angle R β L is the angle of the middle motion of a planet from the Aphelion, or the angle of the simple excentricke anomaly, and therefore the angle R M E is the mean anomaly also, whose compliment to a semicircle is the angle M E H in the Diagram of the preceding Chapter. When a Planet therefore descends from E to K, the angles at the axis of the Cone, or at M the umbilique point of the Ellipsis do always increase, and therefore the mean anomaly is increased, for the angles of its circle Equant do answer to more degrees at the axis, and those angles also, are always degrees or parts of greater circles, and therefore the planets increase in the swiftness of their motion in such proportion as the circles, Diameters, or Radii of those circles equant do increase. For Demonstration whereof let the line E ψ be made parallel to the axis of the Cone, then shall the parts of the semidiameters of the circles equant comprehended between those parallels E ψ and A I be equal to the semidiameter of the least circle E O, and the parts intercepted between that parallel E ψ and the side of the triangle A B, shall be the proportional excess above the least motion in E O. And the mean acceleration is in that circle equant whose plain parallel to the base of the cone doth pass by the centre of the Ellipsis, that is in the circle V D T, for seeing that M X & Z X are equal, as also V D & Z X, V D must needs be the difference between the semidiameter of the least circle E L & the middle circle V T, & the excess of that semidiameter, above the semidiameter of the least circle, must be equal to M X or the excentricity, but the distance of this circle from the Aphelion is 90 degrees, and may be called the Diacentrick circle, and is the Radius of the circle of the equated anomaly E X And the difference between the semidiamater of V T, and the parallel circled ω K is also equal to M X, for as E V to E ω so is E X to E K, and again, as E V to E ω so is V D to ω ψ, and because E X is the half of E K, therefore V D shall be equal to ω Y or to the half of ω ψ, and therefore ω Y is also equal to M X, when a planet therefore is in the circle V T, it is swift in motion, and is in the middle between the swiftest and the slowest motion, and because that middle acceleration of the planets, is the acceleration in a quadrant, therefore as E X to V D, so is E M to G π. That is, as Radius to the excentricity, so is the versed sine of the distance from the Aphelion, to the part proportional of the planets acceleration; and therefore also (faith Bullialdus) it is as the whole sine, to the whole difference, so is the sine of the distance of the middle motion from the Aphelion, to the part of the difference answering to that distance. From hence and the two following problems of Vieta, he propounds a method for the finding of the Aphelion and distance of the umbilique points. Problem 1. Three points in the circumference of a circle being given, to find a diameter▪ upon which there being perpendiculars let fall from the points given; the segments of the diameter intercepted by these perpendiculars shall be proportional to another proportion given. Let the line C B be cut in E, so as C B may be to E B, as S to R, and let D E, cut the Diameter F G at right angles in H. Then is F G the Diameter sought, upon which seeing the lines B ay, C K, D H do fall perpendicularly, K I shall be to H I as S to R. For the right lines C B are parallel, or not parallel, if they be parallel, C B shall be equal to K I, and E B to H I, and then by construction K I shall be H I, that is C B to E B, in the given proportion as S to R. But if they can meet, let the point of their meeting be at L. Then it shall be as L C to L K, so L E to L H, and so is L B to L I. And then dividing and changing the terms, it shall be as K I to H I, so is C B to E B, or so is S to R as was required. And thus likewise K H and H I, with the arches B C, C D, and B D, being given, we may find the arch B G, and the Diameter F G in the same parts with K H and H I, for the arches C D and D B being given, the subtenses of those arches and angles opposite to them in the triangle B C D shall be given also in the parts of the Diameter F G, and therefore the sides E B and D B with the angle E B D being given, the angle E D B or D B M shall be given also, which being deducted from the arch B M D shall leave B M or the double of B G. Problem 2. Two points in the circumference of a given circle being given, to find the Diameter, upon which perpendiculars being let fall from the points given, the segment of the Diameter intercepted by those perpendiculars shall be equal to a line given. In the circle B C whose centre is A, let the given points be B C, let the given line be Z. Subttend the periphery B C, and let the right line B C be made the Diameter of a circle, in which draw the line C D equal to Z. But by the centre let there be drawn E F the Diameter of the circle B L C parallel to D C, and then the perpendicular B D being let fall upon M C, the angle B D C shall be a right angle. And because E F and D C are parallel, B D shall cut E F at right angles in the point K, and B K shall be parallel to C I, and therefore D C and K I shall be equal, therefore in the circle B C, the points B and C being given, there is found the Diameter E F, upon which the perpendiculars B K and C I being let fall, the segment K I intercepted by those perpendiculars is equal to C D that is to Z the line given. Thus likewise the sum of the arches, and the sum of the Sins of these arches being given, we may distinguish the arches and the Sins if the centre A be between K and I. Or the difference of the arches and the difference of their sins being given, we may distinguish the arches and the sins, if the point K be between the centre A and the point I When three places therefore in the apparent motion of the Sun orany other planet, with the interval of time are given, the middle motion of the planet shall be given also, with the difference between the middle and apparent in those intervals, and the rest from these. For if the points B C D in the Diagrams of the first problem be given, to wit, three places in the apparent motion, & the middle motion in the intervals of time B C, C D, the difference between the middle and apparent motion shall be given also; let K I the part of the diameter F G, be the difference of the middle from the apparent in the interval B C, and let H I be the difference in the interval B D. Then in the triangle B C D, the arches B C and C D are known, and therefore the angles at D and B are known also, and by consequence the third angle at C, and from thence the subtense C B, now that we may find the angle E D B, the side C B must be cut in the same proportion as the line K I is cut in H. That so K I may be to H I as C B to E B. And so we shall have E B in the like parts with B D; and the sides E B, B D, with the angle at B, in the triangle B E D being given, the rest shall be given also, and the angle at D being given, we shall have the arches M B and M D. And lastly, F G shall be given in the like parts in which K H, and H I are given. For as the sum of the Sins compliment B I and C K, to K I, so is the Diameter F G, to the same diameter in the parts of K E and so the first inequality shall be given, and the diameter from whence it begins. CHAP. 5. Of the inequality of the Earth's annual motion, and of the Diameter in which the Aphelion and Perihelion are placed. THe inequality of the Earth's annual motion, if we suppose the motion to be exactly circular, may from the Observations of Copernicus made at Fruenburg in Prussia, 1525, or rather as they were corrected by Tycho, 1584. be they found; Between the Autumn and the Vernal Equinox, according to Tycho there were days 178. 43333. 33333. And between the Autumn Equinox, and the middle of Mars there were days 45. 15416. 66667. Upon the Centre F describe the Sun's Orb A B C, let A be the Vernal Equinox the the Autumn, D the middle of Mars, and let D E intersect A C in the point G, and draw the line A D: Then is the ark of middle motion C D 44 degrees, 5061111111, and therefore the angle C A D, 22. 25305. 55556. and the angle of apparent motion C G D 45 degrees, which being deducted from 180 degrees, give the obtuse angle A G D, 135 degrees. And therefore the angle C D G 22. 74694. 44444. And the arch A E 45. 49388. 88889. Again, the ark C D A, 175 deg. 87500. 00000. from which deducting C D 44. 50611. 11111. the remainder is D A, 1●1. 36888. 88889. The subtense A D 18225828. to which A E being added, the whole is D E, 176. 86277. 77778. and the subtense of D E, 19992506. And because that neither of these Segments do make a Semicircle, we must find the Aphelion in the other part of the circle E B C. Let the line E B represent the Aphelion and Perihelion, G F the excentricity, F H then being drawn perpendicularly shall bisect D E and make right angles in the point H. And in the triangle A G D, the angles being given with the side A D, there is also given G D 9763585, which being deducted from the half of D E there shall remain G H 232668, and the perpendicular F H may be thus found, D A E wants deg. 3. 13722. 22222 of a semicircle, the half whereof is 1. 56861. 11111, whose sine 273740 is the side F H, now then H G and F H being given, we may find the angle F G H 49. 63666. 66667, which with the arch A E 45. 49388. 88889 makes 95. 13055. 55556, therefore the Aphelion is ♋ 5. 13055. 55556, or in sexagenary numbers, in 5 degrees of Cancer 7 min. 50 seconds. And the excentricity F G 359261. But the method for the finding of the Aphelion and excentricity which we propounded in the last chapter, is more suitable to the Elliptical motion of the planets, and according to that method the earth's Aphelion and Excentricity, or semidifference of the umbilique points, from the accurate observations of Tycho in the year 1588. may be thus found. From the middle of Taurus to the middle of Leo there were days in the apparent motion, 94. 24662. 03703. From the middle of Leo to the Autumn Aequinox there were days 46. 40277. 77778. From the middle of Taurus to the Autumn Aequinox there were therefore days 140. 64939. 81481. In the annexed Diagram let C represent Taurus 15 deg. D 15 deg. of Leo. Then shall the arch of apparent motion C D be 90 deg. and D B 45, but in the middle motion the arch C D shall be 92. 89277, and D B 45. 73777, and CB 138. 63055. First, we will work with the arches of apparent motion. Arch. Deg. Angles Deg. Sides C D 90. 00000 C B D 45. 00 C D 70711 D B 45. D C B 22. 50 D B 38268 C B 135. C D B 67. 50 C B 92388 The half differences of the middle from the true. 1 Deg. 1. 44638 K H 2524 2 Deg. 0. 36888 H O 644 Deg. 1. 81526 K O 3168 Asdruball K O 3168 co. arith. 6. 4992149 To C B 92388 4. 9656155 So is H O 644 2. 8088858 To E B 18780 4. ●7●7152 And now in the triangle E D B we have the sides D B 38268, ● B 18780, and the angle E B D 45 deg. to find the angle E D B. As the sum of D B and E B 57048 co. are. 5. 2437596 To their difference 19488 4. 2897673 So the tangent of ½ D and E 67. 50 10. 3827756 To the tang. ½ the difference 39 51283 9 9163025 The angle E D B 27. 98717 and the double thereof is the arch B M N 55. 97434 from whence taking M N ●q●al to D B 45 there rests B M 10. 97434, and the half of that is B G 5. 48717, and the sum of D B and B G 50. 48717, now D represents the 15 deg. of Leo and the compliment of D G to a quadrant is the arch D L 39 51283 from the vernal Equinox to the 15 deg. of Leo is 135 deg. from which deducting D L 39 51283, there rests for the point of the Aphelion at L 95. 48717, that is in Cancer deg. 5. 48717. And now to find the Semidistance of the umbiliques, As the sum of the Sin●s of the compliments of B O and C K, is to K O, So is the Radius A G to the same Radius A G. Now if you deduct 15 deg of Taurus from Cancer 5. 48717 the arch C L will be 50. 48717 and B G 5. 48717 being deducted from L G 90, there rests L B, 84. 51283 the sine of L C is K A 77●●8 and the sine of A O 99541 and the sum of K A and A O is 176●8● now then, As the sum of K A and A O 176689 co. are. 4. 7527●94 Is to the ½ difference K O 3168 3. 5007851 So is the Radius A G 100000 To the same Radius A G in the parts of K O 1792 8. 2534945 or degrees 1. 02139 half the inequality desired. But if we take the arches of Middle motion the calculation will be as followeth, Arch. Deg. Add Ded. Sides. C D 92. 89277 C B D 46. 446 85 C D. 72473 D B 45. 73777 D C B 22. 868885 D B. 38862 C B 138. 63054 C D B C B. 93554 Half the differences of the middle from the true▪ as before. 1 Deg. 1. 44638 K H 2524. 14119 2 Deg. 0. 36888 H O 643. 81259 Deg. 1. 81526 K O 3167. 95378 As K O 3168 co. arith. 6. 4992149 Is to C B 93554 4. 9710623 So is H O 644 2. 8088858 To E B 19018 4. 2791630 And in the triangle E D B the angle at D may be thus found. The side D B is 38862 The sine E B is 19018 The sum is 57880 5. 2374765 The difference 19844 4. 2976292 Tangent ½ D & E 66. 77681 10. 3674618 To the tangent ½ 38. 62586 9 9025625 28. 15095 the angle E D B and the double thereof is the arch B M N 56. 30190 & from thence taking M N equal to D B 45. 73777 There rests B M 10. 56413 and the half of that is B G 5. 282065. and the sum of D B and B G 51. 01997. Now D represents the 15 degrees of Leo, and the compliment of D G to a quadrant is D L 38. 9800●. from the Vernal Equinox. to the 15 deg. of Leo, is 135 deg. from which deducting D L. 38. 98003, there rests for the point of the Aphelion at L, 96. 01997. that is in Cancer, 6 deg. 01997, from which the difference between the true and mean motion in that interval being deducted 73776, the place of the Aphelion will be in Cancer, 5. 28221. And to find the Semidistance of the umbiliques deduct 15 deg. of Taurus from Cancer 5. 28221, there will remain for the arch C L 50. 28221, and B G 5. 28206 being deducted from L G 90 there rests for the arch, L B 84. 71779, the sine of C L is K A 76921 The sine of L B is A O 99575 As their sum 1764964 co. are. 4. 7532652 Is to K O 3168 3. 5007851 So is the Radius A G 10. 0000000 To the same A G 1795 8. 2540503 This excentricity Bullialdus corrects by the apparent places of the planets in the centre of the Ellipsis, and that angle according to the Method of our calculation may be thus found. From 15 degrees of Taurus, or from 225. deg. Deduct the Aphelion 095. 28221 There rests the angle M H E 129. 71779 whose compliment to 180 deg. is 50. 28221 the sum of M E H and E M H and the half thereof 25. 14110 The side H E 200000 The side M H 3590 The sum 203590 4. 6912436 The Differ. 196410 5. 2931636 Tang. ½ sum 25. 14110 9 6714590 Tang. ½ differ. 24. 35902 9 6558662 The sum 49. 50012 E M H Difference 00. 78208 M E H being doublled is the angle M B H 1. 56416 From E M H 49. 50012 Deduct M E H or E M B 00. 78208 There rests B M H 48. 71804 As the sine of M B H 1. 56416 co. are. 1. 5638976 Is to the side M H 3590 3. 5550944 So is the sine of B M H 48. 71804 9 8759126 4. 9949046 To the side B H 98833 The side X H 1795 The Sum 100628 co. are. 4. 9972811 The Differ. 97038 4. 9869418 Tang. ½ sum 25. 14110 9 6714590 9 6556819 Tang. ½ Dif. 24. 34989 Differ. 00. 79121 X B H. From the 15 deg. of Taurus or from 45 45. Deduct the angle X B H 00. 79121 There rests the place required 44. 20879 Again, from 0 deg. of Libra or from 180. Subtract the Aphelion 95. 28221 There rests the angle M H E 84. 71779 And therefore ½ of M E H and E M H 47. 64110 The side H E 200000 The side H M 3590 The Sum 203590 co. are. 4. 6912436 The Differ. 196410 5. 2931636 Tang. ½ sum 47. 64110 10. 0400951 Tang. ½ Differ. 46. 61542 10. 0245023 Aggregate 94. 25652 E M H Difference 1. 02568 M E H which being doubled is the angle M B H 2. 05136 From E M H 94. 25652 Deduct M E H 1. 02568 There rests B M H 93. 23084 whose compliment is A M B 86. 76916 The sum 101927 co. are. 4. 9917108 The differ. 98337 4. 9927169 Tang. ½ sum 47. 64110 10. 0400951 Tangle ½ differ. 46. 61677 10. 0245228 Differ. 1. 02433 The angle X B H. And therefore the Earth's place 181. 02433 Now then from the Aphelion 95. 28221 Subtract Taurus, that is 44. 20879 There rests the arch C L 51. 07342 And from L G 91. 02433 Deduct B G 5. 28206 There rests the arch L B 85. 74227 77795 is the sine of 51. 07342 99724 is the sine of 85. 74227 Sum 177519 As the sum 177519 come. are. 4. 7505576 Is to K O 3168 3. 5007851 So is A G 100000 5. 0000000 To the same A G 1784 3. 2513427 But according to this method, the Aphelion may be somewhat more exactly found, if we take the Arithmetical mean, between the apparent and middle motion, and so; Arch. Deg Angle Deg. Side C D 91. 44638 C B D 45. 723●9 C D 71597 D B 45. 36889 D C B 22. 68444 D B 38565 C B 136. 81527 C D B 68 40763 C B 9●983 Now then to find E B I say, As K O 3160 co. are. 6. 4992149 Is to C B 92983 4. 9684035 So is H O 644 2. 8088858 To E B 18902 4. 2765042 Then in the triangle E D B, we have known the side D B 38565, the side E B 18902, and their contained angle E B D 45. 72318, whose compliment to a semicircle is 134. 27681. The half sum 67. 13840. As the sum of D B and EBB 57467 co. are. 5. 2405815 Is to their differ. 19663 4. 2936497 So is Tang. ½ D and E 67. 13840 10. 3750715 To the Tangle ½ differ. 39 06019 Differ. 28. 07821 the angle E D B The angle E D B 28. 07821 E D B doubled is the arch B M N 56. 17926 From which subtract M N or D B 45. 36889 There rests B M 10. 78753 The half of B M is the arch B G 5. 39376 And D B being added to B G, D G is 50. 76265 And the compliment there of is D L 39 23735 Which being deducted from ♌ or 435. 00000 There rests the Aphelion at L 95. 76265 And the half difference D B 0. 36889 Being deducted there rests 95. 39377 The Aphelion then is in Cancer 5 deg. 39377 And to correct the excentricity from the 15 degree of Taurus or adding a semicircle from 225. Deduct the Aphelion 95. 39●77 There rests in the Ellipsis M H E 129. 60623 whose compliment to 180 is the sum of the opposite angles M E H and EMH 50. 39377 In the Triangle therefore of the last Diagram M E H, we have, 1. The side H E 200000 2. The side H M 3568 3. The angle M H E given As the sum 203568 co. are. 4. 6912904 To the difference 196432 5. ●932122 So tang. half sum 25. 19688 9 6724222 To tang. half differ. 24. 41154 9 6569248 Aggregate 49. 60842 the angle E M H Difference 00. 78534 the angle M E H Differ. doubled is 1. 57068 the angle M B H Differ. subtracted 48. 82308 is the angle B M H▪ As the sine of M B H 1. 57068 co. are. 1. 5620900 To the side M H 3568 3. 5524248 So is the sine of B M H 48. 82508 9 8766104 To the side H B 97977 4. 9911252 The side X H 1784 The sum 099761 co. are. 5. 0010393 The differ. 96193 4. 9831434 Tangle ½ sum 25. 19688 9 6724222 Tang. ½ differ. 24. 39566 9 6566049 Differ. 00. 80122 the angle X B H which being subtracted from 15 degrees of Taurus, or from 45 deg. there rests 44. 19878 the Aphelion 95. 39377 Place of the earth subtract 44. 39878 There rests the arch C L 51. 19499 Again from 0 degrees of Libra or from 180. Deduct the Aphelion 95. 39377 There rests in the Ellipsis M H E 84. 60623 And therefore the ½ sum of the angles E M H and M E H 47. 69688 As the sum 203568 co. are. 4. 6912904 To the differ. 196432 5. 2932122 So tang. ½ sum 47. 69688 10. 0409444 To tang. ½ differ. 46. 67763 10. 0254470 Aggregate 94. 37451 angle E M H Difference 01. 01925 angle M E H Differ. doubled 2. 03850 angle M B H Differ. subtract 93. 35526 angle B M H As the sine of M ● H 2. 0385 co. are. 1. 4489043 To the side M H 3568 3. 5524248 So is the sine of B M H 86. 64474 9 9992548 To the side H B 100134 5. 0095839 The side X H 1784 The sum 101918 co. are. 4. 9917492 The differ 98●50 4. 9927743 The tang. ½ sum 47. 69688 10. 0409444 Tang. ½ differ. 46. 67901 10. 0254679 Difference 01. 01787, X B H which being added to ♎ the place will be 181. 01787, from which subtract B G 5. ●9376 there rests 175 or L B 85. 62411. The sine of C L 77927 The sine of L B 99707 As the sum 177634 co. are. 4. 7504740 Is to K O 3168 3. 5007851 So is A G 10000 5. 0000000 To A G 1783 3. 2512591 which comes so near to the Excentricity before found that we may without manifest error make use of either. CHAP. 6. Of Stating the Earth's middle motions by sundry observations. TO find the Earth's middle motion for any time under a year, the way already prescribed in the first Chapter (as to the use for which it was intended) is exact enough, but to state the true quantity of the Earth's annual motion, the apparent Equinoctials must be reduced into the mean, which cannot be done unless the Aphelion be first found, having found that therefore by the observations of Tycho, we will now find it by the observations of Albategnius, in the year from the death of Alexander, 1206, and the interval of time then between the Autumn and the Vernal Equinox was days 178. 51250, and the middle motion for that time, is deg. 175. 95083. The true motion is 180. From which subtract 175. 95083 Their difference is 4. 04917 The half difference is K L 2. 02458 Therefore as A E 3568 come. are. 6. 4475752 To A E 100000 5. 0000000 So is K L 3533 3. 5481436 To K L 99019 4. 9957188 Half the arch H I L is 87. 97541, whose sine 99938 is the side H L, and therefore, This Autumn Equinox was observed September the 19th, from the death of Alexander 1206 years, that is in the year of our Lord 882. In the beginning therefore of the year of Christ 883, the Aphelion was in Gemini 24 d. 25176 And in June 1588., the Aphelion was in Cancer 5. 39377 Their difference is 11. 14201 And between both observations there are 706 Egyptian years, now then to find the mean motion of the Aphelion for a year I say, If 706 years give 11. 14201, what shall one year or 365 days give? and the answer is Deg. 0. 0157818838 And again, if 365 days give 0157818838 one day shall give o deg. 0000432380. In 882 Julian years there are 322150 days, by which if you multiply 0000432380 the product will be deg. 13. 9291217, which being deducted from the aphelion before found, Gemini 24. 25176, the aphelion in the beginning of the Christian Aera will be in Gemini 10. 3226383, that is, 19 21 29. But from Hypparchus, that is from 177 year from the death of Alexander to the 1205 year complete in the same account, there are 1028 Egyptian years, and the mean motion of the Aphelion in that time is, Deg. 16. 2237765464 Gemini 24. 2516600000 Gemini 08. 0278834536 which being deducted from there rests for the aphelion at that time. And therefore the vernal Equinox observed by Hypparchus in the year from the death of Alexander 178 Mechir 26. 95833333, was distant from the Aphelion deg. 68 027883, which being deducted from a Semicircle the angle in the Ellipsis of the next Chapter A M E will be found to be 111. 972117, and this angle is the sum of the angles M E H and M H E, and therefore the equation to be subtracted may be thus found. The side M E 200000 The side M H 3568 Logarithms The sum 203568 co. are. 4. 6912905 The Differ. 196432 5. 2932122 The tang. ½ sum 55. 98606 10. 1707846 Tang. ½ differ 55. 03186 10. 1552873 Differ. 00. 95420 angle M E H Differ. doubled. 01. 90840 angle M B H or the Equation sought: which may be converted into time thus, if the parts of a degree of equal motion, 98564 give one day; 1. 90840 snall give 1. 93620, and this being added to the true Equinoctial, Mechir 26. 95833 the middle will be Mechir 28. 8945●, or deducting 05625; for the difference of meridians between Uraniburge and Alexandria, it will be at Uraniburge; Mechir 28. 83828. And the vernal Equinox observed by Tycho at Uraniburge 1588., was March the 9 86458, and the Earth's aphelion than was in Cancer 5. 39377; and therefore the arch answering to the excentricity 3568, viz. deg. 2. 04529 being converted into time as before, will be days 2. 07508, which being added to the former time the middle Equinoctial will be March the 11. 93966. And in the Egyptian account from the death of Alexander it was 1912 Pharmuthi 23. 93966, from which if you deduct in the same account 178, Mechir 28. 83828 between both observations there will be found, 1734 Egyptian years, days 55. 10138, which being converted into days give 632965. 10138. Hence to find the quantity of the Tropical year, I say, if 1733 Zodiacs give days 632965. 10138, that one Zodiac shall give days 365. 2418357126. And to find the earth's middle motion for a year, I convert 1733 Zodiacs into degrees, and they amount to 623880 degrees; then I say, if 632965. 10138 give 623880, that 365 days shall give 359. 76106661098 that is in Sexagenary numbers 359 deg. 45 minutes, 39 seconds, 50 thirds, 24 fourth's. And to find the mean motion for a day, I say, if 365 days give 359. 76106661098, that one day shall give 9856467579, that is in Sexagenary numbers 0 degrees, 59 minutes, 8 seconds, 19 thirds, 41 fourth's, 57 fifths. And the daily motion of the Aphelion is 0000432380, which being deducted from the diurnal longitude gives the daily motion of the Anomaly 985603599, these things premised we will now determine the Epochaes of the middle motions. The middle Equinoctial Anno Christi 1588., March 11. 9●966, is from the Aera Nabonassari 2336 Pharmuthi●3 ●3. 93966. 2335 years being multiplied by 359. 761067 the product will be 840042. 091445, and the diurnal motion 985647, being multiplied by 232 days, the product will be 228. 670104 and the middle motion answering to the parts of a day, 93966, is 926173, the which being added togethea do amount to 840●71 degrees 687722 parts of a degree, that is, rejecting the whole circles 31 d. 687722, which being deducted from 360, the remainder 328. 312278 or 10 Signs 28 degrees and 312278 parts, is the Radix of the earth or Suns mean longitude in the beginning of the Aera Nabonassari. To which if you add deg. 258. 692408 the middle motion for 424 years, the whole circles being rejected, the Radix of the earth's middle motion to the beginning of the Aera Alexandri shall be 227. 004686 or 7 sins 17 deg. 004686 parts. And adding to this Epocha, deg. 51. 944398, which is the middle motion for 323 years 131 days, the whole circles being rejected, the Radix of the earth's middle motion in the beginning of the Christian Aera shall be deg. 278. 949084 or 9 signs, 8 deg. 949084, to which if you add 034223 the equal motion belonging to 034722 the difference between the Meridian's of Uraniburge and London, the Radix of middle motion at London will be 278. 983307 And the Aphelion 70. 322638 And the Mean Anomaly 208. 660669 CHAP. 7. To calculate the Sun's true place and distance from the Earth. HAving composed tables of the Sun's middle motions, according to the directions of the last Chapter, his true place in the Zodiac, and distance from the earth may thus be found. 1 Write out the Epocha next before the given time and severally under that, set the motions belonging to the years, months, and days complete, and to the hours and scruples current, every one under his like (only remember that in the Bissextile year, after the end of February, the days must be increased by an Unite) then adding them altogether, the sum shall be the Sun's mean motion for the time given. Example. Let the time given be May the 12th. hour 11 parts 15 before noon at London in the Bissextile year 1656, and the Sun's place to be soughts The numbers are thus, Suns Longitude Suns Apogeon Deg. parts Deg. parts The Epocha 1640 291. 24777 96. 22265 Years comp. 15 359. 37294 23686 April 118. 27760 519 Days 12 011. 82776 52 Hours 23 94458 Scruples 15 616 Suns Mean Longitude 421. 87681 96. 46522 2 Subtract the Apogaeum from the Mean Longitude, there rests the mean Anomaly. Example. The Sun's mean longitude 421. 67681 Apogaeum subtract 96. 46522 Rest mean Anomaly 325. 21459 Whose compliment to a Circle 34. 78541 is the angle A M E in the Ellipsis. And the compliment of A M E to a semicircle is the angle E M H 145. 21459. The side M E 200000 The side M H 3568 The sum 203568 co. are. 4. 6912905 Differ. 196432 5. 2932122 Tang. ½ sum of the opposite angles 17. 39270 9 4958787 17. 39270 Tang. ½ Differ 16. 81799 9 4803814 Differ 57471 is the angle M E H. Difference doubled 1. 14942 is the angle M B H 3 The mean Anomaly being above 180 deg. the Aequation found must be added to the sunsmeane longitude, so have you the Sun's true place. Example. The Sun's mean longitude 421. 67681 Aequation add 1 14942 The Suns true place 422. 82623 or 2 Signs 2 degrees 82623 parts of a degree Last, to find his distance from the earth, I say, As the sine of M B H 1. 14942 co▪ are. 1. 6977118 Is to the side M H 3568 3. 5524249 So is the sine of B M H 34. 78541 9 7562590 To the side B H 5. 0063957 or distance required 101483 Thus we have found the Sun's place by calculation, we will now show how to reduce the Sun's mean longitude to his true, by the Table of Aequations of the Sun's eccentric. The Sun's Anomaly in this example is 325. 21459 The Aequation of 325 is 1. 15566 326 1. 12648 Difference is 02918 Now then I say if one deg. co. are. 5. Give 2918 3. 4650853 What shall 21459 4. 3316095 The answer is 6●6 2. 7966948 Aequation of 325 deg. 1. 15566 Part proportional subt. 626 Aequation equated 1. 14940 The Snns mean longitude 61. 67681 Aequation add 1. 14940 Suns true place 62. 82621 And in like manner the Logarithme of the Sun's distance from the Earth will be found to be 5. 0063633, which being more necessary than the distance itself, in the calculation of the places of the other planets, we have as most convenient placed in the table. CHAP. 8. Of the Aequation of Civil Days. SOme there are of late, which allow not of any Aequation of Civil Days, others will have the inequality proceed from two causes. First, from the unequal motion of the Sun in the Zodiac, and the other from the Zodiacs obliquity; Tycho (whom we shall follow in this particular,) doth make the difference between the Sun's true longitude and his Right Ascension; to be the absolute Aequation of natural days, the which is also clearly demonstrated, according to the Copernican Systeme by Thomas Street in his Ephemeris for the year 1655; which being but short is here inserted. The Aequation of time demonstrated. Let A be the centre of the Sun, and E of the Earth, ♎ E the earth's longitude from the Equinoctial point in the ecliptic, ♎ F the like arch projected in the Equator, ♎ B the Right Ascension of the Earth's or Sun's true place, G H is a diameter of the Equinoctial and Meridian of the earth's apparent diurnal revolution, A B the semidiameter of the true meridian, and equinoctial supposed in the heavens; and G H parallel to A B (though here they appear as one right line. Then let C D parallel to A F be likewise a diameter of the Equinoctial and Meridian of the mean or equal diurnal revolution. Hence C E G the angle of the earth's libration, equal to B A F the difference of longitude and Right Ascension is the true Equation of time or the difference between the equal and apparent time. And according to this Demonstration is our Table (entitled, A perpetual Table for the Equation of time) composed. In which you must enter with the sign and degree of the Sun's place either in the uppermost and left hand columns descending, or in the lowermost and right hand ascending, and in the common angle is the Equation (according to the titles) to be added or subtracted to or from the equal time, that it may be made apparent; But to reduce the apparent to the equal, take the contrary title. CHAP. 9 Of the Theory and Motion of the Moon. THe Moon according to our Hypothesis is a secondary planet, moving about the earth, as the earth and other planets do about the Sun, and so not only the earth, but the whole Systeme of the Moon is also carried about the Sun in a year, And hence according to Hypparchus there ariseth a twofold, but according to Tycho a threefold inequality in the Moon's motion. The first is periodical, and is to be obtained, after the same manner, as was the excentrique Equation of the Sun or Earth; in order whereunto her middle motions should be first stated, the which Bullialdus by the rules delivered in the fourth and fifth Chapters preceding hath for the Meridian of Uraniburge determined to be as followeth. From the Equinoctial to the beginning of the Christian Aera, the Moons middle motion was 135d. 16′ 27″ The Mean Anomaly 355 5 18 And the Radix of her latitude 366 29 56 These then we will take for granted, until there be a more exact, and true Geometrical way propounded to us,; only we will convert them into decimal numbers, and reduce them to the Meridian of London. From the Equinoctial to the beginning of the Christian Aera, The Moons middle motion in decimal numbers at Uraniburge was 135. 27417 For the Difference of Merid. add . 45750 The Moons mean longitude at London 135. 73167 The Mean Anomaly, At Uraniburge 355. 08833 Differ. Merid. add . 45361 Mean Anomaly at London 355. 54194 The Radix of Latitude At Vraniburge 366. 49889 Differ. Merid. add . 45944 Latitude at London 366. 95833 d. The Diurnal Motion of the Moons Mean longitude 13. 17639 Anomaly 13. 06500 Latitude 13. 22944 The Annual Motion. In longitude 129. 38389 Anomaly 88 71889 Latitude 148. 71278 According to which limitations of the Moon's middle motions, we have composed our Tables, by help whereof and the Semi-excentricity of the Moon's Orb, which according to Bullialdus is 4362 the Moons excentrique equation, or place first equated may be found, as before was showed in the Sun. Save only that here the Moon's Anomaly is given without subtraction. Example. Anno 1587., August 17 ho. 19 41667 in the apparent time, or ho. 19 28973 in the middle time, the Moon being in the meridian of Vraniburge noble Tycho observed her in 26 deg. 38333 of Gemini with latitude 5 deg. 23333 S. from which middle time if you subtract 83333 for the difference of the meridians of London and Vraniburge, the time in our meridian is, ho. 18. 45640. And the Sun's true place 154. 07347. The Sun's distance from the Earth 100895. The Log●rithme of that distance 5. 0038707 The Moons middle motions for the same time are as here you see them. Time given ☽ Longitud ☽ Anomaly ☽ Latitude Years 1500 072. 88194 313. 06916 017. 17805 80 174. 24805 158. 80139 281. 61167 6 069. 48028 18●. 37750 185. 50583 july 27●. 39555 249. 77639 284. 62194 D●yes 16 ●10. 82222 209. 0●972 211. 66944 H●●res 18 ●9. 88222 9 79861 9 92222 Paris 4564 . 250●1 . 24848 . 25152 Mean Longitude 810. 96077 1126. 11125 990. 76067 Deduct 720. 1080. 720. There rests 90. 96077 46. 11125 270. 76067 The Moons mean Anomaly 46. 11125 is the angle A M E in the preceding Ellipsis, or the sum of the angles M E H and M H E. Therefore in the triangle M E H we have given, 1. The side M E 200000. 2. The side M H 8724. 3. The angle E M H the compliments of the Moon's Anomaly, to find M E H, whose double, is the excentrique Equation M B H. I say then, As the sum of M E and M H 208724 co. are. 4. 6804276 Is to their difference 191276 5. 2816605 So is the tang. half sum of the opposite angles, 23. 05562 9 6290228 To the tang half diff. 21. 30786 9 5911109 Differ. 1. 74776 is the angle M E H Differ▪ doubled 3. 49552 is the angle M B H or the equation sought which being subtracted from the Moons mean longitude, because the Anomaly is less than a semicircle you shall have the Moon's place first equated. Example. The Moon's mean longitude 90. 96077 Equation subtract 3. 49552 The Moon's place first equated 87. 46525 And to find her distance from the Umbilique point at H. As the sine of M B H 3. 49552 co. are. 1. 2148808 Is to the side M H 8724 3. 9407156 So is the Sine of B M H 46. 11125 9 8577468 To the side B H 103120 5. 0133432 But whilst the Moon is thus making her own periodical revolution, her whole Systeme is by the motion of the Earth removed from the proper seats thereof, whence there ariseth another revolution which is called Synodical, the beginning whereof is the line which passeth through the centre of the earth to the Sun, and therefore the Moon in that line is void of this second inequality, which is both at the Conjunction and opposition, but being in or about her quarters, where she is farthest removed from the said Zyzigiacal line the angle of her evection is 2 deg. 50′ as is clearly proved by the observations of Tycho and Bullialdus, whose method we follow, in our calculation of this inequality of the Moon, making 4362 the sine of the greatest evection to be the Diameter K D in the little circle K C D H. The motion of this libration of the Moon must be measured by her double distance from the Sun, because she is void of this inequality at her conjunctions and oppositions as was said before. Now then let the angle M H B represent the Moon's equated Anomaly, found by subtracting the former Equation from the simple Anomaly, which is 46. 11125 Aequation subtract 3. 49552 Aequated Anomaly 42. 61573 And if from the place of the moon first equated 87. 46525 You subtract the Sun's true place 154. 07347 Their distance is 293. 39178 The double distance 226. 78356 is the arch K C D H and drawing the lines F H and H K there shall be made the equicrural Triangle H F K, whose exterior angle H F D is known, viz. the excess of the Sun and Moons double distance above a se micircle 46. 78356. The half whereof is the angle D K H 23. ●9178, equal to the angle A H G, which being subtracted from the Equated Anomaly A H B 42. 61573. The angle G H B or the Synodical Anomaly will be 19 2239●, whose compliment to a semicircle is the angle B H K 160. 77605. The side H B 103120 as before, and the side H K may be found in this manner. The arch H V K is the compliment of the double distance of the Sun and Moon to a whole circle 13●. 21644 the subtense of this arch is H K, H V the half arch is 66. 60822, and H X is the right sine thereof. Now then, As the Radius, Is to the Diameter K D 4●62. 3. 6396857 So is the sine of H V or H X 66. 60822 9 9627533 To the Subtense H K 4003 3. 6024390 Therefore in the Triangle B H K we have known, 1. The angle B H K 160. 77605. 2. The side H B 103120 To find the angle H B K. 3. The side H K 4003 To find the angle H B K. As the sum 107123 co. are. 4. 9701173 To the differ. 99117 4. 9961481 So tang. ½ the opposite ang. 9 61197 9 2287638 To the tang. ½ differ. 8. 90502 9 1950292 Their difference 0. 70695 is the angle of the evection, H B K to be added if the Synodical Anomaly be more than 180, and to be subtracted from the place of the Moon first equated when less, as here it is in our example, and therefore to be subtracted from the Moon's place 87 46525, and then her place secondly equated will be 86. 7●830. And according to this Analogy may be made a table of the Moon's evection, when she is in quadrature or 90 degrees distant from the Sun; for then the equated and Synodical Anomalies are both the same, and therefore in the Triangle E M H we have give the angle E H M, or the equated Anomaly which suppose 25 degrees, the side M H 8724 and the side H E ●00000, to find the angle at E. As the sum of H E and M H 208724 co. are. 4. 6804276 Is to their difference 191276 5. 2816605 So is the tang. half sum 10. 6542447 To tang. half differ. 76. 40435 10. 6163328 Their differ. 1. 09565 is the angle M E H Whose double is 2. 19130 is the angle M B H Then as the sine of M B H 2. 1913 co. are. 1. 4175273 To the sine of B M H 27. 1913 9 6598808 So is the side M H . 8724 3. 9407156 To the side B H 10. 4161 5. 0181235 or the Moon's distance from the umbilique. Hence in the first Diagram of this Chapter, in the Triangle B H K we have given A H B the equated Anomaly, 25 degrees, the Moon's distance H B 104161, with the side H K, or rather D K, the Diameter of the little circle 4362, to find the angle H B K. As the sum of H B and H K 108523 co. are. 4. 9644782 To their difference 99799 4. 9991262 So is tang. half sum 12. 50 9 3447552 To tang. half differ. 11. 52314 9 3093596 whose difference. 97686 is the evection sought and by Bullialdus. 97805 which is so little differing from what we have found, that I have taken his Table and converted it into decimal numbers. And for the finding the part proportial between the quadrature and the Zyzygia, Bullialdus whom we follow, hath annexed scruples of proportion in this manner. As Radius to 60 minutes or one degree; so is the fine of half the degrees of the equated Anomaly to the scruples of proportion required. But this proportion in the Sexagenary Canon will not give the scruples either so easily or so exactly as the Decimal Canon will, because the seconds must still be found in that Canon by the part proportional, which in the beginning of the Canon cannot be true, but working by a Decimal Canon the natural sins of half the degrees, are the decimal parts required, as the natural sine of 4 degrees; 069756, are the decimal parts for 8 degrees of equated anomaly, and so of the rest. Having done with the first and second inequalities of the Moon, we come to the third which Tycho calls the variation, Bullialdus the Reflection for as the Moons Systeme is carried about by the earth, the place of her Apogaeon is changed, or doth reflect contrary to the succession of the Signs, by reason of which reflection the angle of her Evection is sometimes more sometimes less than it will be found by the former directions, but the quantity of this variation according to Tycho doth never exceed 40′ 30″ or in Decimal numbers 67500, to be added to or subtracted from the place of the Moon secondly equated, and the proportion by which he finds it is thus, As the Radius To the sine of the compliment of the double distance of the Sun and Moon if less than a Semicircle: To the excess if more: So is the sine of the greatest variation, or Reflection. To the variation required, which is to be added to the Moon's place, secondly, equated if the double distance be less than 180 deg. to be subtracted, when it is more. Therefore in our Example, As the Radius To the sine of H F D 46. 78356 9 8625917 So is the sine of 67500 8. 0711591 To the variation 49189 7. 9337508 The Moon's place secondly equated 86. 75830 Variation subtract 49189 The Moon's place in her Orb 86. 26641 Lastly, to find the Moon's latitude and place in the Ecliptic, take the middle motion of her latitude for the time propounded, the which rejecting the whole circles is 270. 76067 and in which according to Tycho there is a twofold variation, The first is occasioned by the various intersection of the Moon's orb with the Zodiac, and the other by the reciprocal progression and retrogradation of the Nodes. In the New and Full Moons the limits of her greatest latitude, are 4. 97500, but in her quarters 5. 29167, as Tycho hath experimented by many diligent and accurate observations, whose method of calculation is as followeth. From the mean motion of the Moon's latitude 270. 76067 Subtract the Moon's absolute Equation 4. 694 6 The Equated latitude of the Moon 266. 06631 Then to find the Equation of the Nodes, let the line A D or the angle A T D 5. 13333 represent the mean inclination of the Moon's Orb with the Ecliptic, let the least inclination be represented by A B 4. 97500, and the greatest by A C 5. 29166. And from the distance of the Sun and Moon before found, 293. 39178 Subtract the evection and variation A 1. ●9884 True distance of the Sun and Moon 292. 19●94 The double thereof is 224. 385●8 which being numbered from B by C to F in the Triangle F D A we have known A D 5. 13333 the mean inclination of the Moon's Orb. 2. D F 15833 the half difference of the least and greatest inclination. 3. With the angle F D A 135. 61412, the compliment of the double distance of the Sun and Moon to a whole circle: whence to find the angle F A D the Aequation of the Nodes, by the Doctrine of spherical Triangles say, First, As the Radius To the cousin of F D C 44. 38588 9 8540905 So is the tang. of D F 15833 7. 4413175 To the tang of D C 11321 7. 2954080 Add the arch A D 5. 13333 Sum is A C 5. 24654 2 As sine D C 11321 c●. are. 2. 7046002 To the sine A C 5. 24654 8. 9611430 So cotang. F D C 44. 38588 10. 0093107 To cotang. F A D 1. 21062 11. 6750539 From the Moon's latitude equated 266. 06787 Equation Nodes subtract 1. 21062 True motion of the Moon's latitude. 264. 85725 whose compliment to a whole circle 95. 14275 And to find A F or the angle of 〈◊〉 A T ●, the 〈…〉 of the Sun and Moon being more than 180 degrees, and less th●●●●●▪ I deduct the Moon's double distance 224 d. 3858● being numbered ●● the little circle, from B by C to F, from the Arch B C F G 270, there remains F G 45. 61412, and then the Analogy is, As the Radius D C 10. 0000000 To the sine of F G or D F 45. 61412 9 8540305 So is the sine of the arch, D C . 15833 7. 4413159 To the sine of the arch D E . 11319 7. 2953464 The aggregate is B E. 27152 which being added to the least angle of inclination A T B, or the arch A B 4. 97500 the present inclination is A F or the angle A T F 5. 24652. Hence to find the Moon's true latitude, I say, As Radius 10. 0000000 To the sine of A T F 5. 24652 8. 9611413 So is the sine of A T 84. 85725 9 9982481 To the sine of A F 5. 22533 8. 9593894 or the angle A S F. And by these Analogies may be made the Table of the Moon's latitude which we have borrowed of Tycho, converting it only into decimal numbers.) For supposing the Moon to be in her Syzygial points, the angle of Inclination is always A T B 4. 975, and then her latitude for every degree of her true motion of latitude may be found by the last Analogy; As Radius Example. To the sine of A T B 4. 975 8. 9381242 So is the sine of A T 45. 9 8494850 To the sine of A B 3. 51564 8. 7876092 And her latitude when she is in Quadrature or 90 degrees distant from the Sun may be found by the same analogy, if you make the angle of Inclination A T C 5. 29166. Example. As Radius To the sine of A T C 5. 29166 8. 9648517 So is the sine of A T 45. 9 8494850 To the sine of A F 3. 73910 8. 8143367 Subtract A B 3. 51564 there rests the Excess to be placed in the Table 0. 22346. The proportipnal part of which excess to be added to the Moon's laitude must be found by scruples of proportion, and the Scruples themselves for every degree of the Moon's distance from the Sun may thus be had. As Radius▪ To the Co●ine of the Moon's double distance D H 40 9 8842539 So is the sine of D B 0. 15833 7. 4413575 To the sine of D H 0. 12142 7. 3256114 Their differ▪ is B H 0. 03691 Than as the Diameter B C 31666 5. 4994068 Is to the Diameter B C 100 000 5. 0000000 So is B H 0. 03691 3. 5671440 To B H 0, 11656 4. 0665508 Or more readily thus D H 76604 is the sine of 50 or the Cousin of 40 the Moons double distance from the Sun, which being deducted from Radius, the remainder is the versed sine B H 23396 the half 11698, are the scruples of proportion answering to 20 deg. of the Moon's single distance from the Sun, From the Moon's place in her Orb 86. 26641 Subtract the Moon's true latitude 264. 85725 The Moon's Node ascending 181. 40916 Lastly, for her Reduction▪ As Radius To the Cousin of A T F 5. 24775 9 9981757 So tang. of A T 84. 85725 11. 0458587 To tang. of T F 84. 83689 11. 0440344 Difference 02036 is the Reduction sought From the place in her Orb 86. 26641 Subtract her Reduction . 02036 The Moon's place in the Ecliptic 86. 24605 CHAP. 10. To calculate the true Motion of the Moon by Tables. HAving gathered the mean motions of the Moon's Longitude, Anomaly, and argument of Latitude, as in the last Chapter, by the Anomaly find the Moon's Eccentrick equation, and by that her Eccentrick place. 2 Apply her eccentrick Equation acoording to the title both to the mean Anomaly, and to the motion or argument of Latitude; So have you the equated Anomaly and motion of Latitude, first equated. Example. Anno 1587., August 17 ho. 18. 45640 the Moons mean Longitude was before found to be 90. 96077 Her mean Anomaly 46. 11125 Her motion of Latitude 270. 76067 Her Eccentrick equation to 47 deg. 3. 54892 46 deg. 3. 48880 Differ. 0. 06012 Now then as 1 deg. 5. 0000000 Is to 06012 3. 7790190 So is 11125 4. 0463000 To 00668 2. 8253190 To the Equation of 46 deg. 3. 48880 Add the part proportional 668 The Moons eccentrick Equation 3. 49548 which being subtracted from her mean Longitude, Anomaly and Latitude. Her place first equated is 87. 46529 Her equated Anomaly 42. 61577 Her Latitude first Equated 267. 26519 3. By her mean Anomaly you must also find the Logarithme o●he● distance from her umbilique. The Logarithme to 46 Deg. is 5. 0133649 47 Deg. is 5. 0131474 Differ. 2175 As if one Degree 5. 0000000 Is to 2175 3. 3374592 So is 11125 4. 0463000 To 241 2. 837592 Which being deducted from 5. 0133649 The Moon's Logarithme is 5. 0133408 4▪ Subtract the true place of the Sun, from the Moon's eccentrick place, so have you the distance of the luminaries, with the double whereof seek in the Table the eccentricity of the Moon's evection, and the quantity of her variation or reflection, using the part proportional if need require. 5 If the double distance of the luminaries with which you enter the Table be less than a semicircle, add half the compliment thereof unto the equated Anomaly, or if it be more than a semicircle, deduct half the excess above a semicircle from the equated Anomaly, than the sum or difference if less than a Semicircle, is the sum of the opposite angles, or if it be more, take the compliment, to a whole circle. Example. ☉ Longitude ☉ Apogaon Years 1500 290. 20076 94. 01167 80 . 59826 1. 26342 6 359. 55205 . 09473 july 208. 95710 917 Days 16 15. 77035 69 Hours 18 . 73923 Parts 4564 . 01874 Suns Longitude 875. 83649 95. 37968 Apogaeon subtract 095. 37968 Mean Anomaly 060. 45681 The Suns eccentrick to 61 deg. 1. 77254 The Suns eccentrick to 60 deg. 1. 75464 Difference 1790 As one degree 5. 0000000 Is to 1790 3. 2528530 So is 45681 4. 6597●56 To 817 2. 9125886 The equation to 60 deg. 1. 75464 Add th● part proportional 817 The absolute Equation subtract 1. 76281 From the Sun's mean Longitude 155. 83649 The Suns true place subtract 154. 07368 From the Moon's eccentrick place 87. 46529 The distance of the Sun and Moon 293. 39161 The double distance 226. 78322 The Logarithme of the Eccentrick to 226 deg. 3. 6037118 The Logarithme of the Eccentrick to 227 deg. 3. 60208●4 Difference 16284 As one degree 5. Is to 16284 4. 2117610 So is 78322 4. 8938837 To 12753 4. 1056447 which being subtracted from 3. 6037118 The Logarithme of the Eccentricity is 3. 6024365 Thus we have found the Logarithms of the two lateral distances, namely of the distance of the Moon from her Umbilique▪ 5. 0133408 and of the Eccentricity of her Evectioon 3. 6024365. And because the double distance of the Sun and Moon is more than a semicircle 226. 78322 Deduct 180 there rests 46. 78322 The half whereof 23 39161 Deduct from the equated Anomaly 42. 61577 There resteth the Synodical Anomaly ●9. 22416 or sum of the opposite angles. Hence to find the Evection, Say, As the greater Logarithme co▪ are. 4. 9866502 Is to the lesser 3. 6024365 So is Radius ●0. 000●●●0 To the tang. of 2 deg. 22494 8. ●890●●● Add 45 2 Operation. As Radius 10. 0000000 To the Cotang. 47. 22494 9 9662367 So tang. half sum 9 61208 9 2287955 To the tang. half dif. 8. 90555 9 1950324 Evection 0. 70653. Subtract because the Synodical anomaly is less than 180. Then for the variation, I enter the Table with the Moon's double distance 22678322; and using the part proportional I find it to be 0. 49186 subtract. The Evection to be subtracted is 0. 70653 The Variation to be subtracted is . 49186 Their sum 1. 19839 Subtract from the Moons Eccentrick place 87. 46529 There rests the Moon's place in her Orb 86. 26690 Otherwise thus. Enter the Table entitled Bullialdus his Table of Evections, with the Synodical Anomaly 19 224●6, and using the part proportional you shall find it to be 75942, subtract, then take from thence with the Moon's double distance 226. 78322 the scruples of proportion also, the which observing the part proportional are; 91781, by which the Evection found is thus to be corrected. As 1 degree is to 75942: so is 91781 to the Evection sought 69701 subtract, and this subtracted according to the title from the Moon's Eccentrick place 87. 46529 There rests her place secondly equated 86. 75828 Then for the variation enter this or the former table with the Moons double distance 226. 78322, and using the part proportional you shall find it to be 49186 as before, with the title Subtract; and therefore the Moon's place in her Orb 86. 26742, but little differing from the former. And from these two Tables of Evection & Variation, we have composed a third Table, entitled a compounded Table of the Moons second and third inequalities, for the yet more speedy finding of these equations, whose construction is thus. First, enter the Table of the Moon's Evection with her Synodical Anomaly to find the Evection, and with her double distance from the Sun to find the Scruples of proportion. The Moon's double distance may be supposed, and the Synodical anomaly easily made from it: as suppose the Moon's distance from the Sun to be 3 degrees thereof to a quadrant 87 being added to the equated Anomaly which you may also suppose to be what you please, will give the synodical Anomaly, thus if the equated Anomaly be 25, add 87 thereto, and then the synodical Anomaly will be 112 and the angle of evection answering thereto 2. 38861 subtract: and the scruples of proportion answering to 6 degrees 52335. Hence to find the true evection. I say, As 1 degree 1. 00000 0. 0000000 Is to the evection in the table 2. 38861 0. 3781452 So are the Scruples of prop. 0. 52335 1. 7187912 To the evection sought, Sub. 0. 12500 0. 0969374 The variation to 6 deg. add 0. 07055 And because the evection and variation are of different titles therefore there difference 05445 is the compounded equation sought, which I place against 25 degrees of equated Anomaly in the column of 3 deg. of the Moon's distance from the Sun, with the title subtract, because the title of the biggest number was subtract. And therefore the second and the third inequalities of the Moon are to be found in this table by entering it with the Moon's distance from the Sun in the head or foot of the table, and with the equated Anomaly in the sides, for so the common angle using the part proportional, if need require, will give the Equation sought to be applied to the Moon's place according to the title. Example. Suppose the distance of the Sun and Moon were 293. 39161, that is, deducting a Semicircle 113. 39161, and her equated Anomaly 42. 61577 because the Moon's distance from the Sun is found in the bottom of the table, I number the equated Anomaly in the first column towards the right hand ascending, and in the common angle (by making proportion for the intercepted degrees) I find the Equation to be 1. 188 S. that is the title subtract, and therefore this Equation being subtracted from the Moon's Eccentrick place, what remaineth shall be the Moon's place in her orb. CHAP. 11. To find the Moon's true Latitude and place in the Ecliptic. TO the motion of Latitude first Equated, according to the title apply the agregate of the Moons second and third Equations, so have you the motion of Latitude secondly equated. 2. To the distance of the Sun and Moon before found apply the agregate of the Moons 2 d. and ● d. Equations according to the title, so have you the true distance of the Sun and Moon. Example. Motion of Latitude first equated 267. 26519 Second and third equations sub. 1. 19839 Motion of Latitude secondly equated 266. 06680 Distance of the Sun and Moon as before 293. 39161 Second and third Equation sub. 1. 19839 True distance of the Sun and Moon 292. 19322 3. With the true distance of the Sun and Moon enter the table of the Equation of the Nodes, and take thence the Equation of the Nodes, which according to the title, apply to the motion of Latitude secondly Equated, and you have the true and absolute motion of Latitude. At the same entrance take out also the scruples of proportion and reserve them. Example. With the true distance of the Sun and Moon 292. 19322 I find the Equation of the Nodes, subt. 1. 21103 From the Latitude secondly Equated 266. 06680 So the true motion of Latitude 264. 85577 And the scruples of proportion 85729 4. With the true motion of Latitude enter the table of Latitude, and thence take the Latitude and the excess, then say, as one degree to the excess in the table: so are the scruples of proportion before reserved, to the excess sought, which being added to the Latitude found by the table, the sum shall be the true Latitude of the Moon, which is North when the true motion of Latitude is less than 6 ●ignes, and South when it is more. Example. The true motion of Latitude 264. 85577 Gives The Latitude 4. 95490 Gives The Excess 31519 As one degree 1. 00000 To the excess in the table 31519 1. 4985724 So the scrupls of propor. 85729 1. 9331277 To the excess desired 27020 1. 4317001 Which being added to the Latitude 4. 95490 It gives the true Latitude▪ South 5. 22510 5. If the true motion of Latitude be subtracted from the Moon's true place in her orb, there resteth the Node Ascendant. As The Moon's true place 86. 26690 As The Motion of Latitude subt. 264. 85577 The Node ascendant 181. 41113 6. With the true motion of Latitude enter the table of Reduction, and take out the Reduction, which according to the title apply to the Moon's place in her orb, you have her true place in the Ecliptic. Example. The true motion of Latitude 264. 85577 Gives the reduction to be subt. 02067 From the Moon's place in her Orb 86. 26690 The Moons place in the Ecliptic 86. 24623 CHAP. 12. Of the motion of the fixed Stars. THe motions of the fixed Stars are by the observations of all ages found to be equal, and the quantity of that equal motion, Noble Tycho by comparing his own observations with those of the ancients hath determined to be exact 51 seconds, Bullialdus' 50″ 55‴ ferè, and the place of the first Star in Aries in the year of our Lord 1600 complete to be 27 deg. 37 min. which being converted into decimals the Radix of the middle motions of the fixed Stars at that time will be 27. 61667 and the yearly motion. 01414, that is the decimal of 50 seconds 55 thirds. Hence to find their places at any time assigned, we have exhibited a table of the longitudes and latitudes of some of the most notable fixed Stars for the year 1650 complete, which by the motions of the fixed stars in the tables of the Suns mean motions, may thus be done for any other time. Take the difference between the time given and 1650 complete, and the motion agreeing to that difference, this motion subtract from the place in the table when the time given is before 1650, or else add it, and you have the place desired. The Latitudes and Magnitudes are still the same. Example. The time given 1683 September. Difference from 1650 compl. 33 year 8 Month's Motion Correspondent . 476●8 Place of Oculus ♉ 1650 compl. ♊ 4. 91667 Place required ♊ 5. 39305 Latitude South 5. 51667 CHAP. 13. Of the Motion of Saturn. OUr Tables of Satur's mean motions as of the other Planets, are he same with those of Bullialdus, being only reduced to the Meridian of London, and converted into decimal numbers whose eccentrick being so easy to be found, and the investigation of his true place, with the places of Jupiter, Mars, Venus and Mercury, being out of curiosity, rather than use▪ we shall content ourselves with the trigonometrical calculation only, first, of Saturn for the time before given 1587. August 17: h: 18: 4564: and then of the rest. An. Christ. Longit. ♄ Aphel. ♄ Node ♄ 1500 064. 98279 262. 82583 109. 79361 80 258. 76528 2. 5●694 0. 57611 6 73. 39056 . 19078 0. 04306 july▪ 7. 10111 . 01833 . 00444 D 16 . 53183 . 00139 . 00030 H 18 . 02500 P 4564 . 00063 Mean Mot. 404. 801 20265. 57327110. 41752 Aphel. Subt. 265. 57327 Rests Anomaly 139. 22793 The half of Satur's first inequality, or his eccentricity supposing the Semidiameter of Satur's orb to be 100 000. is 5774. and the Semidiameter of the Earth's orb 10480. As they are computed by Bullialdus, but the Semidiameter of the Earth's orb being before supposed to be 100 000 the Semidiameter of Satur's orb will be 954198, for as 10480 is to 100 000. So is 100 000. to 954198. and Satur's eccentricity in the same parts will be 55145. for as 100 000 is to 954198. So is 5774 to 55145. whose double 110200 is the side M H in the figure following; in the triangle therefore M E H, we have known, 1. The Angle H M E 40. 77207, the compliment of Satur's Anomaly to a semicircle ●●9. 22793 or the half sum of the angles M E H and M H E viz. half the anomaly 69. 61396. 2. The side M E 1908396 To find the Angle M E H. 3. The side M H 110290 To find the Angle M E H. As there sum 2●18686 co. are. 3. 694931● Is to their differ. 1798106 6. 2548153 So is tang. half sum 69. 61396 10. 4299016 To tang. half diff. 67. ●5375 10. 3796482 Difference 2. 26021 is the angle M E H. Difference doubled 4. 52042 is the angle M B H, or the Equation sought, to be subtracted from Satur's mean Longitude, the Anomaly being less than a semicircle. Satur's mean Longitude 44. 80120 Equation Subt. 4. 52042 Satur's eccentrick place 40. 28078 2. To find his distance from the Sun. As the sine M B H 4. 52042 co. are. 1. 1034042 Is to the side M H. 110290 5. 0425361 So sine E M H 40. 77207 9 8149473 To the side B H 913876 5. 9608876 ●. From the eccentrick place of Saturn subduct the Node, there resteth the argument of Latitude: by help whereof and the angle of his greatest inclination, which according to Bullialdus is 2 d. 50, or 4362, we may easily find his Reduction, but the side E B 4362 in the parts of 100 000, must be reduced into the parts of Satur's semidiameter 954198, to find the curtation. As 100 000 is to 954198, so is 4●62 to 41622. Satur's eccentrick place Example. 40. 28078 Node subtract 110. 41752 Argument of Latitude 289. 86326 Whose compliment is K L 70. 13674 As Radius To cousin of XKL 2. 50 9 999586 So is tang. of KL 70. 13674 10. 4421682 To tang. of 70. 12929 10. 4417546 Whose difference . 01745 is the Reduction sought: And to be subtracted from the ecceutrick place, if he move from either Node towards the limits of his greatest latitude, but if he depart from the limits and approach towards the Nodes the reduction is to be added, for so the sum or difference will be the place in the Ecliptic. As in our example, Saturn is passed the limits of his greatest latitude, and is approaching towards his Node, and therefore the reduction is to be added. Satur's eccentrick place 40. 28078 Reduction add . 01745 The eccentrick reduced 40. 29823 The inclination of his orbite from the eccliptique represented in the second figure following by the line XL, may thus be found. As the Radius KE 90. To the greatest in clination EBB 41622 4. 6193229 So is the sine of KL 70. 13674 9 9733616 To the side XL ●9145 4▪ 5926845 which is the inclination agreeing to the common Radius 954 198, whereas the distance of Saturn from the sun is to be put for the Radius, and then XL will be but 37491. As DL 954198 co. are. 4. 0203616 To ALL 913876 5. 9608876 So is XL 39145 4. 5926845 To XL 37491 4. 5739336 The distance of Saturn in his orbite from the Sun being given with the inclination of his orbite from the eccliptique, the distance corrected by curtation may thus be found. To find Satur's second inequality. Subtract the sun's place from the Eccentrick reduced, or this from it, so that less than 180 degrees may remain, this remainder is the Anomaly of the orb, the compliment whereof is the angle NAS, or the half, is the half sum of the opposite angles. Example▪ Satur's Eccentrick reduced 40. 29823 The Suns true place 154. 07347 The Anomaly of the orb 113. 77524 The angle NAS 66. 22476 The half Anomaly 56. 88762 As the greater side AN 913107 co, are. 4. 0394781 Is to the less AS 100895 5. 0038707 So Radius, to the tang. 6. 30541 9 0433488 Add 45. As Radius To cotang. of the sum 51. 30541 9 9036304 So is tang. half sum 56. 88762 10. 1856192 To tang. half differ. 50. 84613 10. 0892496 Sum 107. 73375 Angle ASN. Differ. 6. 04149 Angle ANS. Because Saturn eccentrick reduced was subtracted from the Sun's true place, therefore the angle of his Elongation ASN 107. 73375 must be subtracted also, and then Satur's place will be 125. 19972. To find Satur's distance from the Earth. To find the latitude of ♄ from the earth. As SX. 877291 Co. are. 4. 0568610 Is to Radius 10. 0000000 So is XL, 37491 4. 5739336 To the tang. of XSL, 2. 44711. 8. 6307946 which is the quantity of ♄ Southern Latitude, because the argument of Latitude was more than 6 signs, when it is less than 6 signs, the Latitude is North. CHAP. 14. Of the Motion of Jupiter. THe investigation of the place of this and the other Planets, is well nigh the same with that of ♄, they differ more in the Dimensions of their Orbs, then in the manner of their calculation. Yet that there may be no mistake, we will not only give you the Dimensions of their several orbs, but makes examples of their calculation to the former time given. The mean motions of Jupiter. Anno Christi. Longitude ♃ Aphelion ♃ Node ♃ Years 1500 004. 50000 185. 54833 097. 93889 80 269. 04444 1. 98000 . 54722 6 182. 13667 . 14833 . 04111 july 17. 62333 . 01444 . 00389 Days 16 1. 33000 . 00104 . 00030 Hours 18 . 06222 Parts 4564 . 00154 Mean motion. 474. 69820 187. 68414 98. 53141 Aphelion subt. 187. 68414 Rests Anomaly 287. 01406 The half of Jupiter first inequality, or his eccentricity, supposing his Semidiameter to be 100 000 by the computation of Bullialdus is 4856, and the Semidiameter of the Earth's Orb 19138▪ and therefore to find ♃ Semidiameter, when the Semidiameter of the Earth's Orb is 100 000 the proportion is, As 19138. Is to 100 000 so is 100 000 to 522520, the Semidiameter required, which being doubled is the Diameter of the Ellipsis, or the side M E 1045040. And to find the eccentricity in the same parts, say, as 100 000. is to 522520, so is 4856, to 2537●. the excentricity, and the double thereof. 50746 is M H the distance of the foces. The compliment of the Anomaly 72. 98594 is the angle A M E, and the half compl: 36. 49297, is the half sum of the opposite angles M E H and M H E. The side M E 1045040 The side M H 50746 Sum 1095786 co. are. 3. 9602744 Differ 994294 5. 9975147 Tang. ½ sum 36. 49297 9 8690974 Tang. ½ differ 33. 87162 9 8268865 Differ. 2. 62135 Angle M E H Double differ. 5. 24270 Angle M B H or the Equation sought, and to be added to Jupiter's mean longitude, the Anomaly being above a Semicircle. Jupiter's mean longitude 114. 69820 Equation add 5. 24270 Jupiter's eccentrick place 119. 94090 The Node subt. 98. 53141 Argument of Latitude. 21. 40949 By help whereof, and the angle of his greatest inclination 1. 36333, or E B 2379, we may find the reduction: but to find the parts of inclination in proportion to the given Radius 522520. say, As 100 000. is to 2379, so is 522520 to 13619. the parts required. To find the Reduction. As Radius So Cousin of X K L. 1. 36333 9 9998770 To tang. of K L. 21. 40949 9 5933823 To tang. of X K. 21. 40353 9 5932593 Differ. . 00596 Reduction. Because the argument of Latitude is less than 90. the Reduction must be subtracted from the eccentrick place. Jupiter's eccentrick place 119. 94090 Reduction subt. . 00596 Eccentrick reduced 119. 93494 To find the Inclination. As Radius To the greatest inclin: E B 13619 4. 1341452 So is the sine of K L 21. 40949 9 5623296 To the side X L 4971 3. 6964748 which are the parts of inclination agreeing to the common Radius 522520, but the distance of ♃ from the ☉ is to be put for the Radius, the which distance may thus be found. As the sine of M B H 5. 24270. Co. are. 1. 0391741 Is to the side M H 50746 4. 7054018 So is the fine of E M H 72. 98594 9 9805636 To the side B H 531055 5. 7251395 As the common Rad: D L 522520 Co. are. 4. 2818971 To Jupiter dist: B H or A L 531055 5. 7251●95 So is X L 4971 3. 69647●8 To X L 5052 3. 7035114 To find ♃ distance corrected by Curtation. As A L 531055 Co. are. 4. 2748605 Is to Radius 10. 0000000 So is L X 5052 3. 7035114 To the sine of L A X 54515 7. 9783719 As the Radius To A L 531055 5. 7251395 So is the Cousin of L A X 9 9999831 To A X 531034 5. 7251226 To find the second inequality of Jupiter. We must have given, 1. The angle N A S, which is to be found by subducting the ☉ place from ♃ eccentrick or reduced, or this from it, so that less than 6 Signs may remain, this remainder is the Anomaly of the Orb, and the Compliment thereof is the Angle N A S, or the half is the half sum of the opposite angles. Example. Jupiter's eccentrick reduced 119. 9●494 ☉ True place 154. 07347 The Anomaly of the Orb 34. 13893 The angle N A S 14. 86107 The half Anomaly is 17. 0694● These given with the sides N A and A S, I say. As the greater side A N 531034 co. are. 4. 2748774 Is to the Radius 10. 0000000 So is the lesser side A S 100895 5. 0038707 To the tang. of 10. 75783 9 2787481 Add 45 Asdruball Radius to Co-tang. 55. 75783 9 8329403 So tang: of ½ sum 17. 06946 9 4872186 To tang. of ½ differ. 11. 80522 9 3201589 Sum 28. 87468 Angle A S N Differ. 5. 26424 Angle A N S Because ♃ eccentrick reduced was subtracted from the ☉ place, therefore the angle of his Elongation A S N 28. 87468 must be subtracted also, and so ♃ place 125. 19839. To find the distance of Jupiter from the Earth. As the sine of A N S 5. 26424 co. are. 1. 0373985 To the side A S 100895 5. 0038707 So the sine of N A S 34. 13893 9 7491287 To the side S N 603111 5. 7803979 To find the latitude of ♃ from the Earth. As the side S N 603111 co. are. 4. 2196021 To the side X L 5052 3. 7035114 So is the Radius 90 10. 0000000 To tang. of X S L 0. 47998 7. 9231135 Which is the quantity of ♃ Northern latitude. CHAP. 15. Of the Motion of Mars. THere being no other variety in calculating the place of this Planet, than what hath been already showed, in the motions of Saturn and Jupiter, we will proceed in the same method, and gather first the middle motions for the former time given, and then show the Dimensions of his several Orbs, as we shall have occasion for them. An. Christ. Longit. ♂ Aphel. ♂ Node ♂ Years 1500 245. 61611 146. 80916 45. 40250 80 193. 32778 1. 75139 1. 07194 6 68 23750 . 13139 . 08028 july 111. 10306 . 01250 . 00778 D 16 8. 38500 . 00096 . 00057 H 18 . 39306 P 4564 . 00996 Mean Mot. 627. 07247 148. 70540 046. 56307 Aphel. Subt. 14. 70540 Rest Anom. ●19. 36707 Supposing the Semidiameter of ♂ his Orb 100 000 His eccentricity according to Bullialdus is 9239 Semidiameter of the Earth's Orb 656●8 The sine of his angle of Inclination 3230 And the Arch answering thereto 1. 85111 And therefore suppose the R. of the Earth's Orb 100 000 The eccentricity of Mars will be 14075 The Semidiameter of his Orb 152350 The parts of his greatest Inclination 4921 The Anomaly 119. 36707 is the angle A M E in the Ellipsis of the 13 Chapter, and therefore the half of it is the half sum of the angles M E H and M H E 59 68353 2. The side M E 304700 3. The side M H 28150 Sum 332850 co. are. 4. 4777515 Differ. 276550 5. 4417726 Tangle: ½ sum 59 68353 10. 2330382 Tangle: ½ diff: 54. 86290 10. 1525633 Difference 4. 82063 Angle M E H Difference doubled 9 64126 Angle M B H or the Aequation sought, and to be subtracted from the planets mean Longitude, because the Anomaly is less than 180. viz. 119. 36707. Mean longitude of Mars 267. 07247 Aequation subtracted 9 64126 Mars his Eccentrick place 257. 43121 To find his distance from the Sun. As the sine of M B H 9 64126 co. are. 0. 7760404 To the side M H 28150 4. 4494783 So is the sine of M B H 60. 63293 9 9402403 To the side B H 146473 5. 1657590 From the eccentrick place sub: Node. 119. 36707 Argument of Latitude 128. 06614 Whose compliment is K L 51. 93586 To find the Reduction. As the sine of 90 To Cousin the great inclin: X K L 1. 85111 9 9997732 So tang: of K L 51. 93494 10. 1061739 To tang: of X K 51. 92039 10. 1059471 Differ. . 01455 Reduction. Because the argument of Latitude is more than 90, the Reduction must be added to the Eccentrick place. The eccentrick place of Mars 257. 43121 Reduction add . 01455 Eccentrick reduced 257. 44576 To find the present inclination. As Radius To the greatest inclin: E B 9921 3. 6920533 So the sine of K L 51. 93494 9 8960878 To the X L 3873 3. 5881411 Which are the parts of inclination agreeing to the common Radius, 152350. But the distance of Mars from the ☉ is to be put for the Radius, and then the parts of inclination will be 3724. For as common Radius D L 152350 co. are. 4. 8171576 To ♂ distance B H or A L 146473 5. 1657590 So is X L 3873 3. 5881411 To X L 3724 3. 5710577 To find the distance of ♂ corrected by Curtation. As A L 146473 co. are. 4. 8342410 To Radius 10. 0000000 So is X L 3724 3. 5710577 To the sine of L A X 1. 45703 8. 4052987 As Radius To A L 146473 5. 1657590 So Cousin of L A X 1. 45703 9 9998596 To A X 146426 5. 1656186 To find the second inequality of Mars. We must have given, 1 The angle N A S, which is to be found by subducting the ☉ place from the eccentrick of ♂ reduced, or this from it, so that less than 6 signs may remain, this remainder is the Anomaly of the Orb, and the compliment thereof is the angle N A S, or the half, is the half sum of the opposite angles. Example. The eccentrick of ♂ reduced 257. 44576 The ☉ true place 154. 07347 Anomaly of the Orb 103. 37229 Compliment is N A S 76. 62771 Half Anomaly 51. 68614 These given with the sides N A & S A, I say, As the greatest side N A 146426 co. are. 4. 8343814 Is to Radius 10. 0000000 So is the lesser side S A 100895 5. 0038707 To the tang. of 34. 56887 9 8382521 Add 45 Asdruball Radius To co-tang. 79. 56887 9 2650444 So tang. ●/● sum 51. 68614 10. 1022929 To tang. ½ diff. 13. 11536 9 3673373 Sum 64. 80150 angle A S N Differ. 38. 57078 angle A N S Because the Sun's place was subtracted from the eccentrick of ♂ reduced, therefore the angle of elongation A S N 64. 80150 must be added to the ☉ place 154. 07347 and then the place of ♂ will be 218. 87497. To find the distance of ♂ from the Earth. As the sine of A N S 38. 57078 co. are. 0. 2051769 To the side A S 100895 5. 0038707 So sine of N A S 76. 62771 9 9880626 To the S N 157438 5. 1971102 To find the latitude of Mars from the Earth. As the side S X 157438 co. are. 4. 8028898 To the side X L 3724 3. 5710577 So is Radius 10. 0000000 To tangent of X S L 0. 13560 7. 3739475 Which is the quantity of ♂ his Northern latitude. CHAP. 16. Of the Motion of Venus. HAving done with the three superior Planets, Saturn, jupiter and Mars, we come to the two inferior, Venus and Mercury, the investigation of whose places is much after the same manner with the former, the difference is in the second inequality, occasioned by their motion under the earth, the Orbs of the other Planets being above it; that this difference may be the better discerned, we have added an example in each for the time before given. The mean motions of Venus. An. Christ. Longit. ♀ Aphel. ♀ Node ♀ Years 1500 333. 11667 303. 97639 073. 28944 80 15. 48472 1. 12694 . 67028 6 270. 36028 . 08444 . 05028 july 339. 65833 . 00806 . 00500 D 16 25. 63472 . 00062 . 00039 H 18 1. 20194 P 4564 . 03048 Mean Mot. 265. 48714 305. 19645 074. 01537 Aphel. Subt. 305. 19645 Rest Anom. 320. 29069 The Semidiameter of the orb of Venus, in such parts of which the Earth's orb is 100 000, by the computation of Bullialdus is 72398, her Eccentricity 575. The parts of her greatest inclination 4270. And the angle itself 3. 38111. In the triangle therefore of the following Diagram M E H, we have three things given. 1. The half sum of the angles M E H and M H E 19 85465, viz. the half compliment of the mean Anomaly to a circle. 2. The side M E 144796 3. The side M H. 1150 Sum 145946 co. are. 4. 8358079 Difference 143646 5. 1572934 Tang. half sum. 19 85465 9 5576273 Tangent half difference 19 56560 9 55072●6 Difference . 28905 Angle M E H. Differ. doubled . 57810 Angle M B H. or the Equation to be added to the mean longitude, because the Anomaly is more than a semicircle. The mean Longitude of Venus 265. 48714 Equation add . 57810 The eccentrick place of Venus 266. 06524 Node subtract 74. 01537 Argument of latitude K L 192. 04987 To find the distance of Venus from the Sun. As the sine of M B H 0. 57810 co. are. 1. 9961373 To the side M H 1150 3. 0606978 So the sine of H M B 39 70931 9 8054279 To the side B H 72822 4. 8622630 To find the Reduction. As the Radius To the Cousin of the great inclina. X K L 3. 38111 9 999●433▪ So tangent of K L 12. 04987 9 329●295 To tangent of X K 12. 02950 9 3285728 Difference . 02037 Reduction. Because the Argument of Latitude is more than 180, the Reduction must be subtracted from the eccentrick place. The eccentrick place of Venus 266. 06524 Reduction subtract . 02037 Eccentrick reduced 266. 04487 To find the present inclination. As Radius To the greatest inclinat. E B. 4270 3. 6304●78 So sine of K L 12. 04987 9 3196533 To the inclinat. X L 891 2. 9500811 Which are the parts of inclination agreeing to the common Radius 72398, but the distance of Venus from the Sun, 72822 being put for Radius, the inclination will be 896. As the common Radius D L 72398 co. are. 5. 1402735 To Venus' distance B H or A L 72822 4. 8622630 So is X L 891 2. 9508115 To X L 896 2. 9526176 To find the distance corrected by Curtation. As A L 7●822 co. are. 5. 1377370 To Radius, so is X L 896 2. 9526176 To the sine of L A X 0. 70550 8. 0903546 As Radius To A L 72822 4. 8622630 So Cousin of L A X 07055 9 9999671 To A X 72816 4. 8622301 To find the second inequality of Venus. We must have given, 1. The angle N A S which is to be found by subducting the Sun's place from the eccentrick of Venus reduced, or this from it so that less than 6 signs may remain, this remainder is the Anomaly of the orb and the compliment is the angle N A S, or the half is the half sum of the opposite angle. Example. The eccentrick of Venus reduced 266. 04487 The Suns true place 154. 07347 Anomaly of the orb 111. 97140 Compliment is N A S 68 02860 Half Anomaly 55. 98570 These given with the sides N A and S A the Analogies are. As the greater side S A 100895 co. are. 4. 9961293 Is to Radius 10. 0000000 So is the lesser side N A 72816 4. 8622300 To the tangent of 35. 81815 9 8583593 Add 45. As Radius To cotangent 80. 81815 9 2085475 So tang. half sum 55. 98570 10. 1707787 To tang. half diff. 13. 46926 9 3793262 Sum 69. 45496 Angle A N S Difference 42. 51644 Angle A S N In the superior Planets, Saturn, jupiter, and Mars, the sum of these angles is the elongation, but in the inferior Venus and Mercury there difference is the Elongation sought, and in our Example is to be added to the Sun's place, because the Sun's place was subtracted from the Eccentrick of Venus reduced. Sun's true place 154. 07347 Elongation A S N add 42. 51644 True place of Venus 196. 58991 To find the distance of Venus from the Earth. As the sine of A N S 69. 45496 co. are. 0. 0285403 To the side A S 100895 5. 0038707 So sine of N A S 68 02860 9 9672296 To the side S N 99917 4. 9996406 To find the latitude of Venus from the Earth. As the side S X 9991. 7 co. are. 5. 0003594 Is to Radius 10. 0000000 So is X L 896 2. 9526176 To the tangent of X S L 0. 51417 7. 9529770 which is the South latitude of Venus. CHAP. 17. Of the Motion of Mercury. THe form of calculating the place of this Planet is the same with Venus, the Dimensions of whose orbs we shall give you, as the learned Bullialdus hath computed them, but first we will set down the middle motions thereof to the former time. The middle motions of Mercury. An. Christ. Longit. ☿ Aphel. ☿ Node ☿ 1500 352. 53750 248. 73556 039. 85639 80 59 53472 2. 31611 2. 12417 6 326. 41889 . 17361 . 15917 july 147. 58583 . 01694 . 01528 D 1● 65. 47806 . 00126 . 00117 H 18 3. 06917 P 4564 . 07781 Mean Mot. 234. 70198 251. 24348 42. 15618 Aphel. Snbt. 251. 24348 Rest Anom. 343. 45850 The proportion between the Earth's orb, and the orb of Mercury is as 100 000 to 38585 Semicentricity in the same parts is, 8105. The parts or greatest inclination 4635. And the angle itself 6. 90. In the triangle therefore M E H, of the first Diagram of the former Chapter we have known. 1. The half sum of the opposite angles M E H and M H E, 8. 27075 the half of 16. 54150 which is the compliment of the mean Anomaly, 343. 4585 to a circle. 2. The side M E 77170 3. The side M H 16210 Sum 93380 co. are. 5. 0297462 Differ. 60960 4. 7850449 So tang. half sum. 8. 27075 9 1628126 To tang. half differ. 5. 42532 8. 9776037 Difference 2. 84543 Angle M E H Difference doubled 5. 69086 Angle M B H or the Equation to be added to the mean longitude, because the Anomaly is more than a semicircle. Example. The mean Longitude of Mercury 234. 70198 Equation add 5. 69086 Eccentrick place 240. 39284 Node subtract 42. 15618 Argument of Latitude K L 198. 23666 To find the distance of Mercury from the Sun. As the sine of MBH 5. 69086 co. are. 1. 0036592 To the side MH 16210 4. 20978●0 So sine of EMH 16. 54150 9 4544022 To the side BH 46541 4. 6678444 To find the Reduction. As Radius, to cousin of XKL 6. 90 9 9968431 So tangent of KL 18. 23666 9 5178453 To tangent of XK 11. 11322 9 5146884 Reduction 12344 And because the argument of Latitude is more than 180, it must be subtracted from the eccentrick place 240. 39284 And then the eccentrick reduced will be. 240. 26940 To find the present inclination. As Radius To the greatest inclination EBB 4635 3. 6660497 So sine of KL. 18. 23666 9 4954646 To the inclinat. XL 1450 3. 1615143 Which are the parts of inclination agreeing to the common Radius 38585. But the distance of Mercury from the Sun being put for Radius, the inclination will be. 1749 For as Radius DL 38585 co. are. 5. 41358●5 To Mercury dist. BH or ALL 46541 4. 6678444 So is XL 1450 3. 1615143 To XL 1749 3. 2429402 To find the distance corrected by Curtation. As ALL 46541 co. are. 5. 3321556 To Radius 10. 0000000 So is XL 1749 3. 2429402 To the sine of LAX 2. 15437 8. 5750958 As Radius 10. 0000000 To ALL 46541 4. 6678444 So cousin of LAX 2. 15437 9 9996929 To AXE 46509 4. 6675373 To find the second inequality of Mercury. We must have given, 1. The Angle NAS which is to be found by subductiug the Sun's place, from the eccentrick place of Mercury reduced, or this from it, so that less than 6 signs may remain, this remainder is the Anomaly of the orb, and the compliment thereof is the Angle NAS, or the half, is the half sum of the opposite angles. Example. The eccentrick of Mercury reduced 220. 26940 The Suns true place 154. 07347 Anomaly of the orb 96. 19593 Compliment is NAS 83. 80407 Half Anomaly 48. 09796 These given with the sides NA and SA. the Analogies are As the greater side SA 100895 co. are. 4. 9961293 Is to Radius 10. 0000000 So is the lesser side NA 46509 4. 6675373 To the tangent of 24. 74799 9 6636666 Add 45. As Radius To the cotang. of 69. 74799 9 5669785 So tang. half sum 48. 09796 10. 0470559 To tang. half difference 22. 35160 9 6140344 Sum 70. 44956 Angle ANS Difference 25. 74636 Angle ASN Because the Sun's place was subtracted from the eccentrick of Mercury reduced, therefore the angle of Elongation ASN must be added to the Sun's place. 154. 07347 Elongation ASN add 25. 74636 True place of Mercury 179. 81983 To find the distance of Mercury from the Earth. As the sine of ANS 70. 44956 co. are. 0. 0257891 To the side AS 100895 5. 0038707 So the sine of NAS 83. 80407 9 9974556 To the side SN 106442 5. 0271154 To find the Latitude of Mercury from the Earth. As the side SX 106442 co. are. 4. 9728846 Is to Radius 10. 0000000 So is XL 1749 3. 2429402 To the tang. of XSL 0. 94169 8. 2158248 Which is the south Latitude of Mercury. CHAP. 18. Of the Semidiameters of the Sun, Moon, and shadow of the Earth. THe angle of the Sun's apparent Semidiameter, in his nearest distance to the Earth, Bullialdus hath by observation found to be 16′ 45″, or in decimal numbers 27917. And by an Eclipse of the Moon, December 1638, he found her Semidiameter to be 16′ 54″ or 28167, and the Semidiameter of the Earth; shadow 44′ 9″, or 7 583, at which time (being the time of incidence) her distance from the Earth by his computation was 97908 parts of the Semiaxis of the Elipsis 100 000. By this and another observation in the same Eclipse, he showeth how to find her apparent semidiameter, in all the other intervals. The inferior limb of the Moon and the first Star in the foot of the former Twin, (whose place then according to Tycho was Gemini 28. 25′ 17″, or Gemini 28. 42138 with South Latitude, 0 d. 58′ or 0. 96667.) being in the same Azimuth, was 8′ or 13333 higher than the Star and the Altitude of the heart of Hydra then taken by him at Paris was 30 deg. 37′, or 30 d. 61667. From whence the hour was found, 30 h. 40′, or 13 h. 66667 and the hour being given the altitude of the Star is also given, deg. 56. 42′ 15″, or deg. 56. 70416. The apparent altitude of the centre of the Moon was deg. 57 7′ 9″, or deg. 57 11916, but by her latitude and place it should have been deg. 57 40′ 4″, or deg. 57 66778 and therefore her parallax of altitude 32′ 55″, or 54861. The situation of the Moon and Azimuth in which her interior limb and the Stars were, being given, her aparent Longitude was almost in Gemini, deg. 28 38′ 30″, or Gemini deg. 28 64167, her parallax of longitude 18 min. or 30000 and therefore the centre of the Moon in her true motion in Gemini 28 d. 57 min. fere. or in Gemini 28 d. 95000, her parallax of Latitude is 19 min. or 31667. to which 21′ or 35007, the difference of the observed latitude of the Moon and Stars, being added the true difference is 50 min. or 83333 min. and thence the Moon's Latitude 8 min. or 13333 S. Now then to find the distance of the Moon from the Earth, in this Eclipse, the Earth's semidiameter being one degree, Let FEC represent the true Horizon, BDE, the vertical at Paris E the centre of the earth, D the City of Paris: the Moons true altitude, AEF, deg. 5766778, the observed altitude ADG, deg. 5711916. The parallacticall angle DAE, deg. 0. 34861. Therefore in the Triangle ADE we have given all the angles, and the find DE one Semidiameter of the Earth, to find A, for which the anolagy is. As the sine of DAE 0 d. 54861 co. are. 2. 0188745 To the side DE 1 0. 0000000 So is the sine of ADB 32 d. 88084 9 7347147 To the side A 56. 70 1. 7535892 This foundation being laid, he proceedeth to the rest: and to show how we may possibly fall into some absurdity, he supposeth the Moon's distance from the Earth in this Eclipse to be but 55 semidiameters, or the side BC in the following figure, the apparent angle of the semidiameter of the Earth's shadow CHI, 0. 73583 AEF represents the Sun, his semidiameter A, the angle of his apparent Semidiameter when he is Perig. AGE 16. 45, or in decimals 27916 BHG represents the Earth. BG the Semidiameter thereof, hence to find HI in the triangle HIC the proportion is. As the sine of HIC 89. 26417 co. are. 0. 0000358 To the side HC 54 1. 7323937 So is the Radius HCI 90 10. 0000000 To the Hypothenusal HI 54. 004 1. 7324295 2. In the triangle HBI we have given the sides BH. 1. and HI 54. 004 with the angle BHI 179. 26417, hence to find the Angle BHI, the Analogy is. As the greater side H I 54. 004 co. are. 8. 2675705 Is to the less H B 1. 0. 0000000 So is Radius 10. 0000000 To the tangent of 1. 06082 8. 2675705 Add 45. As Radius 10. 0000000 To the Cotang. of 46. 06082 9 9839145 So Tang. half sum 36791 7. 8075980 To tang. half differ. 35454 7. 7915125 Angle B I H 01337. And the angle C B I 72246 3. In the triangle C B I, we have given the angles and the side B C 55 to find C I. Therefore say, As Radius To the tangent of C B I 72246 8. 1007064 So is B C 55 1. 7403627 To C I 0. 6935 = to B K 1. 8410691 and therefore K G 3065, and the angle K I G 0. 31857. For, ●● I K 55 co. are. 8. 2596373 To Radius 10. 0000000 So is K G 0. 3065 1. 4864305 To the tangent of K I G 0. 31857 7. 7450678 and the angle B D G is equal thereunto, but so the angle of the Sun's apparent Semidiameter A G E 27916 by observation, is less than the angle A D E, which is absurd, and therefore some part assumed is false. The Semidiameters of the Sun and Moon must not be changed, constant experience agreeing with these observations. In this Eclipse therefore Bullialdus doth take for the distance of the Moon from the earth, B C 57 85 Semidiameters of the earth, and the Semidiameter of the earth's shadow, C B I 75111. Hence to find C I, the analogy is. As Radius To the side B C 57 85 1. 7623034 So the tang. of B C 0. 75111 8. 1176019 To C. I. 0. 75841 1. 8799053 Let B K be equal to C. I. So is K G 24159. The● As I K 57 85 co. are. 8. 2376066 To Radius 10. 0000000 So is K G 24159 1. 3830789 To the tang. of K I G. 23928 or B D G 7. 6207755 equal to E D A, and the Sun's apparent Semidiameter being given A G E, 27916, the angle G A B, or the difference between the angel's A G E, and E D A shall be given also, viz. 03988. the Suns Horizontal parallax when he is Perigaeon. And the Moons Perigaeon distance from the earth, in Syzigiis, 56. 50 Semidiameters of the earth. For, as 97908 co. are. 5. 0091819 To 57 85 1. 7623034 So is 95638 4. 9806304 To B C 56. 50 1. 7521157 Hence to find the Moons Horizontal parallax when she is perigaeon, the analogy is, in the preceding Diagram. As E G or B C 56. 50 co, are. 8. 2478843 Is to Radius: So is D E 1. 0. 0000000 To the sine of E G D 1. 01399 8. 2478843 The Horizontal parallax of the Sun when he is perigaeon or the angle B A G was found to be . 03988 The Moons Horizontal parallax is 1. 01399 Their aggregate 2. 05387 Semidiameter of the Sun subtract . 27916 There rests the angle C B I . 77471 or the apparent semidiameter of the earth's shadow in loco transitus Lun●, Perig. In the triangle therefore B C ay, we having the angles and the side B C given, C I shall be also given. For, As the sine of 90 deg. Is the side B C 56. 50 1. 7521157 So tang. of C B I 77472 8. 1310339 To the side C I 7640 = B K 1. 8831496 And therefore K G ●360 And in the triangle A G B having the angles and B G given the side A B is also given, for As the tang. of B A G 03988 co. are. 3. 1585620 Is to B G 1. So is Radius 10. 0000000 To A B 1440. 66 3. 1585520 which is the distance of the Earth from the Sun, when he is Perihelion. And because the Sun's eccentricity is 1784, his Apogaean distance is 101784, hence to find his distance, in Semidiameters of the earth, say, As his Perigaean distance 98216 co. are. 5. 0078178 Is to his distance 1440. 66 3. 1585620 So is his Apog. distance 101784 5. 0076794 To his Apog. dist. 1493. 03 3. 1740692 Then as B S 1493. 03. or E G 6. 8259308 To Radius, so is E D. 1 10. 0000000 To the sine of E G D 0. 3855 6. 8259308 The Suns Horizontal parallax when he is Apogaeon. As Radius, to A B: 1440. 66 3. 1585620 So is tang. of A B E 27916 7. 6877120 To A E 70189 0. 8462740 Then as B S 1493. 03 co. are. 6. 8259308 To Radius, so is S T 70189▪ ☉ Semid. 0. 8462740 To the tang. of S B T 26936 7. 6722048 The apparent Semidiameter of the Sun when he is Apogaeon. The Sun being Perigaean, we have given B G 1. K B. 75841. KG. 24159 and B C. 56. 50, the distance of the Moon from the Earth when she is Perigaean; from whence the longitude of the earth's shadow may thus be found. As K G 2360 co. are. 10. 6270880 To K I 56. 50 1. 7521157 So is C I 7640 1. 8831496 To C D 182. 93 2. 2623533 Add B C 56. 50 then is B D 239. 43. the longitude of the earth's shadow. Let B S be the Apogaean distance of the Sun, 1493. 03 The angle of the Sun's apparent Semidiameter S G T 26936 The Perigaean Semidiameter or the angle A G E 27916 Their difference is the angle Z G E 00980 Let TG be produced to N, then shall the angle I G N be equal to the angle Z G E, but the Sun being Perigaean, the angle B D G was found to be o. degrees 239●8. whose compliment is the angle B G D 89. 76072 therefore when the Sun is Apogaean, it shall be 89▪ 77052, therefore B X G 0. 22948, equal to K N G. Hence to find K G the analogy is. As Radius 90 10. 0000000 To K I 56. 50 1. 7521157 So tang. of K I G 0. 22948 7. 6006035 To K G 22632 1. 3547192 And K B 77368. Then to find C B N. Say. Asdruball B C 56. 50 co. are. 8. 247●843 To Radius 90 10. 0000000 So C I or rather C N. 77368 1. 8885613 To the tang. of C B N 7844● 8. 1364456 The Sun being Apogaean; and the angle C B I, the Sun being Paerigaean, was before found to be 77471, and therefore the difference of the earth's shadow between the Sun's Apogaean and Perigaean is, 00971. Then, As K G 22632 co. are. 10. 6452808 To K I 56. 50 1. 7521157 So is C N 77368 1. 8885613 To C X 19●. 18 2. 2859578 Add B C 56. 50. Then is B X 249. 68 The semidiameter of the Moon, when she is Perigaean, is greater than the semidiameter of the Sun, being Apogaean, and therefore Bullialdus doth make it 17. or 28333, and because the eccentricity of the Moon is given 4362, her Apogaean distance in Syzygiis 104362, the Moon being Perigaean her distance from the earth is, 95638, and in semidiameters of the earth 56. 50 and therefore her Apogaean distance in semidiameters of the earth, by the analogy following, As 95638 co. are. 5. 0193696 To 56. 50 1. 7521157 So is 104362 5. 0185423 To 61. 66 1. 7900276 As her Apogaean dist. 61. 66 Co. are. 8. 2099724 To the Moons Perig. semid. 28333 1. 4522925 So is the Moon Perig. dist. 56. 50 1. 7521157 To the Apog. semid. 25964 1. 4143806 We have the semidiameter of the Cone C I 76400, and her Perigaean distance 56. 50, and D C 182. 93, but when the Moon is Apogaean, D C will be no more than 177. 77. found by abating K I or K N 61. 66. from B D 239. 43. Hence to find C I or C N in the same parts say. As D C 182. 93 co. are. 7. 7376467 To C I 7640 1. 8831496 So is C D 177. 77 2. 2498584 To C I 7424 1. 8706547 Then as B C 61. 66 co. are. 8. 2099724 Is to Radius 90 10. 0000000 So is C I 7424 1. 8706547 To the tang. of C B I . 68981 8. 0806271 Here then we have determined Apogaeon 26936 The Sun's Semidiameter Perigaeon 27916 Apogaeon 1493. 03 His distance from the earth Perigaeon 1440. 66 Apogaeon ☉ 249. 68 The Axis of the earth's shadow Perigaeon ☉ 239. 43 The Semidiameter of the shadow, when the Sun is Apogaeon. In loco ●ransitus Lunae, Apog 78442 Perig. 77471. Apogaeon 25964 The Semidiater of the Moon in Syzygiis Perigaeon 28333 Apog. 61. 66 The distance of the Moon from the earth in Syzygiis Perig. 56. 50 Perig. 23928. Semiangle of the Cone Apog. 22948. CHAP. 19 Of the Proportion and Magnitude of the three great bodies, the Sun, Moon and the Earth. THat it is a hard matter exactly to determine the true Magnitude of the celestial bodies, is not I believe denied by any, it will be therefore sufficient if we shall determine them so, as that there be no sensible error in them; and to such exactness, we may train by the rules and proportions following. As the Semidiameter of the Earth's shadow C B I. Is to the Semidiameter of the shadow in parts of the Earth's Semidiameter C I = B K: So is the apparent Semidiameter of the Moon. To the Semidiameter of the Moon in parts of the Earth's Semidiameter, that is As C B I 77471 co. are. 10. 1108609 To C I 7640 1. 8831496 So is the Moon's semid. 28333 1. 4522925 To the Moon's semid. 27945 1. 4463030 And Spheres being in triplicated proportion of their diameters, the proportion of the earth to the Moon will be as 1. 00000. 00000. 00000. the Cube of the earth's Semidiameter to 02182. 28939. 33625. the Cube of the Moon's semid. 27945. and therefore dividing the earth's Semidiameter by the Moons, the quotient will be 45. 823, and so many times is the body of the Moon contained in the Earth. The proportion between the Semidiameter of the Earth and the Semidiameter of the Sun, may be found by this analogy, As Radius 90 To A B 1440. 66 3. 1585614 So is tang. A B E 27916 7. 687706● To A E 7. 0189 0. 8462683 But if to A B 1440. 66 You add B D 239. 43 Their sum is A D 1680. 09 And then, As Radius 90 To the side A D 1680. 09 3. 2255415 So is tang. of A D E or K I G 23928 7. 6207755 To A E 7. 0197 0. 8463170 And now if you take the lesser semidiameter of the Sun, the Cube thereof will be ●45. 781, but taking the Semidiameter of the Sun to be but 7 semidiameters of the earth, the Sun will be 343 times bigger than the Earth. The proportion of the Semidiameter of the earth and the Moon is as 1 to 27945, of the Sun and the Earth as 7 to 1, and therefore of the Sun and the Moon as 7 to 27945. The Cube of 7 is 343, the Cube of 27945 is 02182, &c, by which dividing the Cube of the Sun's semidiameter the quotient will be 15717. 47 and so many times is the Moon contained in the Sun. CHAP. 20. Of the proportion between the Orbs of the superior and inferior Planets, and the Orb of the Earth. WHat proportion the Orbs of these Planets have to the earth's Orb, we have set down in those Chapters, in which we have showed the manner of computing their places, and by what means the truth of those proportions may appear, we shall set down in this, and because we have used those proportions which Bullialdus hath with great diligence computed; we shall exhibit here an Example in Saturn according to which method the proportions between the orb of the earth and the orbs of the other planets are also to be found. And Satur's proportion to the earth's orb, as Bullialdus hath determined it, and which we have used, Chap. 13. is as 100 000 to 10480. The observation from whence this proportion is gathered was made Anno Christi 1587. January the 9th. Hour 9th. 75 parts, at which time Saturn was observed to be in Aries 26, 13333. with South latitude, deg. 2. 46667. The Sun's true place than was in ♉ deg. 29, 41778. and his distance from the earth, 98374. Satur's true place from the Sun by calculation was in ♉ deg. 2, 31416. whose difference from his observed place, deg. 6, 18083. is the parallax of the orb or the angle A N S, and the angle N A S, 87. ●0362, is found by deducting Satur's place from the place of the Sun, which with his distance from the Sun or side A N 95596 being given, the side A S will be found to be 10310. Now as the Sun's distance from the earth, 98374 Is to the distance, 10310 So is the Semidiameter of ♄ orb, 100 000 To the Semidiameter of the earth's orb, 10480 By a second Observation made Anno Christi 1590., February 8, about 8 of the clock in the evening; Saturn was in Gemini, deg. 7. 53333. with South latitude, deg. 1. 50. The true place of the Sun at the same time was in Pisces, deg. 0. 02805. and his distance from the earth, 98953. And Satur's place from the Sun by calculation was in Gemini, deg. 13. 82167. from which deducting his place taken by observation, their difference, 6. 28834 is the parallax of his orb, represented by the angle A I S. And subtracting Satur's place 73. 82167 from the Sun's place 330. 02805 their differences 256. 20638 reject a semicircle is the angle, I A S 76. 20638 and Satur's distance from the Sun represented by A I 94338 and hence the side A S 10423. And now as the Sun's distance from the earth 9893 Is to the distance A G 10423. So is the Semidiameter of Satur's orb 100 000 To the Semidiameter of the earth's orb 10533 By a third observation made in the same year of Christ 1590. Septemb. 7 at midnight, Satur's place was in Gemini deg. 28. 1 with South latitude deg. 1. 18333. The Sun's true place at the same time was in Virgo deg 24. 49833. And his distance from the earth 100300. Saturn's place from the Suns by calculation, was in Gemini deg. 21. 76722, which being deducted from his place taken by observation, their difference is the parallax of his o●●e, or the angle A K L 6. 33278, and deducting Satur's place from the place of the Sun the angle A L K is 9●. 73111, and therefore the side A L 10415. Now as the Sun's distance from the earth 100300 Is to the distance A L 10415 So is the Semidiameter of Satur's Orb 100000 To the Semidiameter of the earth's orb 10383 But Bullialdus whom we follow doth retain the first of these 10480 as being the mean, and most agreeable to Tycho's observation; And from these three observations the inclination of Satur's orb may thus be found. The Triangles L D. N. I D O, and D G M of the following Diagram, have their sides and angles equal with the triangles, N A S. I A S and L A K in the Diagram preceding, being drawn from the same observations; in every of which we are to compute ♄ distance from the earth; for which in the triangle L D N by the first of these observations we have given the angle L N D 86. 71556. The angle L D N 87. 10362 and ♄ distance from the Sun L D 95596 to find L N. As the sine of L N D 86. 71556 co. are. 0. 0007130 Is to the side D L 95596 4. 9804397 So the sine of L D N 87. 10362 9 9994447 To the side L N 95630 4. 9805974 Then in the right angled triangle L K N right angled at K, we have given the angle of South latitude L N K 2. 46667, and the side L N 95630, to find L K. As Radius 10. 0000000 Is to L N 95630 4. 9805974 So is the sine of L N K 2. 46667 8. 6338534 To the side L K 4116 3. 6144508 Hence to find the angle of Latitude at the Sun say, As the side L D 95596 co. are. 5. 0195603 Is to Radius 10. 0000000 So is the side L K ●116 3. 6144508 To the Sine of L D K 2. 46756 8. 6340111 By the second observation in the triangle I D O we have given the angle I O D 97. 50528 whose compliment is 82. 49472 the angle I D O 76. 20638, and ♄ distance from the Sun I D, to find his distance from the earth I O. As the sine of I O D 82. 49472 co. are. ●. 00373●● Is to the side I D 94338 4. 974686● So is the sine of I D O 76. 20638 9 9872910 To the side I O 92409 4. 9657145 Then in the right angled Triangle H I O right angled at H, we have given the angle of Satur's South latitude H O I 1. 50, and the side I O to find H I By the third observation in the triangle GMD we have given the angle M D G 87. 26889 the angle M G D 86. 39833 the side G D 94239 to find M G. As the sine of G M D 86. 39833 co. are. 0. 0008588 To the sine of M D G 87. 26889 9 9995064 So is the side G D 94239 4. 9742306 To the side M G 94318 4. 9745958 Then in the right angled triangle G M F right angled at F we have given the angle of Satur's South latitude G M F 1. 18333, and the side G M to find G F. As Radius 10. 0000000 Is to the side M G 94318 4. 9745958 So is the sine of G M F 1. 18333 8. 3149535 To the side G F 1948 3. 2895493 Hence to find the angle of latitude at the Sun, As the side D G 94239 co. are. 5. 0257694 Is to Radius 10. 0000000 So is the side G F 1948 3. 2895493 To the sine of G D F 1. 18434 8. 3153187 These things premised the places of the Nodes and the angle of inclination of the planes may thus be found. In the following Diagram let the place of the first observation be at A, and the angle of latitude at the Sun D G 2. 46756. The second at B, and the latitude G E 1. 4693●. The third at C, and the latitude G F 1. 18434. The Arches of apparent motion from the First observation to the second A B 41. 50751 Second to the the third B C 7. 94555 First to the third A C 49. 45306 The half of these arches are the measure of the angle B A C 3. 97277 whose sins are the sides A B 35435 of the angle B C A 20. 75375 whose sins are the sides B C 6929 whose sins are the sides A C 41828 The angles of Latitude at the Sun found be L D K 2. 46756 whose sins are the sides G D 4306 I D K 1. 46932 whose sins are the sides G E 2617 G D F 1. 18434 whose sins are the sides G F 2064 The difference between G E and G F is F E 553 The difference between G D and G F is F D 2242 The difference between G E and G D is E D 1689 Hence to find the side A L in the triangle A B L use this analogy As F D 2242 co are. 6. 6493644 Is to C A 41828 4. 621467● So is E D 1689 3. 2276296 To A L 31511 4. 4984611 Then to find the angle A B L We have given the side A B 35435 and B A L 3. 97277 We have given the side A L 31511 and B A L 3. 97277 whose compliment is 176. 02723, and the half thereof 88 01361 is the half sum of the opposite angles. As the sum of A B and A L 66946 co. are. 5. 1742754 Is to their difference 3924 3. 3937289 So the tang. half sum 88 01361 11. 4598852 To the tang. half differ. 59 38668 10. 22889● The sum 147. 40029 is the angle A L B The difference 28. 62693 is the angle A B L whose double 57 25386 is the arch A M, ●o which if you add the arch A B 41. 50751 their sum is the Arch B A M 98. 76137, whose compliment to 180 gives the arch B H and M I 81. 23863, and the half thereof is the arch B H 40. 61931. Now than the point B is in 73. 82167 To which if you add B H 40. 61931 The Node ascending is 114. 44098 And deducting B C from B H 40. 61931 whose natural sins are G E 65098 Their difference is C H 32. 67376 whose natural sins are G F 53980 The sum of H B and B A is H A 82. 12682 whose natural sins are G D 99057 To find the angle of Inclination by the first observation, say As G D 99057 co. are. 5. 0041149 To G D 4306 3. 6340740 So is G K Radius 10. 0000000 To G K the sine of deg. 2. 48908 8. 6381889 To find the angle of Inclination by the second observation, say As G E 65098 co. are. 5. 1864324 To G E 2617 3. 4178037 So G K Radius 10. 0000000 To G K the sine of D. 2. 30397 8. 6042361 To find the angle of Inclination by the third observation, say As G F 53980 co. are. 5. 2677672 To G F 2064 3. 3147096 So is G K 100 000 or Radius 10. 0000000 To G K the sine of deg. 2. 19128 8. 5824768 But by reason of this variety, we may well suspect the truth of one or other, of the observations given; and therefore Bullialdus hath assigned another place for the point of the Node ascending; viz. deg. 110. 42333 and the angle of Inclination somewhat more than that found by the first observation. viz. deg. 1. 50 that so he might make these observations to agree as near as might be. And now if you suppose the Node ascending to be 110. 42333 And from thence deduct the place of the 2d. observation 73. 82167 Their difference shall be the arch H B 36. 60166 and the sine thereof is G E 59624. Again deducting B C 7. 94555 from B H, their difference will give C H 28. 65611, and the sine thereof G F 47954. And by adding A B 41. 50751 to H B their sum shall be H A 78. 10917 and the sine thereof G D 97854. For the latitude agreeing to the first observation As G K 100 000 5. 0000000 Is to G K deg. 2. 50 8. 6396795 So is G D 9 7854 4. 9905785 To G D or the latitude 2. 44632 8. 6302580 whereas it should have been 2. 46667. For the latitude agreeing to the second observation As G K 100 000 5. 0000000 Is to K G deg. 2. 50 8. 6396795 So is G E 59624 4. 7754210 To G E or the latitude 1. 49029 8. 4151005 whereas it should have been 1. 56667. For the latitude agreeing to the third observation As G K 100 000 5. 0000000 Is to G K or the angle of inclin. 2. 50 8. 6396795 So is G F 47954 4. 6808248 To G F or the sine of latit. 1. 19856 8. 3205043 whereas it should have been but 1. 19 CHAP. 21. To find the mean Conjunction and Opposition of the Sun and Moon. FOr this purpose the Table which Shakerley transcribed from Bullialdus, we have here exhibited in decimal numbers, the use whereof, as he hath explaind the same is this: Set down first the Epoch● next preceding the year given, than the years and months complete having a care of the year Bissextile, and to every one set down the time answering in the Table; then add them altogether, and the sum subtract from the next greater in the Canonian, under the title●, if you ●ee● a Conjunction, or ☌, if an opposition, the remainder showeth the time required complete from the beginning of the month current. Example. I would know the time of the mean opposition of the Sun and Moon in March, 1652. The work is this. How. Parts The Epocha 1640 701. 96639 Years complete 11 20. 14722 February complete Bissextile 022. 53539 The sum subtract 744. 64500 From the Opposition next greater 1063. 10139 Rests the mean opposition 318. 45639 that is 13 days 6 hours and 45639 parts. CHAP. 22. To find the true Opposition or Conjunction of the Sun and Moon. FOr the time of the mean Conjunction or Opposition given, find the true place of the Sun, and the eccentrick place of the Moon, and compare them; if they either be precisely the same or precisely opposite, the time of the true Conjunction or Opposition agrees with the mean; but if they differ take the difference, by subtracting the less from the greater, and that call the distance of the Sun and Moon. 2 Out of the Table of Semidiameters, and hourly motions; with the mean Anomalies of the Sun and Moon, take out their hourly motions, and subtract the hourly motion of the Sun, from the hourly motion of the Moon, by the remainder (which is the hourly motion of the Moon from the Sun) divide the distance of the Sun and Moon before kept, the quotient gives the time, which must be added to the mean time of Conjunction or Opposition, if the excess be in the Sun's place, or subtracted, if in the Moon's place. 3 At this time thus corrected, find again the true place of the Sun and eccentric place of the Moon, together with their distance, and repeat your former work, till you find them absolutely to concur, and the time thus found shall be the true time of Conjunction or Opposition. As in the Example, D. How. parts At the time of the mean ☍ March 13 6. 45639 The true place of the Sun is 4. 85039 The Eccentrick place of the Moon 180. 38631 The Distance of the Sun from ☍ Moon 4. 46408 Mean Anomaly of the Sun 266. 40860 His hourly motion . 04112 Mean Anomaly of the Moon 30. 26681 Her hourly motion . 51827 Hourly motion of the Moon from the Sun . 47715 By which dividing the distance 4. 46408 The quotient gives Hours 9 3558 to be added. So the time first corrected March 13 15. 81279 The true place of the Sun is 5. 23520 The eccentrick place of the Moon 1●5. 15798 The distance of the Sun from ☍ of the Moon . 07722 Which divided by the hourly motion of the Moon from the Sun . 48114 Gives in time to be added . 16049 So the time secondly corrected 13 15. 97328 The true place of the Sun is 5. 24180 The eccentrick place of the Moon 185. ●4010 The distance of the Sun from ☍ the Moon . 00170 Which divided by the hourly motion of the Moon from the Sun . 48121 Gives in time to be added . 00353 So the true time 13 15. 97681 The true place of the Sun is 5. 24194 The eccentrick place of the Moon 185. 24190 4 For this time find out the true motion of the Moon's Latitude, and thereby the Reduction, which divide by the hourly motion of the Moon from the Sun, and the quotient contrary to the title of Reduction, apply to the last corrected; so have you the true time. In our Example. The true motion of Latitude 174. 04881 The Reduction Add . 02398 The quotient Subt. . 04983 So the true opposition 13 15. 92698 5 Lastly, apply the equation of time to this equal time to make it apparent. The true time of the ☍ 13 15. 92698 The equation of time Subt. . 02884 The apparent time of the ☍▪ 13 15. 89814 CHAP. 23. To find whether there will be an Eclipse or not. THere are two ways to know this, of which the one is more easy, the other more certain, The first is this; At the true conjunction, if the true motion of latitude be within 17 degrees backward or forward of 6 or 12 signs, or at the opposition within 12 degrees, there is a possibility of an Eclipse, otherwise not. In our Example the Moons true motion of latitude is 174 deg. 04881, which being not fully 6 degrees distant from 6 signs, shows the necessity of an Eclipse. The other way is this. If at the visible conjunction the visible latitude of the Moon be less than the aggregate of the Semidiameters of the Sun and Moon, there must be an eclipse or else not. 2. If at the true opposition the true latitude of the Moon, be less than the sum of the Semidiameters of the Moon and the earth's shadow, there must be an Eclipse otherwise not. This latter way is most certain, only subject to this inconvenience, that a great part of the calculation is performed before we come to the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉, or power to judge of the possibility. CHAP. 24. To find the Quantity of a Lunar Eclipse. BY the true motion of the Moon's Latitude, find her true latitude, according to the former directions: this in our example is 0. 51496 North Descendant. 2 Find out the Semidiameter of the Moon by her mean anomaly out of the Table, as also h●● horizontal parallax; and with the mean anomaly of the Sun, take out the Semiangle of the Cone of the shadow; and this subtract from the Moons horizontal parallax, there rests the Semid. of shadow. 3 Add together the Semidiameter of the shadow, and Semidiameter of the Moon, and from the sum subtract the Latitude of the Moon, the remainder is the scruples of the Moon's diameter eclipsed. Example. horizontal parallax of the Moon . 94409 Semiangle of the Cone Subt. . 23455 Semidiameter of the shadow . 70954 Semidia metre of the Moon . 26431 Sum of the Semidiameters . 97385 Latitude of the Moon, Subt. . 51496 Scruples deficient . 45889 4 Convert these Scruples into digits or parts, whereof the Moon's body contains 12, thus, As the Moon's diameter 52862 co. are. 5. 276857 Is to the Scruples deficient 45889 4. 661708 So is 12 digits 1. 079181 To the digits eclipsed 10. 417 1. 017746 Yet note that Lunar Eclipses are of three sorts. 1 Partial, when the Scruples deficient are less than the diameter. 2 Totall without continuance when they are equal. 3 Totall with continuance when the scruples deficient are greater than the diameter, and in these the digits eclipsed are more than 12, which are so to be understood, as that they show how far the eclipse is over the body of the Moon. CHAP. 25. To find the duration of a Lunar Eclipse, or the continuance of the total darkness, where the Eclipse is total. Found the scruples of Incidence thus: Take the Logarithmes of the sum and difference, of the Moon's latitude and the sum of the Semidiameters of the Moon, and the shadow, half the sum of the two Logarithmes shall be the Logarithme of the Scruples of incidence required. Example. Summe of the Semidiameters 97385 Latitude of the Moon 51496 Their sum 1. 48881 5. 172836 Their difference . 45889 4. 661308 Sum of the Logarithmes 9 834544 Scruples of incidence 82656 4. 917272 2 Divide the Scruples of incidence by the hourly motion of the Moon from the Sun, the quotient gives the time of incidence or half duration of the Eclipse. This subtracted from the true time of the opposition▪ gives the beginning of the Eclipse; or added to it gives the ending. Example. The Scruples of incidence 82656 4. 917272 Divided by the hourly motion of the Moon from the Sun 48121 4. 682326 Time of incidence, hours 1. 7177 0. 234946 The true time of the opposition 13 d. 15. 89814 Time of incidence subt. 1. 71770 The beginning of the Eclipse 14. 18044 Time of incidence added, gives the end 17. 61584 The whole duration 3. 43540 3 If the Eclipse be total and you desire to know the continuance of total darkness, take the difference of the Semidiameters instead of the sum, and thereby work as you are directed in the first example of this Chapter, and you have the half tarrience in the shadow, whose double is the thing sought. CHAP. 26. To find the Moon's Latitude at the beginning and end of the Eclipse. MUltiply the Sun's hourly motion, by the time of incidence, the product being added to the scruples of incidence, gives you the motion of the Moon agreeing to the time of incidence. 2 From the true motion of latitude at the true opposition subtract, this motion of the Moon; there rests the true motion of latitude at the beginning of the Eclipse; or if you add it you have the motion of latitude at the ending, with which out of the Table of latitude you may find out the latitude, answering to the beginning and end, as in our Example. The time of incidence 1. 7177 The Suns hourly motion . 0411 Their product is . 07059 The scruples of incidence . 82656 The sum . 89715 Motion of Latitude at true ☍ 1●4. 04882 Motion of Latitude at beginning 173. 15166 Latitude at beginning North Desc. . 59223 Motion of Latitude at ending 174. 94596 Latitude at ending North Desc. . 43746 CHAP 27. To find the middle of the Eclipse or greatest darkness. THe time of the true Conjunction or Opposition the most received, is when the Sun and Moon are in one line perpendicular to the Ecliptic, to find this with the Moons true Latitude at the true opposition, enter the little Table of the difference of the true Conjunction or opposition from the greatest obscuration, and you shall find the difference with the title, which divide by the hourly motion of the Moon from the Sun, and the quotient according to the title, apply to the time of the true opposition; so have you the time of the greatest darkness, or middle obscuration. Example. The Moon's Latitude, North Descend. . 51496 The difference add . 04489 Which divide by the hourly motion of the Moon . 48121 Gives the difference in time to be added . 09328 To the true opposition March 13. 15 . 89814 So the middle of the Eclipse 13. 15h. 99142 The Calculation of the forementioned Eclipse according to the preceding directions. d. ho. Mean opposition March 13 6. 45639 Interval Add 9 35580 True opposition 13. 15. 97681 True place of Sun 5. 24194 Eccentrick place of the Moon 185. 24190 Mean Anomaly of the Sun 266. 79954 Mean Anomaly of the Moon 35. 44378 True motion of Latitude 174. 04881 True Latitude North descend. . 51496 Reduction Add . 02398 Hourly motion of the Sun . 04111 Hourly motion of the Moon 0. 52232 Hourly motion of the Moon from the Sun . 48121 Reduction in time Subt. . 04983 True opposition corrected 13 15. 92698 Equation of time Subt. . 02884 T●uest opposition 13. 15. 89814 horizontal Parallax of the Moon . 94409 Semiangle of the Cone . 23455 Semidiameter of the shadow . 70954 Semidiameter of the Moon . 26431 Sum of the Semidiameters . 97385 Scruples deficient . 45880 Digits eclipsed 10. 4197 Scruples of incidence . 82656 Time of incidence 1. 71770 Beginning of the Eclipse 13 14. 18044 End of the Eclipse 13 17. 61584 The whole duration 3. 43540 Latitude of the Moon at the beginning North D. . 59223 Latitude of the Moon at the ending North D. . 43746 Difference from the middle, Added . 09328 The middle of the Eclipse 13. 15 . 99142 CHAP. 28. Of the Calculation of the Sun's Eclipse. THis Eclipse is not properly, the Eclipse of the Sun, but of the earth in regard it is not the Sun, but the earth which looseth light the Sun being only apparently dark, the earth in truth, we will how ever use the name, that others have given it, and show you the manner of the Calculation. Find the mean conjnction, and from thence the true, which correct by the Reduction and Equation of time in all things as in the Moon. Example of a Solar Eclipse, which happened March 28. 1652. D Mean Conjunction March 28 0. 82333 Suns place 19 36150 Eccentrick place of the Moon 20. 89832 Distance of the Moon from the Sun 1. 53682 Mean Anomaly of the Sun 280. 96132 His hourly motion . 04090 Mean Anomaly of the Moon 223. 17513 Her hourly motion . 60109 Hourly motion of the Moon from the Sun . 56019 which dividing the distance 1. 53682 Gives in the quotient subt. 2. 74336 So the time first corrected ●7 22. 07997 True place of the Sun 19 24962 The Eccentrick place of the Moon 19 29533 The distance of the Sun from the Moon . 04571 which divided by the hourly motion of the Moon from the Sun . 56137 Gives in time subtract . 08143 So the time secondly corrected 27 21. 99854 True place of the Sun 19 24631 Eccentrick place of the Moon 19 24766 Distance of the Sun from the Moon . 00135 which divided by the hourly motion of the Moon from the Sun▪ . 56140 Gives in time subtract . 00240 So the true time of Conjunction 27 21. 99614 The true pl●ce of the Sun 19 24621 Eccentrick place of the Moon 19 24625 True motion of Latitude 8. 80745 The Reduction Subtract 0. 03536 The quotient . 06298 So the true Conjunction . 27 22. 05912 Equation of time subtract . 09970 The apparent time of the ☌ . 27 21. 95942 CHAP. 29. To find the Parallaxes of Longitude and Latitude. BY the rules delivered in the former part, find at the true Conjunction the Midheaven, with its altitude and the Meridian angle. Example. The Sun's place ♈ 19 246 The Suns Right Ascension 17. 749 Time in Degrees 329. 391 Right Ascension of Midheaven 347. 140 Midheaven ♓ 16. 022 Meridian angle 67, 078 Declination of Midheaven 5. 533 Altitude of the Equator at London 38. 467 Altitude of Midheaven 32. 834 2 The angle of the Ecliptic and Horizon, or altitude of the Nonagesime degree, and his distance from the Midheaven is thus found, by the 17 Chapter of the first part. As the Radius To the sine of the Meridian angle 67. 07 9 9642509 So is Cousin of the Altitude of M C 32. 83 9 9244255 To the Cousin of the Angle, etc. 39 30 9 8886764 Then as Radius To the Cousin of the Meridian angle 67. 07 9 5906259 So is cotang. of the altitude of the M. C. 32. 83 10. 1903074 To the tang. of the distance of the M. C. from the Nonagesime degree 16. 02 9 7809333 This M C falling between Capricorn and Cancer this distance is to be added to the Midheaven ♓ 16. 02 And the Nonagesime degree will be in ♈ 17. 14 3 Find the Node Ascendent and Subtract it from the Nonagesime degree, with the remainder enter the Table of the Moon's latitude, which if North add to the angle of the Ecliptic and Horizon; if South subtract it from it, so have you the altitude of the Nonagesime degree of the Moon's orb. Example. The Node Ascendent Subt. 10. 439 The Nonagesime degree 17. 140 There rests 6. 701 Which gives the Moon's Latitude Add . 570 The angle of the Ecliptic and Horizon 39 300 Altitude of the Nonagesime degree of the Moon's orb 39 870 4 Take the distance of the S●n from the Nonagesime degree, which in our Example of the true Conjunction is ● d. 10. 5 Out of the table of horizontal parallaxes, take the horizontal Parallax of the Sun and Moon, the difference of them is the Horizantall parallax of the Moon from the Sun. Example. The horizontal parallax of the Sun is . 03912 The horizontal parallax of the Moon . 99396 horizontal parallax of the Moon from the Sun . 95484 6 Add the Logarithme of the horizontal parallax of the Moon from the Sun, the sine of the Altitude of the Moon's orb, and the sine of the distance of the Sun from the Nonagesime, their sum subtracting twice Radius, is the Logarithme of the parallax of longitude. Example. horizontal parallax of the Moon from the Sun 95484 1. 9799306 Altitude of Nonagesime in the Moon's orb, sine 39 87 9 8068904 Distance of the Sun from the Nonagesime, sine 2. 10 8. 5639994 Parallax of longitude 02243 2. 3508204 Here note that whensoever the Sun's place is less than the Nonagesime degree, the Parallax of Longitude, makes the luminaries appear more west than the truth, and in the occidental Quadrant, when more than in the oriental. 7 Add the Logarithme of the horizontal parallax of the Moon from the Sun to the Cousin of the Nonagesime in the Moon's orb; the sum rejecting Radius is the Logarithme of the parallax of Latitude. Example. horizontal parrallax of the Moon from the Sun 95484 1. 979930● Altitude of Nonag. in the Moon's orb, Cousin 39 87 9 8850789 Parallax of latitude 0. 73284 1. 8650095 CHAP. 30. To find the visible motion of the Moon from the Sun for any time assigned. AT the beginning and end of the time proposed find the parallax of the Moon from the Sun in Longitude, and then observe these rules. 1 If during all the time proposed, the luminaries be in the oriental quadrant, and the parallax of longitude increase or be greater at the end of the time given then at the beginning, add the differences of the two parallaxes of longitude unto the true motion of the Moon from the Sun agreeing to the time given, or if it decrease, subtract it and you have what you desire. 2 If during all the time the luminaries be in the occidental quadrant, and the parallax of longitude increase, subtract the said difference from the true motion, if it decrease, add it, and you have the visible motion. 3 If at the beginning of the time the luminaries be in the oriental quadrant, and at the ending in the occidental, subtract the said difference from the true motion, and you have the visible motion during that time. Example. Let it be proposed to find the visible motion of the Moon from the Sun, for one half hour before the true Conjunction. In our Example, the true half hourly motion is . 28070 Parallax of Longitude at the beginning . 07628 Parallax of Longitude at the end . 02243 Their difference is Subtract . 05385 from the true half hourly motion Rests . 22658 the visible half hourly motion before the Conjunction. CHAP. 31. To find the time of the visible Conjunction of the Sun and Moon. USe this Analogy, As the apparent motion in any time assigned (found by the former Chapter) is to the time assigned; so is the parallax of longitude at the true Conjunction to the difference in time between the true and visible Conjunction. This difference in the oriental quadrant must be subtracted from the time of the true Conjunction, in the occidental quadrant added thereto; so have you the visible Conjunction. Example. As the visible half hourly motion 22685 co. are. 0. 644262 Is to the time assigned 50′ 1. 698970 So parallax longitude 02243 2. 350829 To the difference betwixt the true and visible Conjunction 04943 2. 694061 The true Conjunction 27 21. 95942 Difference subtract . 04943 The visible Conjunction 27 21. 90999 At this time find out the true distance of the Moon from the Sun, as also the parallax of longitude, if they agree it is a sign that the visible Conjunction is truly found, otherwise repeat the former work till there be a concurrence. Example At the visible Conjunction, March 27 21. 90999 The true distance of the Moon from the Sun . 0●847 The Parallax of Longitude . 02775 Their difference . 00072 which being so small showeth that the visible Conjunction is precisely enough found. CHAP. 32. To find the visible Latitude of the Moon, at the time of the visible Conjunction. IN these Northern regions which we inhabit, the parallax of latitude always makes the Moon to appear more South than indeed she is to find the visible latitude therefore observe these rules. 1 At the time of the visible conjunction find out the true latitude of the Moon thus. If the Eclipse happen in the oriental quadrant, add the parallax of longitude to the motion of the Sun, agreeing to the difference between the true and visible Conjunction, and the sum subtract from the true motion of latitude at the time of the true Conjunction; or if the Eclipse happen in the occidental quadrant add the said summ● thereto, and you have the true motion of latitude at the visible Conjunction, by which as formerly taught, find out the true Latitude of the Moon. Example. Motion of the Sun agreeing to 04943 . 00202 Parallax of Longitude at visible ☌ . 02775 The Sum Sub●. . 02977 Motion of Latitude at true ☌ 8. 80745 Motion of Latitude at visible ☌ 8. 77768 True Latitude at visible ☌ North . 75808 At the same time find the parallax of latitude, and compare it with the true latitude. If the latitude be South, add them together, the sum is the South visible latitude of the Moon, but if North, subtract the less from the greater; there remains the visible latitude of the Moon, which shall be North when the latitude is greater than the parallax, otherwise South. Example. The true latitude of the Moon, North 0. 75808 Parallax of Latitude 0. 73633 The visible latitude North . 02175 CHAP. 33. To find the quantity of a Solar Eclipse. THis differs very little from that in the 24 Chapter, for finding the quantity of a lunar Eclipse, for it with their mean Anomalies you enter the Table, and thence take out the Semidiameter of the Sun and Moon, and add them together; and from the sum subduct the visible latitude of the Moon, at the visible Conjunction, there rests the Scruples of the Sun's body deficient, which as in the Moon, so here in the Sun convert into digits. Example. Semidiameter of the Sun . 27386 Semidiameter of the Moon . 27815 Sum of the ●emidiameters . 55201 Visible latitude Subtracted . 02175 Scruples deficient . 53026 So the digits eclipsed 11. 61500 CHAP. 34. To find the beginning and ending of the Sun's Eclipse. BY the visible latitude of the Moon, and the sum of the Semidiameters of the Sun and Moon, find the Scruples of incidence, as in the Moon's Eclipse Chap. 25. 2 For one hour before the visible Conjunction, find by the 30 Chapter, the visible hourly motion of the Moon from the Sun, by which divide the Scruples of incidence, the quotient is the time of incidence, which subtracted from the time of the visible Conjunction, leaves the beginning of the Eclipse 3 For one hour after the visible Conjunction, find the visible hourly motion of the Moon from the Sun, by which divide the Scruples of incidence, the quotient is the time of Repletion: which added to the time of the visible Conjunction, gives the end of the Eclipse. Example. Summe of the Semidiameters . 55201 Visible latitude . 02175 Scruples of Incidence . 55158 At 1 ho. before the visible ☌ March 27 20. 90999 Parallax of longitude Orient. . 13209 True hourly motion of the Moon from the Sun . 56140 Visible hourly motion . 45174 Time of incidence 1. 22150 Beginning of the Eclipse March 27 20. 68849 At 1 ho. after the visible ☌ 27 22. 90999 Parallax of longitude Occid. . 10119 Visible hourly motion of the Moon from the Sun 48796 Time of repletion 1 h.. 1303● End of the Eclipse 27 23. 04029 The whole duration 2. 35180 CHAP. 35. To find the Visible latitude of the, Moon at the beginning and end of the Sun's Eclipse. FOr the beginning, add to the minutes of Incidence the motion of the Sun agreeing to the time of Incidence, and the sum subtract from the true motion of latitude at the time of the visible Synod, so have you the true motion of latitude at the beginning, by which find the true latitude, and by these according to the second rule of the 32 Chapter, may be had the visible latitude. Example. The Scruples of incidence . 5515● Motion of the Sun answering to the time . 05016 The sum subt. . 60174 Motion of latitude at visible ☌ 8. 77768 Motion of latitude at beginning 8. 17594 True latitude North . 70648 Parallax of latitude . 82004 Visible latitude South . 11353 2 For the end, add to the minutes of incidence the motion of the Sun agreeing to the time of repletion and the sum add to the true motion of latitude at the time of the visible Conjunction; so have you the true motion of latitude at the end; by which proceed as before, to find the visible Latitude. Example. Scruples of Incidence . 55158 Motion of the Sun agreeing to the time of repl. . 04642 The Sum Add . 59800 Motion of Latitude at the visible ☌ 8. 77768 Motion of Latitude at the ending 9 37568 True Latitude North . 80925 Parallax of Latitude . 65218 Visible Latitude North . 15707 CHAP. 36. To Delineate the Eclipses▪ of the Sun and Moon. FOr the Moon draw the lines AC and BD to intersect one another at right angles in E, which point of intersection is the place of the Ecliptic where the Eclipse happens: upon which as a Centre draw the periphery ABCD, of the quantity of the sum of the Semidiameters of the Moon and the earth's shadow (which may be done by help of a Scale or Sector of equal divisions) also to the quantity of the Semidiameter of the earth's shadow, draw upon the same centre another periphery. Then because the Moon's Eclipse begins on the east part of her body, you must upon the west side of your plane, note down the latitude of the Moon in the arch BCD, which here▪ represents the west part▪ and may be thus done, From E upon the line BD prick out the latitude at the beginning; towards B, if the Latitude be North, towards D if South, and it terminat●s at G, from which draw a parallel to AC, and in the arch BC it marks out F. Also for the end of the Eclipse proceed in like manner on the other side, and you have the latitude terminated at I, and the parallel falling at H. Then draw a line between F and H and where it intersects BD mark it with K. Lastly, upon the centres F, K and H, draw three equal circles, having for Radius the Semidiameter of the Moon, and the work is done. Typus Eclipseos Lunae praedictae. Example of the forementioned Eclipse of the Moon March 15. 1652 Sum of the Semidiameters EBB . 97385 Semidiameter of shadow EM . 70954 Initial latitude of the Moon EGLANTINE, North . 59223 Final latitude of the Moon EI North . 43746 Semidiameter of the Moon MB . 26431 2 For the Eclipse of the Sun, it differs nothing at all from this of the Moon, but only that instead of the Semidiameter of the shadow of the earth you use the Semidiameter of the Sun; and the visible latitude for the true. Example of the forementioned Sol●● Eclipse March 28. ●652. Summe of the Semidiameters EBB . 5520● Semidiameter of the Sun EM . 27386 Initial visible latitude EGLANTINE South . 11353 Final visible latitude EI North . 15707 Semidiameter of the Moon MB . 27815 Typus Eclipseos Solis pr●dict●. CHAP. 37. The use of the Table of Refractions. ALthough the Table of Refractions, belongs not to the calaulation of these Tables, yet will it not be amiss to show its use in comparing of observation with calculation. Know then that Refraction, causeth the stars to appear higher then really they are. Therefore with an observed altitude enter this Table and take out the Refraction, which subtract from the observed altitude, and you have the true altitude, or having the true altitude, the apparent is found by adding the Refraction thereto. FINIS. This Scheame hath particular relation to page 103, and is there printed in most Copies, but in some Copies there is another Scheame placed instead thereof, the Reader is therefore desired (where it is wanting) to insert it. Errata. Page 7. line the last, for the North read C the North. Page 8. line 10 read or the arch H ♋. Page 21. line 20 for else of that, read else that. Page 29. line 39 for ED 38 read ED 30. Page 37. line 23 for paraallctical read parallactical. Page 76. line 14 for plane parallel read plane is parallel. In the Tables. Page 26 against degree 11 for 0, 38836 read 0, 38336. Page 27 against degree 90 for 5, 0201387 read 5, 0001387. Page 27 against degree 117 for 4, 9961795 read 4, 9965795. Page 34 against degree 56 for 3, 04 etc. read 4, 04 etc. Page 35 against degree 87 for 5, 0010809 read 5, 0018089. Page 35 against degree 119 for 4, 163 etc. read 4, 463 etc. Page 36 against degree 132 for 3, 874 etc. read 824 etc. Page 36 against degree 139 for 3, 38920 read 3, 38902. Page 36 against degree 126 for 4, 9895915 read 4, 9895925. Page 36 against degree 179 for 0, 69126 read 0, 09126. Page 86 In the Title, for A Table of Declinations, read A Table of Right Ascensions. Let this leaf be folded in at page 168, which is between the second and third Books. This Diagram having particular relation to the 18 Chapter of the second Book, will be in use for divers leaves together, I thought it therefore convenient, to place it so that when the Book is opened in any part, the Dirgram might be in▪ sight, and have therefore ordered it to be folded in. Astronomia BRITANNICA The third Part: Exhibiting Tables, for the converting of Sexagenary Numbers into Decimal and the contrary, for Astrononomical Chronologie with the Ecclesiastical Computation, and the Calculation of the places of the Planets, Eclipses of the Luminaries and Doctrine of the Sphere. bookseller's logo LONDON. Printed by R. and W. Leybourne Anno Domini 1656. A view of the more notable Epochae. Epochae Years of the Julian Period Months The julian Period 1 januar. 1 Creation of the World 765 januar. 1 Aera of the Olympiades' 3938 july 8 The building of Rome 3961 April 21 Epochaes of Nabonassor 3667 Febru. 26 The beginning of Meton's Circle 4281 june 26 The beginning of the Periods of Calippus 4384 june 28 The Death of Alexander the great 4390 Nove. 12 Aera of the Chaldees 4403 Octob. 15 The Aera of Dyonisius 4429 Marc. 25 The beginning of the Christian Aera falls in the 4713 Year of the Julian period complete. Years of Christ Month. The Diocletian Aera 284 Augu. 29 The Turkish Aera or Negyra 622 july 16 The Persian Aera from Jesdagird 632 june 16 The Aera of the Persian Sultan 1079 Marc. 14 Days in years of the Julian account Egypt. and Persian account 1 0 0 0 365 2 5 0 1 0 0 0 365 0 0 0 2 0 0 0 730 5 0 0 2 0 0 0 730 0 0 3 0 0 0 1095 7 5 0 3 0 0 0 1095 0 0 4 0 0 0 1461 0 0 0 4 0 0 0 1460 0 0 5 0 0 0 1826 2 5 0 5 0 0 0 1825 0 0 0 6 0 0 0 2191 5 0 0 6 0 0 0 2190 0 0 0 7 0 0 0 2556 7 5 0 7 0 0 0 2555 0 0 8 0 0 0 2922 0 0 0 8 0 0 0 2920 0 0 0 9 0 0 0 3287 2 5 0 9 0 0 0 3285 0 0 0 10 0 0 0 3652 5 0 0 10 0 0 0 3650 0 0 0 Days in Months of the Julian Com. B ss Egyptian Persian account. Januar. 31 1 Thoth 30 Pharvadin 30 Februar. 5● 60 Paophi 60 Aripehest 60 March 90 91 Athyr 90 Chortat 90 April 120 121 Chaeac 120 Tyrma 120 May 151 152 Tybi 150 Mertat 150 June 181 182 Mechir 180 Sachriur 180 July 212 213 Phamenoth 210 Mecherma 210 August 243 244 Pharmuthi 240 Apanma 245 Septem. 273 274 Pachon 270 Wahak 245 Octob. 304 305 Payni 300 Ad●rma 275 Novem 334 335 Ephephi 330 Dima 305 Decem. 365 366 Mesori 360 Pechmam 335 Epagomena 365 Asphander 365 Days in Turkish or Arabical Years. 1 354 2 709 3 . 1063 4 . 1417 5 . 1772 6 . 2126 7 . 2480 8 . 2835 9 . 3189 10 . 3543 11 . 3898 12 . 4252 13 . 4607 14 . 4961 15 . 5315 16 . 5670 17 . 6024 18 . 6378 19 . 6733 20 . 7087 21 . 7442 22 . 7796 23 . 8150 24 . 8505 25 . 88●9 26 . 9213 27 9568 28 9922 29 10276 30 0 10631 0 60 0 21262 0 90 0 31893 0 120 0 42524 0 150 0 53155 0 180 0 63786 0 210 0 74417 240 0 85048 0 270 0 95679 0 300 0 106310 0 Days in Turkish Months. Muharram 30 Sahahen 236 Sephar 59 Ramadhan 266 Rabie I 89 Schevall 295 Rabie TWO 118 Dulkadati 325 Giumadi I 148 Dulhajati 354 Giumadi TWO 177 Dsilhit●sche, Tur●. 354 Regeb 207 In anno abundanti 355 A Table showing the Dominical Letter in both accounts. Years of our Lord Cycle of the Sun Julian accom Greg. accom 1644 1 G F C B 1645 2 E A 1646 3 D G 1647 4 C F 1648 5 B A E D 1649 6 G C 1650 7 F B 1651 8 E A 1652 9 D C G F 1653 10 B E 1654. 11 A D 1655 12 G C 1656 13 F E B A 1657 14 D G 1658 15 C F 1659. 16 B E 1660 17 A G D C 1661. 18 F B 1662. 19 E A 1663. 20 D G 1664 21 C B F ● 1665 22 A D 1666 23 G C 1667 24 F B 1668 25 E D A G 1669 26 C F 1670 27 B E 1671 28 A D A Table showing the Epact in both accounts. Years of our Lord Gold Num. Epac. Julian. Epact Greg. 1653 1 11 1 1654. 2 22 12 1655 3 3 23 1656 4 14 4 1657 5 25 15 1658 6 6 26 1659. 7 17 7 1660 8 28 18 1661. 9 9 29 1662. 10 20 10 1663. 11 1 21 1664 12 12 2 1665 13 23 13 1666 14 4 24 1667 15 15 5 1668 16 26 16 1669 17 7 27 1670 18 18 8 1671 19 29 19 The Anticipation of the Gregorian Calendar. A5Oct. 10 1582 11 1700 A24Fe. 12 1800 13 1900 14 2100 15 2200 16 2●●0 d. A. D. 17 2500 18 2600 19 2700 20 2900 21 3000 22 3100 A Table of movable Feasts in both accounts. Ep DL Lxx L Ash. East. Asce. Pen. Corp. Advent Sun. 25 D Jan 18 Feb. 1 Feb. 4 March Ap. 30 May 1● May 29 Nove. D ●2 24 E 19 2 5 23 May 1 11 22 30 E 21 23 F 20 3 6 24 2 12 23 1 Decem F 20 22 G 21 4 7 25 4 13 24 2 G 19 21 A 22 5 8 26 4 14 25 3 A 18 20 B 23 6 9 27 5 15 26 27 Nove. B 17 19 C 24 7 10 28 6 16 27 28 C 16 18 D 25 8 11 29 7 17 28 29 D 15 17 E 26 9 12 30 8 18 29 30 E 14 16 F 27 10 13 31 9 19 30 1 Decem F 13 15 G 28 11 14 Ap. 1 10 20 31 2 G 12 34 A 29 12 15 2 11 21 June 1 3 A 11 13 B 30 13 16 3 12 22 2 27 Nove. B 10 12 C 31 14 17 4 13 23 3 28 C 9 11 D Feb. 1 15 18 5 14 24 4 29 D 8 10 E 2 16 19 6 15 25 5 30 E 7 9 F 3 17 20 7 16 26 6 1 Decem F 6 8 G 4 18 21 8 17 27 7 2 G 5 7 A 5 19 22 9 18 28 8 3 A 4 6 B 6 20 23 10 19 29 9 27 Nove. B 3 5 C 7 21 24 11 20 30 10 28 C 2 4 D 8 22 25 12 21 31 11 29 D 1 3 E 9 23 26 13 22 June 1 12 30 E * 2 F 10 24 27 14 23 2 13 1 Decem F 29 1 G 11 25 28 15 24 3 14 2 G 28 * A 12 26 Mar. 1 16 25 4 15 3 A 27 29 B 13 27 2 17 26 5 16 27 Nove. B 26 28 C 14 28 3 18 27 6 17 28 C 24 * D 15 Mar. 1 4 19 28 7 18 29 D * * E 16 2 5 20 29 8 19 30 E * * F 17 3 6 21 30 9 20 1 Decem F * * G 18 4 7 22 31 10 21 2 G * * A 19 5 8 23 June 1 11 22 3 A * 27 B 20 6 9 24 2 12 23 27 Nove. B * 26 C 21 7 10 25 3 13 24 28 C 23 A Table of Fixed Feasts January February March April May June July August Septemb October Novem. Decem. 1 Circu. a ●gnat. d d g P. & ja. b e g Lammas c Aegyd. f Remigi. a All Sa. d f 2 b Pu. M. e e Frande P a c Marcel. f Visi M. a d g b All son. e Bibinia g 3 c Blasius f f b Inu. cru. d g b e a c f a 4 d g Lucius g c e a c f b Francis. d Vital. g Barbara b 5 Telesph. e Agath. a a d f b d Ded. M. g c e a c 6 Epfphan. f Doroth. b b e Jo. p. latg c e Transf. a d f b d 7 g c c f a d f b e Marc. p. g c Ambro. e 8 a d d g Ap. SM. b e g c Na. M. f a d Conc. M f 9 b Apollo. e 40 Mar. e a c Primus f a d g Dionys. b e g 10 c f f b d g 7 fratr. b Laurenc e a c Tryph. f a 11 Hygin. d g g Leo Pa. c e Barnab. a c f b d Martin g b 12 e a Gregor. a d f b Nabor d g c e a c 13 f b b e g Anton. c e a d f b Lucia d 14 Hilari. g Valent. c c T. V. M. f Bonifa. a Basil. d Bonav. f b Exal. cr. e Callist. g c e 15 Paul Er. a Fa. & J. d d g b e g Ass. M. c f a d Eusebius f 16 Marcel. b e e a Ubald c f a d Cornel. g b e g 17 Anton. c f f Anicet. b d g Alexius b e a c Gregor. f a 18 Cut. S P d Simeon g g c e a c f b Lucos d g b 19 e a jos. con. a d Prudent. f Gervasi. b d g c e Pontia. a c 20 Fab. & se f b b e g c Margar. e Bernar. a d f b d 21 Agnet. g c Benedi. c f a d f b Mat. E e Hilarion. g Ob. Ma. c Tho. a. e 22 Vincen. a d d Soter. c. g b e M Mag. g c f a d f 23 b e e George a c f a d Linus g b e g 24 Timoth. c S. Ma. f f b d S. I B g b Bart. a. c a c f a 25 Con. P. d g An. Madge S Mar. c Urban. e a Jam. a. c f b Chrysa. d Catarrh. g Na. C. b 26 Policar. e a a d f b d g Cyprian c e a Step●. c 27 f b b e Jo. pap. g c e a d f b Joh. E. d 28 g c c Vitalis f a d f August. b e Si. Iu. g c Innoce. e 29 a d Catarrh. g b Leo e Martha g Decoll. c Mich. A f a d T. Cant. f 30 b e a Felix c Pet. ap. f a d Hieron. g b And. a. e g 31 c f Petrom. d g b e c Silvest. a A Catalogue of some famous places with their Latitude, and distance in Longitude from the Meridian of London. The Names of the Places. Difference of Meridia. H. Parts Height of the Pole D. Parts Aberden in Scotland S 0. 11667 58. 66667 Adrionaplis in Thrace A 2. 06667 43. 3333● Ag●ia in Hungary A 1. 35000 47. 93333 Alba Julia in Transylvania A 1. 53333 47. 00000 Alepus in Syria A 2. 41667 37. 33333 Alexandria in Egypt A 2. 18333 30. 96667 Algiers in Africa A 0. 38333 35. 60000 Amsterdam in Holland A 0. 35000 52. 41667 Antwerp in Brabant A 0. 28333 51. 20000 Aracta in Chaldaea A 3. 30000 36. 00000 Arbela in Assyria A 3. 76667 37. 25000 Astracan upon Volgo in Tarta●ia A 3. 96667 50. 00000 Athens in Greece A 1. 86667 37. 00000 Bamberge in Franconie A 0. 75000 49. 61667 Bononia in Italy A 0. 71667 43. 81677 Brundisium in Calabria A 1. 28333 49. 53333 Bulgaria in Tartary A 4. 03333 56▪ 00000 Burgos in Spain S 0. 25000 42. 66667 Calecutum in India A 5. 83333 11. 50000 Cambridge in England A 0. 03333 52. 33333 Carthage in Africa A 0. 68333 34. 83333 Casan in Tartary A 4. 00000 58. 00000 Cassels in Hessia A 0. 73333 51. 31667 Cair grand in Egypt A 2. 26667 29. 83333 Chalcedon A 2. 33333 43. 25000 Chester in England S 0. 16667 53. 26667 Cochin in India A 5▪ 90000 9 90000 Cola in Lapland A 2. 30000 69. 40000 Colberg in Pomerania A 1. 03333 54. 46667 Compostella in Spain S 0. 63333 43. 00000 Constantinople in Thrace A 2. 30000 43. 00000 Conymbre in Lusitania S 0. 58333 40. 25000 Cracow in Poland A 1. 35000 49. 96667 Crim of Precopensis in Tart●ry A 2. 70000 47. 83333 Damascus in Syria A 3. 26667 34. 00000 Dantzik of Borussia in Poland A 1. 13333 54. 38333 Doüay in Artesia A 0. 23333 50. 40000 Edinburgh in Scotland S 0. 03333 55. 95000 Epidaurus in Peloponnesis A 1. 86667 35. 50000 Famagusta in Cyprus A 2. 95000 35. 00000 Francford upon Other A 0. 55000 50. 11667 Francford upon Maene A 0. 96667 52. 33333 Fruenburg in Borussia A 1. 36667 54. 36667 Grat●um in Stiria A 1. 06667 47. 03333 Groining in Frizia A 0. 43333 53. 25000 Hamburg in Holsatia A 0. 66667 53. 71667 Haphnia in Denmark A 0. 81667 55. 71667 Lipsia in Misnia A 0. 81667 51. 40000 Liverpoole in England S 0. 16667 53. 36667 LONDON in England 0. 00000 51. 53333 Louvain in Brabant 0. 33333 50. 83333 Leyden A 0. 31667 52. 18333 Middleburg in Zealand A 0. 26667 51. 50000 Manchester in England A 0. 15000 53. 40000 Naples in Italy S 0. 96667 40. 70000 Nicomedia in Bythynia A 2. 3●333 42. 50000 Nidrosia in Norway A 0. 56667 63. 20000 Newcastle in England A 0. 01667 55. 05000 No●imberg in Germany S 0. 76667 49. 43333 Orleans in France A 0. 00000 48. 13333 Oxford in England 0. 05000 52. 06667 Paris in France S 0. 13333 48. 65000 corrected by Bullialdus A 0. 03333 48. 85000 Patavium in Liburnia A 0. 76667 45. 10000 Prague in Bohemi● A 0. 93333 50. 10000 Rhodes an Island A 3. 43333 36. 00000 Rochel in Aquitain A 0. 06667 45. 81667 Rochester in England S 0. 03333 51. 50000 Rome in Italy A 0. 83333 42. 03333 Rouen in Normandi● A 0. 00000 49. 63333 Smarcanda in Tartary A 5. 66667 45. 00000 Scutara in Dalmatia A 1. 43333 42. 38333 Sevill in Spain S 0▪ 36667 37. 33333 Spahani in Persia A 4. 33333 31. 50000 Stetin in Pomerania A 0. ●6667 53. 60000 Syracuse in Sicily A 1. ●8333 86. 83333 Toledo in Spain S 0. 23333 39 90000 Tubing Wittenburg A 0. 63333 48. 56667 Valence in Spain A 0. 10000 39▪ 50000 Ulme in Suevia A 0. 70000 48. 40000 Uraniburge in Denmark A 0. 83338 55▪ 91667 York in England S 0▪ 05000 54. 03333 A Table to convert Sexagenary minutes, ′ ″ P 0 00 . 36 01 1. 12 02 1. 48 03 2. 24 04 3. 0 05 3. 36 06 4. 12 07 4. 48 08 5. 24 09 6. 0 10 6. 36 11 7. 12 12 7. 48 13 8. 24 14 9 0 15 9 36 16 10. 12 17 10. 48 18 11. 24 19 12. 0 20 12. 36 21 13. 12 22 13. 48 23 14. 24 24 15. 0 25 15. 36 26 16. 12 27 16. 48 28 17. 24 29 18. 0 30 18. 36 31 19 12 32 19 48 33 20. 24 34 21. 0 35 21. 36 36 22. 12 37 22. 48 38 23. 24 39 24. 0 40 24. 36 41 25. 12 42 25. 48 43 26. 24 44 27. 0 45 27. 36 46 28. 12 47 28. 48 48 29. 24 49 30. 0 50 30. 36 51 31. 12 52 31. 48 53 32. 24 54 33. 0 55 33. 36 56 34. 12 57 34. 48 58 35. 24 59 36. 0 60 36. 36 61 37. 12 62 37. 48 63 38. 24 64 39 0 65 39 36 66 40. 12 67 40. 48 68 41, 24 69 42. 0 70 42. 36 71 43. 12 72 43. 48 73 44. 24 74 45. 0 75 45. ●6 76 46. 12 77 46 48 78 47 24 79 48. 0 80 48. 36 81 49. 12 82 49. 48 83 50. 24 84 51. 0 85 51. 36 86 52. 12 87 52. 48 88 53. 24 89 54. 0 90 54. 36 91 55. 12 92 55. 48 93 56. 24 94 57 0 95 57 36 96 58. 12 97 58. 48 98 59 24 99 60. 0 100 and seconds into Decimals and the contrary 0 36 12 48 24 00000000 1 37 13 49 25 02777778 2 38 14 50 26 05555555 3 39 15 51 27 08333333 4 40 16 52 28 11111111 5 41 17 53 29 13888889 6 42 18 54 30 16666667 7 43 19 55 31 19444444 8 44 20 56 32 22222222 9 45 21 57 33 25000000 10 46 22 58 34 27777778 11 47 23 59 35 30555555 12 48 24 1. 00 36 33333333 13 49 25 1 37 36111111 14 50 26 2 38 38888889 15 51 27 3 39 41666667 16 52 28 4 40 44444444 17 53 29 5 41 47222222 18 54 30 6 42 50000000 19 55 31 7 43 52777778 20 56 32 8 44 55555555 21 57 33 9 45 58333333 22 58 34 10 46 61111111 23 59 35 11 47 63888889 24 1. 00 36 12 48 66666667 25 1 37 13 49 69444444 26 2 38 14 50 72222222 27 3 39 15 51 75000000 28 4 40 16 52 77777778 29 5 41 17 53 80555555 30 6 42 18 54 83333333 31 7 43 19 55 86111111 32 8 44 20 56 88888889 33 9 45 21 57 91666667 34 10 46 22 58 94444444 35 11 47 23 59 97222222 Thirds fourths Fifths 1 0000046296 0000000772 0000000013 2 92593 1573 26 3 138889 2315 39 4 185185 3046 51 5 231481 3858 64 6 277778 4630 77 7 324074 5401 90 8 370370 6173 103 9 416667 6944 116 10 462963 7716 129 11 509259 8488 141 12 555556 9259 154 13 601852 100 1 167 14 648148 10802 180 15 694444 11574 193 16 740741 12345 206 17 78●037 13117 219 18 833333 13889 232 19 879630 14660 245 20 925926 15432 258 21 972222 16204 270 22 1018518 16975 283 23 1064814 17747 296 24 1111111 18518 309 25 1157407 19290 322 26 1203703 20062 335 27 1250000 20833 348 78 1296296 21605 360 29 1342592 22376 373 30 1388888 23148 386 31 0001435184 0000023920 0000000399 32 1481481 24691 412 33 1527777 25463 425 34 1574073 26234 438 35 1620370 27006 450 36 1666666 27778 463 37 1712963 28549 476 38 1759259 29321 489 39 1805556 30092 502 40 1851852 30864 515 41 1898148 31636 527 42 1944444 32407 540 43 1990740 33179 553 44 2037037 33950 566 45 2083333 34722 579 46 2129629 35494 592 47 2175925 36265 605 48 2222222 37037 618 49 2268518 37808 630 50 2314815 38580 643 51 2361111 39352 656 52 2407407 40123 669 53 2453703 40895 682 54 2500000 41666 694 55 2546296 42438 707 56 2592502 43210 720 57 2638889 43981 733 58 2685185 44753 746 59 2731481 45524 759 60 2777778 46296 772 H. M. P 0 0 2. 24 1 4. 48 2 7. 12 3 9 36 4 12. 00 5 14. 24 6 16. 48 7 19 12 8 21. 36 9 A Table to convert the hours and minutes. of a day into Decimals and the contrary. 0 24 48 12 36 000000000 1 25 49 13 37 006944444 2 26 50 14 38 013888889 3 27 51 15 39 020833333 4 28 52 16 40 027777778 5 29 53 17 41 034722222 6 30 54 18 42 041666667 7 31 55 19 43 048611111 8 32 56 20 44 055555555 9 33 57 21 45 062500000 10 34 58 22 46 069444444 11 35 59 23 47 076388889 12 36 5. 17 24 48 083333333 13 37 1 25 49 090277778 14 38 2 26 50 097222222 15 39 3 27 51 104166667 16 40 4 28 52 111111111 17 41 5 29 53 11805555● 18 42 6 30 54 125000000 19 43 7 31 55 131944444 20 44 8 32 56 138888889 21 45 9 33 57 145833333 22 46 10 34 58 152777778 23 47 11 35 59 159722222 24 48 12 36 10. 22 166666667 25 49 13 37 1 173611111 26 50 14 38 2 180555555 27 51 15 39 3 187500000 28 52 16 40 4 194444444 29 53 17 41 5 201388889 30 54 18 42 6 208333333 31 55 19 43 7 215277778 32 56 20 44 8 222222222 33 57 21 45 9 229166667 34 58 22 46 10 236111111 35 59 23 47 11 243055555 36 3. 15 24 48 12 250200000 37 1 25 49 13 256944444 38 2 26 50 14 26●888889 39 3 27 51 15 270833333 40 4 28 52 16 277777778 41 5 29 53 17 284722222 42 6 30 54 18 291666667 43 7 31 55 19 298611111 44 8 32 56 20 305555555 45 9 33 57 21 312500000 46 10 34 58 22 319444444 47 11 35 59 23 326388889 48 12 36 8. 20 24 333333333 49 13 37 1 25 340277778 50 14 38 2 26 347222222 51 15 39 3 27 354166667 52 16 40 4 28 361111111 53 17 41 5 29 368055555 54 18 42 6 30 375000000 55 19 43 7 31 381944444 56 20 44 8 32 388888889 57 21 45 9 33 395833333 58 22 46 10 34 402777778 59 23 47 11 35 409722222 1. 1 24 48 12 36 416666667 1 25 49 13 37 423611111 2 26 50 14 38 430555555 3 27 51 15 39 437500000 4 28 52 16 40 444444444 5 29 53 17 41 451388889 6 30 54 18 42 458333333 7 31 55 19 43 465277778 8 32 56 20 44 472222222 9 33 57 21 45 479166667 10 34 58 22 46 486111111 11 35 59 23 47 493055555 12 36 6. 18 24 48 500000000 13 37 1 25 49 506944444 14 38 2 26 50 513888889 15 39 3 27 51 520833333 16 40 4 28 52 527777778 17 41 5 29 53 534722222 18 42 6 30 54 541666667 19 43 7 31 55 548911111 20 44 8 32 56 555555555 21 45 9 33 57 562500000 22 46 10 34 58 569444444 23 47 11 35 59 576388889 24 48 12 36 11. 23 583333333 25 49 13 37 1 590277778 26 50 14 38 2 597222222 27 51 15 39 3 604166667 28 52 16 40 4 611111111 29 53 17 41 5 618055555 30 54 18 42 6 625000000 31 55 19 43 7 631944444 32 56 20 44 8 638888889 33 57 21 45 9 645833333 34 58 22 46 10 652777778 35 59 23 47 11 659722222 36 4. 16 24 48 12 666666667 37 1 25 49 13 673611111 38 2 26 50 14 680555555 39 3 27 51 15 687500000 40 4 28 52 16 694444444 41 5 29 53 17 701388889 42 6 30 54 18 708333333 43 7 31 55 19 715277778 44 8 32 56 20 722222222 45 9 33 57 21 729166667 46 10 34 58 22 736111111 47 11 35 59 23 743055555 48 12 36 9 21 24 750000000 49 13 37 1 25 756944444 50 14 38 2 26 763888889 51 15 39 3 27 770833333 52 16 40 4 28 777777778 53 17 41 5 29 784722222 54 18 42 6 30 791666667 55 19 43 7 31 798611111 56 20 44 8 32 805555555 57 21 45 9 33 812500000 58 22 46 10 34 819444444 59 23 47 11 35 826388889 2. 14 24 48 12 36 833333333 1 25 49 13 37 840277778 2 26 50 14 38 847222222 3 27 51 15 39 854166667 4 28 52 16 40 861111111 5 29 53 17 41 868055555 6 30 54 18 42 875000000 7 31 55 19 43 881944444 8 32 56 20 44 888888889 9 33 57 21 45 895833333 10 34 58 22 46 902777778 11 35 59 23 47 909722222 12 36 7. 19 24 48 916666667 13 37 1 25 49 923611111 14 38 2 26 50 930555555 15 39 3 27 51 937500000 16 40 4 28 52 944444444 17 41 5 29 53 951388889 18 42 6 30 54 958333333 19 43 7 31 55 965277778 20 44 8 32 56 972222222 21 45 9 33 57 979166667 22 46 10 34 58 9861●1111 23 47 11 35 59 993055555 24 48 12 36 00 000000000 Seconds. Thirds Fourth's Fifths 1 0000115741 0000001929 0000000032 0000000001 2 231481 385● 64 0000000001 3 347222 5787 96 2 4 463963 7716 0000000129 2 5 578704 9645 161 3 6 694444 0000011574 193 3 7 810185 13503 225 4 8 925926 15432 257 4 9 0001041666 17361 289 5 10 1157407 19290 321 5 11 1273148 21219 354 6 12 1388889 23148 387 7 13 1504630 25077 420 7 14 1620371 27006 453 8 15 1736112 28935 486 8 16 1851853 39864 518 9 17 1967593 32793 559 9 18 2083333 34722 582 10 19 2199074 36651 614 10 20 0002314815 0000038580 0000000643 0000000011 21 2430555 40509 675 11 22 2546296 42438 707 12 23 2662037 44367 739 12 24 2777778 46296 771 13 25 2893518 48225 803 13 26 3009259 50254 836 14 27 3125000 52183 869 14 28 3240741 54112 902 15 29 3356482 56041 934 15 30 0003472222 0000057870 0000000965 0000000016 31 0003587963 00000059799 0000000997 0000000016 32 3703704 61728 1030 17 33 3819444 63657 1062 17 34 3935185 65586 1094 18 35 4050926 67515 1126 18 36 4166667 69444 1157 19 37 4282407 71373 1189 19 38 4398148 73302 1222 20 39 4513889 75231 1254 20 40 4629630 77160 1286 21 41 4745370 79089 1318 22 42 4861111 81018 1350 22 43 4976852 82947 1382 23 44 5092592 84876 1414 23 45 5208333 86805 1446 24 46 5324074 88734 1479 24 47 5439814 90663 1511 25 48 5555555 92592 1544 25 49 5671296 94521 1676 26 50 5787037 96451 1680 27 51 5902778 98380 1641 27 52 6018518 100309 1673 28 53 6134259 102238 1705 28 54 6250000 104167 1737 29 55 6365741 106096 1770 29 56 6481481 108025 1802 30 57 6597222 109954 1834 30 58 6712963 111883 1866 31 59 6828704 113812 1898 31 60 6944444 115741 1929 32 A Table converting Hours and parts into Degrees and parts of the Aequator. IV ‴ ″ ″ ′ 0 Ho. Deg. M D. Parts. 1 15 01 00, 15000 2 30 02 00, 30 3 45 03 00, 45 4 60 04 00, 60 5 75 05 00, 75 6 90 06 00, 90 7 105 07 01, 05 8 120 08 01, 20 9 135 09 01, 35 10 150 10 01, 50 11 165 11 01, 65 12 180 12 01, 80 13 195 13 01, 95 14 210 14 02, 10 15 ●25 15 02, 25 16 240 16 02, 40 17 255 17 02, 55 18 270 18 02, 70 19 285 19 02, 85 20 300 20 03, 00 21 315 21 03, 15 22 330 22 03, 30 23 345 23 03, 45 24 360 24 03, 60 25 03, 75 26 03, 90 27 04, 05 28 04, 20 29 04, 35 30 04, 50 31 04, 65 32 04, 80 33 04, 95 34 05, 10 35 05, 25 36 05, 40 37 05, 55 38 05, 70 39 05, 85 40 06, 00 41 06, 15 42 06, 30 43 06, 45 44 06, 60 45 06, 75 46 06, 90 47 07, 05 48 07, 20 49 07, 35 50 07, 50 51 07, 65 52 07, 80 53 07, 95 54 08, 10 55 08, 25 56 08, 40 57 08, 55 58 08, 70 59 08, 85 60 09, 00 61 09, 15 62 09, 30 63 09, 45 64 09, 60 65 09, 75 66 09, 90 67 10, 05 68 10, 30 69 10, 35 70 10, 50 71 10, 65 72 10, 80 73 10, 95 74 11, 10 76 11, 25 77 11, 40 57 11, 55 78 11, 70 79 11, 85 80 12, 00 81 12, 15 82 12, 30 83 12, 45 84 12, 60 85 12, 75 86 12, 90 87 13, 05 88 13, 20 89 13, 35 90 13, 50 91 13, 65 92 13 80 93 13, 93 94 14, 10 95 14, 25 96 14, 40 97 14, 55 98 14, 70 99 14, 85 A Perpetual Table for the Aequation of Time. D ♈ P. Add ♉ P. Add ♊ P. Add ♋ P. Sub. ♌ P. Sub. ♍ P. Sub. D 0 00000 14027 14639 00000 14639 14027 30 1 00555 14333 14362 00611 14917 13722 29 2 01111 14583 14055 01194 15167 13389 28 3 01638 14861 13750 0180● 15389 13055 27 4 02194 15111 13416 02416 15583 12694 26 5 02750 15333 13055 03000 15778 12333 25 6 03305 15527 12667 03583 15944 11944 24 7 03833 15722 12278 04361 16111 11555 23 8 04389 15889 11861 04750 16222 11138 22 9 04917 16027 11444 05333 16333 10722 21 10 05444 16167 11000 05917 16416 10305 20 11 05972 16278 10555 06472 16472 09861 19 12 06472 16389 10083 07000 16527 09389 18 13 07000 16444 09611 07555 16555 08944 17 14 07500 16500 09111 08083 16555 08472 16 15 07972 16555 08611 08611 16555 07972 15 16 08472 16555 08883 09111 16500 07500 14 17 08944 16555 07555 09611 16444 07000 13 18 09389 16527 07000 10083 16389 06472 12 19 09861 16472 06472 10555 16278 05972 11 20 10305 16416 05917 11000 16167 05444 10 21 10722 16333 05333 11444 16029 04917 9 22 11138 16222 04750 11862 15889 04389 8 23 11555 16111 04361 12278 15722 03833 7 24 11944 15944 03583 12667 15527 03305 6 25 12333 15778 03000 13055 15333 02750 5 26 12694 15583 02416 13426 15112 02194 4 27 13055 15389 01805 13750 1486● 01638 3 28 13389 15167 01194 14055 14583 01111 2 29 13722 14917 00611 14361 14333 00555 1 30 14027 14639 00000 14639 14027 00000 0 D ♓ Sub. ♒ Sub. ♑ Sub. ♐ Add ♏ Add ♎ Add D The Sun's mean Motions. Epochae Longit. ☉ Deg. parts Apog. ☉ Deg. parts ● ♈ & Fix. Deg. Parts. Christi. 278. 98331 70. 32264 4. 97537 1600 290. 94859 95. 59094 27. 61667 1620 291. 09815 95. 90680 27. 89968 1640 291. 24771 96. 22265 28. 18270 1660 291. 39724 96. 53851 28. 46571 1 359. 76107 0. ●1578 0. 01414 2 359. 52213 0. 03156 0. 02828 3 359. 28310 0. 04734 0. 04242 B 4 0. 02991 0. 06317 0. 05660 5 359. 79098 0. 07895 0. 07074 6 359. 55205 0. 09473 0. 0848● 7 359. 31311 0. 11051 0. 09903 B 8 0. 05982 0. 12634 0. 11321 9 359. 82089 0. 14212 0. 12735 10 359. 58196 0. 15790 0. 14149 11 359. 34303 0. 17369 0. 15563 B 12 0. 08974 0. 18951 0. 16981 13 359. 85081 0. 20529 0. 18395 14 359. 61187 0. 22107 0. 19809 15 359. 37294 0. 23686 0. 21223 B 16 0. 11965 0 25268 0. 22641 17 359. 88072 0. 26864 0. 24055 18 359. 64178 0. 28425 0. 25469 19 359. 40285 0. 30003 0. 26884 B 20 0. 14956 0. 31585 0. 28302 40 0. 29913 0. 63171 0. 56603 60 0. 44870 0. 94756 0. 84905 80 0. 59826 1. 26342 1. 13206 100 0. 74783 1. 57927 1. 41508 The Suns mean Motions. Years. Longit. ☉ Deg. parts. Apog. ☉ Deg. parts. Fixed ✴. Deg. parts. 100 0, 74783 1, 57927 1, 41508 200 1, 49566 3, 15854 2, 830●6 300 2, 24349 4, 73781 4, 24524 400 2, 99132 6, 31708 5, 66023 500 3, 73915 7, 89635 7, 07540 600 4, 48698 9, 47562 8, 49048 700 5, 23481 11, 05489 9, 90557 800 5, 98264 12, 63415 11, 32065 900 6, 73047 14, 21342 12, 73573 1000 7, 47830 15, 79369 14, 15081 2000 14, 95660 31, 58538 28, 30162 3000 22, 43490 47, 37808 42, 45242 4000 29, 91320 63, 17077 56, 60323 5000 37, 39150 78, 96346 70, 75404 january 30, 55505 0, 00134 0, 00120 February 58, 15315 0, 00255 0, 00228 March 88, 70820 0, 00389 0, 00349 April 118, 27760 0, 00519 0, 00465 May 148, 83265 0, 00653 0, 00586 june 178, 40205 0, 00783 0, 00701 july 208, 95710 0, 00917 0, 00821 August 239, 51215 0, 01051 0, 00941 September 267, 08155 0, 01180 0, 01058 October 269, 63660 0, 01314 0, 01178 November 329, 20600 0, 01444 0, 01294 December 359, 76107 0, 01578 0, 01414 The Suns mean Motions. In Days. ☉ Longit. Deg. Parts. ☉ Apog. Parts. Fixed ✴ Parts 1 0. 98565 . 00004 , 00004 2 1. 97129 . 00008 , 00008 3 2. 95694 . 00013 , 00012 4 3. 94258 . 00017 , 00015 5 4. 92823 . 00022 , 00019 6 5. 91388 . 00026 , 00023 7 6. 89953 . 00030 , 00027 8 7. 88517 . 00034 , 00031 9 8. 87082 . 00039 , 00035 10 9 85647 . 00043 , 00039 11 10. 84211 . 00048 , 00043 12 11. 82776 . 00052 , 00046 13 12. 81341 . 00056 , 00050 14 13. 79905 . 00060 , 00054 15 14. 78470 . 00065 , 00058 16 15. 77035 . 00069 , 00062 17 16. 75599 . 00073 , 00066 18 17. 74164 . 00078 , 00070 19 18. 72729 . 00082 , 00074 20 19 71293 . 00086 , 00077 21 20. 69858 . 00091 , 00081 22 21. 68423 . 00095 , 00085 23 22. 66987 . 00099 , 00089 24 23. 65542 . 00104 , 00093 25 24. 64117 . 00108 , 00097 26 25. 62681 . 90112 , 00101 27 26. 61246 . 00117 , 00105 28 27. 59811 . 00121 , 00108 29 28. 58375 . 00125 , 00112 30 29. 56940 . 00130 , 00116 31 30. 55505 . 00134 , 00120 32 31. 54069 . 00138 , 00124 The Suns mean Motions. In Hours. ☉ Longit. Parts. 1 , 04107 2 , 08214 3 , 12321 4 , 16427 5 , 20534 6 , 24641 7 , 28748 8 , 32855 9 , 36962 10 , 41069 11 , 45175 12 , 49282 13 , 53389 14 , 57496 15 , 61603 16 , 65710 17 , 69817 18 , 73923 19 , 78030 20 , 82137 21 , 86244 22 , 90351 23 , 94458 24 , 98565 The Suns mean Motions. In parts of an Hour. ☉ Long. Parts. 1 , 00041 2 , 00082 3 , 00123 4 , 00164 5 , 00205 6 , 00246 7 , 00287 8 , 00328 9 , 00370 10 , 00411 11 , 00452 12 , 00493 13 , 00534 14 , 00575 15 , 00616 16 , 00657 17 , 00698 18 , 00739 19 , 00780 20 , 00821 21 , 00862 22 , 00903 23 , 00945 24 , 00986 25 , 01027 26 , 01068 27 , 01109 28 , 01150 29 , 01191 30 , 01232 31 , 01273 32 , 01314 33 , 01355 34 , 01369 35 , 01437 36 , 01478 37 , 01519 38 , 01561 39 , 01602 40 , 01643 41 , 01684 42 , 01725 43 , 01766 44 , 01807 45 , 01848 46 , 01889 47 , 01930 48 , 01971 49 , 02012 50 , 02053 51 , 02094 52 , 02135 53 , 02177 54 , 02218 55 , 02259 56 , 02300 57 , 02341 58 , 02382 59 , 02423 60 , 02464 61 , 02505 62 , 02546 63 , 02587 64 , 02628 65 , 02669 66 , 02710 67 , 02751 68 , 02793 69 , 02834 70 , 02875 71 , 02916 72 , 02957 73 , 02998 74 , 03039 75 , 03080 76 , 03121 77 , 03162 78 , 03203 79 , 03244 80 , 03285 81 , 03326 82 , 03368 83 , 03409 84 , 03450 85 , 03491 86 , 03523 87 , 03573 88 , 03614 89 , 03655 90 , 03696 91 , 03737 92 , 03778 93 , 03819 94 , 03860 95 , 03901 96 , 03942 97 , 03984 98 , 04025 99 , 04026 The Aequation of the Sun's Eccentric. Degrees Aeq: Sub: ☉ Distance Degrees D. parts. Logarithm 1 0, 03502 50076781 359 2 0, 06966 50076767 358 3 0, 10512 50076752 357 4 0, 14012 50076724 356 5 0, 17506 50076695 355 6 0, 20996 50076464 354 7 0, 24480 50076253 353 8 0, 27580 50076041 352 9 0, 31426 50075829 351 10 0, 34886 50075561 350 11 0, 38836 50075292 349 12 0, 41776 50075023 348 13 0, 45202 50074782 347 14 0, 48616 50074540 346 15 0, 52014 50074298 345 16 0, 55400 50073888 344 17 0, 58730 50073478 343 18 0, 62120 50073068 342 19 0, 65452 50072656 341 20 0, 68766 50072245 340 21 0, 72062 50071834 339 22 0, 75●34 50071347 338 23 0, 78586 50070859 337 24 0, 81816 50070372 336 25 0, 85020 50069833 335 26 0, 88200 50069294 334 27 0, 91356 50068755 333 28 0, 94424 50068246 332 29 0, 97586 50067736 331 30 1, 00650 50067244 330 31 1, 03700 5. 0066482 329 32 1, 06714 5. 0065720 328 33 1, 09696 5. 0064958 327 34 1, 12648 5. 0064216 326 35 1, 15566 5. 0063474 325 36 1, 18448 5. 0062732 324 37 1, 21296 5. 0061917 323 38 1, 24112 5. 0061102 322 39 1, 26890 5. 0060287 321 40 1, 29630 5. 0059457 320 41 1, 32318 5. 0058615 319 42 1, 34996 5. 0057779 318 43 1, 37620 5. 0056904 317 44 1, 40214 5. 0056029 316 45 1, 42746 5. 0055154 315 46 1, 45248 5. 0054194 314 47 1, 47708 5. 0053230 313 48 1, 50122 5. 0052273 312 49 1, 5●494 5. 0051279 311 40 1, 54820 5. 0050285 310 51 1, 571●0 3. 0049290 309 52 1, 59336 5. 0048354 308 53 1, 61522 5. 0047418 307 54 1, 63662 5. 0046481 306 55 1, 65754 5. 0045293 305 56 1, 67796 5. 0044105 304 57 1, 69790 5. 0042916 303 58 1, 71732 5. 0041810 302 59 1, 73784 5. 0040704 301 60 1, 75464 5. 0039597 300 61 1, 77254 5, 0038450 299 62 1, 79000 5, 0037303 298 63 1, 80670 5, 0036157 297 64 1, 82240 5, 0035286 296 65 1, 83876 5, 0034415 295 66 1, 85396 5, 0033545 294 67 1, 86862 ●, 0031985 293 68 1, 88272 5, 0030425 292 69 1, 89624 5, 0028866 291 70 1, 90920 5, 0027615 290 71 1, 92036 5, 0026364 289 72 1, 93342 5, 0025113 288 73 1, 94466 5, 0023831 287 74 1, 95532 5, 0022549 286 75 1, 96540 5, 0021268 285 76 1, 97488 5, 0019971 284 77 1, 98378 5, 0018674 283 78 1, 99206 5, 0017378 282 79 1, 99976 5, 0016069 281 80 2, 00684 5, 0014760 280 81 2, 01332 5, 0013451 279 82 2, 01920 5, 0012217 278 83 2, 02446 5, 0010984 277 84 2, 02912 5, 0009753 276 85 2, 03317 5, 0008067 275 86 2, 03660 5, 0006681 274 87 2, 03946 5, 0005296 273 88 2, 04158 5, 0003993 272 89 2, 04316 5, 0002690 271 90 2, 04410 5, 0201387 270 91 2, 04444 5, 0000038 269 92 2, 04412 4, 9998690 268 93 2, 04320 4, 9997342 267 94 2, 04168 4, 9995972 266 95 2, 03940 4, 9994602 265 96 2, 03672 4, 9993231 264 97 2, 03328 4, 9991886 263 98 2, 02926 4, 9990542 262 99 2, 02460 4, 9989198 261 100 2, 01932 4, 9987851 260 101 2, 01342 4, 9986506 259 102 2, 00690 4, 9985162 258 103 1, 99974 4, 9983844 257 104 1, 99200 4, 9982526 256 105 1, 98362 4, 9981208 255 106 1, 97468 4, 9979918 254 107 1, 96504 4, 9978628 253 108 1, 95486 4, 9977338 252 109 1, 94406 4, 9975992 251 110 1, 93264 4, 9974648 250 111 1, 92066 4, 9973304 249 112 1, 98082 4, 9972113 248 113 1, 89606 4, 6970824 247 114 1, 88106 4, 9969535 246 115 1, 86668 4, 9968355 245 116 1, 85172 4, 9967075 244 117 1, 83622 4, 9961795 243 118 1, 82000 4, 9964581 242 119 1, 80346 4, 9963366 241 120 1, 78622 4, 9962151 240 121 1, 76844 4, 9960958 239 122 1, 75010 4, 9959766 238 123 1, 73120 4, 9958574 237 124 1, 71290 4, 9957427 236 125 1, 69180 4, 9956279 235 126 1, 67130 4, 9955131 234 127 1, 65114 4, 9954018 237 128 1, 62954 4, 9952906 232 129 1, 60668 4, 9951794 231 130 1, 58100 4, 9950747 230 131 1, 56104 4, 9949700 229 132 1, 53748 4, 9948653 228 133 1, 51356 4, 9947664 227 134 1, 4●892 4, 9946676 226 135 1, 46394 4, 9945688 225 136 1, 43848 4, 9944696 224 137 1, 41258 4, 9943704 223 138 1, 38622 4, 9942712 222 139 1, ●5944 4, 9941772 221 140 1, 33214 4, 9940832 220 141 1, ●0458 4, 9939892 219 142 1, ●7650 4, 9939076 218 143 1, 24804 4, 9938199 217 144 ●, 21918 4, 9937322 216 145 1, 18994 4, 9936519 21● 146 1, 160●0 4, 99●5715 214 147 1, 13030 4, 9934911 213 148 1, 09994 4, 9934180 212 149 1, 06922 4, 9933448 211 150 1, 03818 4, 9932716 210 151 1, 00692 4, 9932045 209 152 0, 97610 4, 9931375 208 153 0, 94308 4, 9930705 207 154 0, 91076 4, 9930116 206 155 0, 87820 49929527 205 156 0, 84526 4, 9928938 204 157 0, 81212 4, 09281●8 203 158 0, 77868 4, 9927619 202 159 0, 74508 4, 9627140 201 160 0, 71116 4, 9926680 200 161 0, 67698 4, 9926239 199 162 0, 64264 4, 9925817 198 16● 0, 60808 4, 9925412 197 164 0, 57332 4, 9925009 196 165 0, 53838 4, 9924606 195 166 0, 50356 4, 9924274 194 167 0, 46802 4, 992●941 193 168 0, 43258 4, 9923609 192 169 0, 39730 4, 9923319 191 170 0, 36134 4, 9●23029 190 171 0, 32554 4, 9922739 189 172 0, 29404 4, 9922573 188 173 0, 25366 4, 9922420 187 174 0, 21756 4, 9922268 186 175 0, 18140 4, 9922193 185 176 0, 14520 2, 9922119 184 177 0, 10896 4, 9622044 183 178 0, 07268 4, 9921970 182 179 0, 03636 4, 6921896 181 180 0, 00000 4, 9921822 180 D Add Logarith. D The Moons mean Motions. Epochae Longit. ☽ Anomaly. ☽ Latitude ☽ Deg. parts Deg. parts Deg. Parts. Christi. 135. 73167 215. 54194 226. 95833 1600 20. 69194 151. 57111 99 19250 1620 154. 25389 191. 27138 259. 59252 1640 287. 81583 230. 97194 59 99833 1660 61. 37805 270. 67222 220. 40139 1 129. 38389 88 71889 148. 71278 2 258. 76805 177. 43750 297. 42555 3 28. 15194 266. 15639 86. 13833 B 4 170. 71250 7. 93972 248. 08028 5 300. 09639 96. 65861 36. 79305 6 69. 48028 ●85. 37750 185. 50583 7 198. 86444 274. 09611 334. 21889 B 8 341. 42472 15. 87972 136. 16111 9 110. 80861 104. 59861 284. 87389 10 240. 19278 19●. 31750 73. 58667 11 9 57667 282. 0●639 222. 29944 B 12 152. 13722 23. 82000 24. 24167 13 281. 52111 112. 53889 172. 97444 14 50. 90500 201. 25750 321. 66722 15 180. 28917 288. 97639 112. 38000 B 16 322. 84944 31. 76000 272. 32222 17 92. 23333 120. 47889 61. 03500 18 221. 61750 209. 19778 209. 74778 19 351. 00139 297. 91667 358. 46055 B 20 133. 56194 39 70028 160. 40278 40 267. 12389 79. 40083 320. 80583 60 40. 68611 119. 15111 121. 20889 80 174. 24805 158. 80139 281. 61167 100 307. 81000 198. 50194 82. 01472 The Moons mean Motions. Years. Longit. ☽ Deg. parts. Anom. ☽ Deg. parts. Latitud. ☽ Deg: parts. 100 307, 81000 198, 50194 82, 01472 200 255, 62000 37, 00361 164, 02917 300 203, 43000 235, 50555 246, 04389 400 151, 24000 74, 00722 328, 05861 500 99, 05000 272, 50917 50, 07333 600 46, 86000 111, 01083 131, 08778 700 354, 67000 309, 51250 214, 10250 800 302, 48000 148, 01444 296, 11722 900 250, 29027 346, 51639 18, 13194 1000 198, 10027 185, 01805 100, 14639 2000 36, 20027 10, 03639 200, 29305 3000 234, 30055 195, 05444 300, 43944 4000 72, 40055 20, 07250 40, 58611 5000 270, 50083 205, 09083 140, 73250 january 48, 46833 45, 01444 50, 10722 February 57, 40722 50, 83417 60, 53167 March 105, 87555 95, 84861 110, 64139 April 141, 16722 127, 79805 147, 52194 May 189, 63555 172, 81250 197, 63167 june 224, 89417 204, 76194 234, 11222 july 273, 39555 249, 77639 284, 62194 August 321, 86389 294, 79055 334, 73167 September 357, 15555 326, 74028 11, 61222 October 45, 62387 11, 75472 61, 72194 November 80, 91583 43, 70417 98, 60250 December 129, 38387 88, 71889 148, 71278 The Moons mean Motions. Day's Longit. ☽ Deg. Parts. Anomaly ☽ Deg. Parts. Latitude ☽ Deg. parts. 1 13, 17639 13, 06500 13, 22944 2 26, 35278 26, 13000 26, 45861 3 39, 52917 39, 19500 39, 68805 4 52, 70555 52, 26000 52, 91722 5 65, 88194 65, 32500 66, 14667 6 79, 50833 78, 39000 79, 37611 7 92, 23472 91, 45500 92, 60528 8 105, 41111 104, 52000 105, 83472 9 118, 58750 117, 58472 119, 06417 10 131, 76389 130, 64972 132, 29333 11 144, 94028 143, 71472 145, 52278 12 158, 11667 156, 77972 158, 75222 13 171, 29305 169, 84472 171, 98139 14 184, 46944 182, 90972 185, 21083 15 197, 64583 195, 97472 198, 44028 16 210, 82222 209, 03972 211, 66944 17 223, 99861 222, 10472 224, 89889 18 237, 17500 235, 16972 238, 12833 19 250, 35139 248, 23472 251, 35750 20 263, 52778 261, 29972 264, 58694 21 276, 70417 274, 36472 277, 81639 22 289, 88055 287, 42972 291, 04555 23 303, 05694 300, 49472 304, 27500 24 316, 23333 313, 55972 317, 50444 25 329, 40972 326, 62444 330, 73361 26 342, 58611 339, 68944 343, 96305 27 355, 76250 352, 75444 357, 19250 28 8, 93889 5, 81944 10, 42167 29 22, 11528 18, 88444 23, 65111 30 35, 29167 31, 94944 36, 88028 31 48, 46805 45, 01444 50, 10972 32 61, 64444 58, 07944 63, 33889 The Moons mean Motions. In Hours. Longit. ☽ D. Parts Anomal. ☽ D. parts Latitude ☽ D. parts 1 0, 54889 0, 54444 0, 55139 2 1, 09805 1, 08861 1, 10278 3 1, 64694 1, 63305 1, 65389 4 2, 19611 2, 17750 2, 20528 5 2, 74500 2, 72194 2, 75639 6 3, 29417 3, 26611 3, 30750 7 3, 84305 3, 81055 3, 85889 8 4, 39222 4, 35500 4, 41000 9 4, 94111 4, 89944 4, 96139 10 5, 49000 5, 44361 5, 51250 11 6, 03917 5, 98805 6, 06361 12 6, 58805 6, 53250 6, 61500 13 7, 13722 7, 07694 7, 16611 14 7, 68611 7, 62111 7, 71750 15 8, 23528 8, 16555 8, 26861 16 8, 79417 8, 71000 8, 81972 17 9, 33305 9, 25444 9, 37111 18 9, 88222 9, 79861 9, 92222 19 10, 43139 10, 34305 10, 47361 20 10, 98028 10, 88750 11, 02472 21 11, 52944 11, 43194 11, 57583 22 12, 07833 11, 97611 12, 12722 23 12, 62722 12, 5●055 12, 67833 24 13, 17639 13, 06500 13, 22944 The Moons mean Motions. In parts of an Hour. Long. ☽ Parts. Anom. Parts. Latit. Parts. 1 , 00549 , 00544 , 00551 2 , 01098 , 01088 , 01103 3 , 01647 , 01633 , 01654 4 , 02196 , 02177 , 02205 5 , 02745 , 02722 , 02756 6 , 03294 , 03266 , 03307 7 , 03843 , 03810 , 03858 8 , 04392 , 04355 , 04410 9 , 04941 , 04899 , 04961 10 , 05490 , 05443 , 05512 11 , 06039 , 05988 , 06063 12 , 06588 , 06532 , 06615 13 , 07137 , 07077 , 07166 14 , 07686 , 07621 , 07717 15 , 08235 , 08165 , 08268 16 , 08794 , 08710 , 08819 17 , 09333 , 09254 , 09371 18 , 09882 , 09798 , 09922 19 , 10431 , 10343 , 10473 20 , 10980 , 10887 , 11024 21 , 11529 , 11432 , 11576 22 , 12078 , 11976 , 12127 23 , 12627 , 12520 , 12678 24 , 13176 , 13065 , 13229 25 , 13725 , 13609 , 13780 26 , 14274 , 14153 , 14331 27 , 14823 , 14698 , 14883 28 , 15372 , 15242 , 15434 29 , 15921 , 15787 , 15985 30 , 16470 , 16331 , 16536 31 , 17019 , 16885 , 17083 32 , 17567 , 17416 , 17633 33 , 18117 , 17966 , 18183 34 , 18665 , 18508 , 18744 35 , 19214 , 19050 , 19300 36 , 19763 , 19600 , 19850 37 , 20317 , 20133 , 20400 38 , 20867 , 20683 , 20950 39 , 21416 , 21233 , 21500 40 , 21967 , 21767 , 22050 41 , 22500 , 223●6 , 22600 42 , 23050 , 22850 , 23150 43 , 23600 , 23400 , 23700 44 , 24150 , 23950 , 24250 45 , 24700 , 24500 , 24800 46 , 25283 , 25050 , 25350 47 , 25800 , 25600 , 25900 48 , 26350 , 26133 , 26450 49 , 26900 , 26683 , 27000 50 , 27450 , 27217 , 27567 51 , 28000 , 27767 , 28117 52 , 28550 , 28300 , 28800 53 , 29100 , 28850 , 29217 54 , 29817 , 29400 , 29767 55 , 30200 , 29933 , 30317 56 , 30733 , 30483 , 30867 57 , 31283 , 31017 , 31416 58 , 31833 , 31567 , 31967 59 , 32383 , 32117 , 32517 60 , 32933 , 32666 , 33083 61 , 33491 , 33206 , 33626 62 , 34039 , 33750 , 34177 63 , 34588 , 34294 , 34728 64 , 35137 , 34838 , 35279 65 , 35685 , 35382 , 35830 66 , 36234 , 35926 , 36381 67 , 36783 , 36470 , 36932 68 , 37331 , 37014 , 37483 69 , 37880 , 37558 , 38034 70 , 38429 , 38102 , 38585 71 , 38979 , 38646 , 39139 72 , 39528 , 39190 , 39690 73 , 40077 , 39734 , 40241 74 , 40626 , 40278 , 40792 75 , 41174 , 40822 , 41343 76 , 41723 , 41366 , 41894 77 , 42272 , 41910 , 42445 78 , 42820 , 42454 , 42996 79 , 43369 , 42998 , 43547 80 , 43918 , 43542 , 44098 81 , 44466 , 44094 , 44651 82 , 45020 , 44638 , 45202 83 , 45568 , 45182 , 45753 84 , 46117 , 45726 , 46304 85 , 46666 , 46270 , 46855 86 , 47215 , 46814 , 47406 87 , 47763 , 47358 , 47957 88 , 48312 , 47902 , 48508 89 , 48861 , 48446 , 49059 90 , 49411 , 48990 , 49610 91 , 49960 , 49538 , 50165 92 , 50509 , 50082 , 50716 93 , 51058 , 50626 , 51267 94 , 51607 , 51170 , 51818 95 , 52155 , 51714 , 52369 96 , 52704 , 52258 , 52920 97 , 53253 , 52802 , 53471 98 , 53801 , 53346 , 54022 99 , 54351 , 53890 , 54573 The Aequations of the Moons Eccentric. Degrees Aeq: Sub D. parts. ☉ Distance from Umb. 5, 085424 Degrees 1 0, 08356 5, 0185341 359 2 0, 16706 5, 0185258 358 3 0, 25068 5, 0185174 357 4 0, 33414 5, 0184826 356 5 0, 41750 5, 0184479 355 6 0, 50076 5, 0184131 354 7 0, 58424 5, 0183845 353 8 0, 66684 5, 0183560 352 9 0, 74962 5, 0183274 351 10 0, 83222 5, 0182718 350 11 0, 91458 5, 0182163 349 12 0, 99670 5, 0181607 348 13 1, 07854 5, 0180979 347 14 1, 16010 5, 0180352 346 15 1, ●4136 5, 0179724 345 16 1, 32228 5, 0178897 344 17 1, 40282 5, 0178071 343 18 1, 48302 5, 0177244 342 19 1, 56280 5, 0176271 341 20 1, 64212 5, 0175298 340 21 1, 72108 5, 0174325 339 22 1, 79908 5, 0173200 338 23 1, 87750 5, 0172075 337 24 1, 95498 5, 0170950 336 25 2, 03190 5, 0169696 335 26 2, 10830 5, 0168443 334 27 2, 18410 5, 0167189 333 28 2, 29594 5, 0165775 332 29 2, 33394 5, 0164362 331 30 2, 40792 5, 0162948 330 31 2, 48144 5. 0161416 329 32 2, 55388 5. 0159884 328 33 2, 62582 5. 0158351 327 34 2, 69688 5. 0156656 326 35 2, 76756 5. 0154962 325 36 2, 83732 5. 0153267 324 37 2, 90628 5. 0151439 323 38 2, 97520 5. 0149611 322 39 3, 04184 5. 0147782 321 40 3, 12824 5. 0145848 320 41 3, 17404 5. 0143915 319 42 3, 22762 5. 0141961 318 43 3, 30266 5. 0140007 317 44 3, 36554 5. 0138052 316 45 3, 42768 5. 0135901 315 46 3, 48880 5. 0133649 114 47 3, 54892 5. 0131474 313 48 3, 60806 5. 0129254 312 49 3, 666●0 5. 0126977 311 50 3, 73358 5. 0124700 310 51 3, 77940 3. 0122423 309 52 3, 83442 5. 0120012 308 53 3, 88836 5. 0117601 307 54 3, 94112 5. 0115189 306 55 3, 99296 5. 0112631 305 56 3, 04358 5. 0110073 304 57 4, 09306 5. 0107514 303 58 4, 14138 5. 0104891 302 59 4, 18854 5. 0102269 301 60 4, 23448 5. 0099646 300 61 4, 27924 5, 0097259 299 62 4, 32278 5, 0094872 298 63 4, 36508 5, 0091485 297 64 4, 40614 5, 0088671 296 65 4, 44708 5, 0085856 295 66 4, 48444 5, 0083041 294 67 4, 52166 5, 0080136 293 68 4, 54774 5, 0077231 292 69 4, 59222 5, 0074326 291 70 4, 62546 5, 0070981 290 71 4, 65612 5, 0067637 289 72 4, 68922 5, 0064292 288 73 4, 71674 5, 0061720 287 74 4, 74506 5, 0059148 286 75 4, 77150 5, 0056575 285 76 4, 79654 5, 0053376 284 77 4, 82020 5, 0050177 283 78 4, 84242 5, 0046977 282 79 4, 86322 5, 0042544 281 80 4, 89534 5, 0038111 280 81 4, 90048 5, 0033678 279 82 4, 91694 5, 0031731 278 83 4, 93196 5, 0029785 277 84 4, 94548 5, 0027838 276 85 2, 95750 5, 0024588 275 86 4, 96806 5, 0021339 274 87 4, 97714 5, 0010809 273 88 4, 98460 5, 0014811 272 89 4, 99078 5, 0011534 271 90 4, 99532 5, 0008256 270 91 4, 99834 5, 0004952 269 92 4, 99988 5, 0001649 268 93 4, 99988 4, 9998345 267 94 4, 99836 4, 9995032 266 95 4, 99532 4, 9991719 265 96 4, 99070 4, 9988405 264 97 4, 98460 4, 9985193 263 98 4, 97696 4, 9981982 262 99 4, 96736 4, 9978770 261 100 4, 95706 4, 9972811 260 101 4, 94476 4, 9966852 259 102 4, 93096 4, 9960892 258 103 4, 91562 4, 9960119 257 104 4, 89874 4, 9959347 256 105 4, 88034 4, 9958574 255 106 4, 86042 4, 9955301 254 107 4, 82944 4, 9952028 253 108 4, 81594 4, 9948754 252 109 4, 79146 4, 9945474 251 110 4, 76544 4, 9942193 250 111 4, 73788 4, 9939013 249 112 4, 70884 4, 9935795 248 113 4, 67888 4, 9932577 247 114 4, 64632 4, 9929358 246 115 4, 61274 4, 9926191 245 116 4, 57778 4, 9923025 244 117 4, 54128 4, 9919859 243 118 4, 50350 4, 9916852 242 119 4, 16386 4, 9913845 241 120 4, 42300 4, 9910837 240 121 4, 38086 4, 9907779 239 122 4, 33720 4, 9904722 238 123 4, 29210 4, 9901664 237 124 4, 24560 4, 9899751 236 125 4, 19772 4, 9897838 235 126 4, 14546 4, 9895915 234 127 4, 09784 4, 9892117 237 128 4, 04550 4, 9888309 232 129 3, 99248 4, 9884500 231 130 3, 93798 4, 9881731 230 131 3, 88206 4, 9878962 229 132 3, 87486 4, 9876193 228 133 3, 76638 4, 9873574 227 134 3, 70738 4, 9870956 226 135 3, 64572 4, 9868337 225 136 3, 58356 4, 9865840 224 137 3, 52020 4, 9863343 223 138 3, 45564 4, 9860846 222 139 3, 38920 4, 9858146 221 140 ●, 32310 4, 9855446 220 141 3, 25514 4, 9853746 219 142 3, 18610 4, 9851518 218 143 3, 11598 4, 9849290 217 144 3, 04478 4, 9847061 216 145 2, 97260 4, 9844966 215 146 2, 89938 4, 9842872 214 147 2, 82518 4, 9840777 213 148 2, 75004 4, 9838882 212 149 2, 67392 4, 9836987 211 150 2, 59686 4, 9835092 210 151 2, 51028 4, 9833262 209 152 2, 44030 4, 9831432 208 153 2, 36074 4, 9829601 207 154 2, 28030 4, 9828019 206 155 2, 19126 4 9826437 205 156 2, 11722 4, 9824855 204 157 2, 03458 4, 9823435 203 158 1, 95120 4, 9822015 202 159 1, 86718 4, 9820595 201 160 1, 78252 4, 9819334 200 161 1, 69724 4, 9818073 199 162 1, 61138 4, 9816811 198 163 1, 52494 4, 9815083 197 164 1, 43800 4, 9813356 196 165 1, 35118 4, 9811628 195 166 1, 26300 4, 9811425 194 167 1, 17430 4, 9811223 193 168 1, 08554 4, 9811020 192 169 0, 99768 4, 9810309 191 170 0, 90692 4, 9809599 190 171 0, 81714 4, 9808889 189 172 0, 72704 4, 9808391 188 173 0, 63724 4, 9807893 187 174 0, 546●8 4, 9807●94 186 175 0, 45546 4, 9807099 185 176 0, 36518 4, 9806804 184 177 0, 27352 4, 9806509 183 178 0, 18242 4, 9806441 182 179 0, 69126 4, 9806373 181 180 0, 00000 4, 9806304 180 D Add Logarith. D A Table for the finding of the second and third inaequalities of the Moon. Subtense of the ☽ double dist. from ☉ Logarithm. Variation Add Parts. 0 0, 0000000 , 00000 360 1 1, 5805276 , 00119 359 2 1, 8815410 , 02389 358 3 2, 0576047 , 03555 357 4 2, 1825049 , 04722 356 5 2, 2793653 , 058●7 355 6 2, 3584859 , 07055 354 7 2, 4253610 , 08222 353 8 2, 4832702 , 09389 352 9 2, 5343290 , 10555 351 10 2, 5799817 , 11722 350 11 2, 6212586 , 12889 349 12 2, 6589203 , 14055 348 13 2, 6935445 , 1●194 347 14 2, 7255502 , 16333 346 15 2, 7553834 , 17472 345 16 2, 7832410 , 18611 344 17 2, 8093878 , 19750 343 18 2, 8339081 , 20861 342 19 2, 8572949 , 21972 341 20 2, 8793554 , 23083 340 21 2, 9003187 , 24194 339 22 2, 9202845 , 25278 338 23 2, 9393410 , 26361 337 24 2, 9575646 , 27444 336 25 2, 9750225 , 28528 335 26 2, 9917737 , 29583 334 27 3, 0078710 , 30638 333 28 3, 0233609 , 31694 332 29 3, 0382853 , 32722 331 30 3, 0326819 , 33750 330 30 3, 0526819 . 34750 330 ●1 3, 0665●45 . 34750 329 32 3, 0800238 . 35750 328 33 3, 0900275 . 36750 327 34 3, 1056210 . 37722 326 35 3, 1178275 . 38694 325 36 3, 1296681 . 39667 324 37 3, 1411621 . 40655 323 38 3, 1523276 . 41555 322 39 3, 1630910 . 42472 321 40 3, 1737374 . 43389 320 41 3, 1840110 . 44278 319 42 3, 1940149 . 45167 318 43 3, 2037611 . 46083 317 44 3, 2132611 . 46889 316 45 3, 2225254 . 47722 315 46 3, 2315637 . 48555 314 47 3, 2403854 . 49361 313 48 3, 2489990 . 50167 312 49 3, 2574127 . 50944 311 50 3, 2655340 . 51694 310 51 3, 2706701 . 52444 309 52 3, 2815277 . 53194 308 53 3, 2892131 . 53916 307 54 3, 2967325 . 54611 306 55 3, 3040913 . 55305 305 56 3, 3012950 . 55972 304 57 3, 3183486 . 56611 303 58 3, 3252569 . 57250 302 59 3, 3320245 . 57861 301 60 3, 3386557 . 58444 300 60 3, 3386557 , 58444 300 61 3, 3451546 , 59058 299 62 3, 3515250 , 59583 298 63 3, 3577708 , 60139 297 64 3, 3638954 , 60667 296 65 3, 3699022 , 61167 295 66 3, 3757945 , 61667 294 67 3, 815752 , 62139 293 68 3, 3872474 , 62583 292 69 3, 3928137 , 63000 291 70 3, 3982770 , 63417 290 71 3, 4036397 , 63805 289 72 3, 4089044 , 64167 288 73 3, 4130733 , 64500 287 74 3, 4191487 , 64861 286 75 3, 4241328 , 65194 285 76 3, 4290277 , 65500 284 77 3, 4338353 , 65778 283 78 3, 4375575 , 66028 282 79 3, 7431962 , 66250 281 80 3, 4477532 , 66427 280 81 3, 4522301 , 66667 279 82 3, 4566282 , 66833 278 83 3, 4609503 , 67000 277 84 3, 4651966 , 67139 276 85 3, 4693690 , 67250 275 86 ●, 4704690 , 67361 274 87 3, 4465979 , 67417 273 88 3, 4814570 , 67444 272 89 3, 4853475 , 67472 271 90 3, 4891707 , 67500 270 90 3, 4891707 , 67500 270 91 3, 4929278 , 67472 269 92 3, 4966198 , 67444 268 93 3, 5002479 , 67417 267 94 3, 5038132 , 67361 266 95 3, 5073166 , 67250 265 96 3, 5107592 , 67139 264 97 3, 5141418 , 67000 263 90 3, 5174656 , 66833 262 91 3, 5207312 , 66667 261 100 3, 5239397 , 66472 260 101 3, 5270918 , 66350 259 102 3, 5301883 , 66028 258 103 3, 5332301 , 65778 257 104 3, 5362178 , 65500 256 105 3, 5391524 , 65194 255 106 3, 5420343 , 64861 254 107 3, 5448644 , 64500 253 108 3, 5476433 , 64167 252 109 3, 5503717 , 63805 251 100 3, 5530502 , 63417 250 111 3, 5556794 , 63000 249 112 3, 5582599 , 62583 248 113 3, 5607923 , 62139 247 114 3, 5632771 , 61667 246 115 3, 5656149 , 61167 245 116 3, 5681062 , 60667 244 117 3, 5704515 , 60139 243 118 3, 5727513 , 69583 242 119 3, 5750061 , 59028 241 120 3, 5772163 , 58444 240 120 ●, 5772163 , 58444 240 121 3, 5793825 , 57861 239 122 3, 5815050 , 57250 238 123 3, 5835842 , 56611 237 124 3, 5856206 , 55972 236 125 3, 5876126 , 55305 235 126 3, 5895666 , 54611 234 127 3, 5917769 , 53916 233 128 3, 5933457 , 53194 232 229 3, 5951739 , 52444 231 130 3, 5969614 , 51694 230 131 3, 5987086 , 50944 229 132 3, 6004159 , 50167 228 133 3, 6029834 , 49361 227 1●4 3, 6037118 , 48555 226 135 3, 6053010 , 47722 225 136 3, 6068516 , 46889 224 137 3, 6083636 , 46083 223 138 3, 6098374 , 45167 222 139 3, 6106733 , 44278 221 140 3, 6126715 , 43389 220 141 3, 6140323 , 42472 219 142 3, 6153558 , 41555 218 143 3, 6166423 , 40611 217 144 3, 6178932 , 39667 216 145 3, 6191052 , 38694 215 146 3, 6208820 , 37722 214 147 3, 6314227 , 36750 213 148 3, 6325273 , 35750 212 149 3, 6235962 , 34750 211 150 2, 6246295 , 33750 210 150 3, 624629 . 33750 210 151 3, 6256273 . 32722 209 152 3, 6265898 . 31694 208 153 3, 6275172 . 30638 207 154 3, 6284096 . 29583 206 155 3, 6292672 . 28528 205 156 3, 6300901 . 27444 204 157 3, 6308784 . 26361 203 158 3, 6316323 . 25278 202 159 3, 6333518 . 24194 201 160 3, 6330372 . 23083 200 161 3, 6336884 . 21972 199 162 3, 6343056 , 20861 198 163 3, 6348890 . 19750 197 164 3, 6354385 . 18611 196 165 3, 6359543 . 17472 195 166 3, 6364364 . 16333 194 167 3, 6368850 . 15194 193 168 3, 6373000 . 14055 192 169 3, 6376817 . 12889 191 170 3, 6380299 . 11722 190 171 3, 6387448 . 10555 189 172 3, 6386265 . 09389 188 173 3, 6388749 . 08222 187 174 3, 6390901 . 07055 186 175 3, 6392722 . 05889 185 176 3, 6394211 . 04722 184 177 3, 6395369 . 03555 183 178 3, 6396295 . 02389 182 179 3, 6396792 . 01194 181 180 3, 6396857 . 00000 180 D Logarithm. Subst. D Bullialdus his Table of Evection. Evection Subst. Scrupl. of proportion. Variation Add D. Parts. Parts. Parts. 0 0, 00000 , 00000 , 00000 ●60 1 0, 04028 , 00873 , 01194 359 2 0, 08055 , 01745 , 02389 358 3 0, 12083 , 02617 , 03555 357 4 0, 16083 , 03489 , 04722 356 5 0, 20083 , 04362 , 05887 355 6 0, 24111 , 05234 , 07055 354 7 0, 28083 , 06105 , 08222 353 8 0, 36028 , 06975 , 09389 352 9 0, 36000 , 07845 , 10555 351 10 0, 39944 , 08715 , 11722 350 11 0, 43889 , 09584 , 12889 349 12 0, 47833 , 10453 , 14055 348 13 0, 51750 , 11320 , 15194 347 14 0, 55667 , 12187 , 16333 346 15 0, 59583 , 13052 , 17472 345 16 0, 63472 , 13917 , 18611 344 17 0, 67333 , 14780 , 19750 343 18 0, 71222 , 15643 , 20861 342 19 0, 75083 , 16504 , 21972 341 20 0, 78917 , 17364 , 23083 340 21 0, 82750 , 18223 , 24194 339 22 0, 86528 , 19081 , 25278 338 23 0, 9027● , 19936 , 26361 337 24 0, 94055 , 20791 , 27444 3●6 25 0, 97805 , 21643 , 28528 335 36 1, 01528 , 22495 , 29583 334 27 1, 052●2 , 23344 , 30638 333 28 1, 08889 , 24192 , 31694 332 29 1, 12527 , 25038 , 32722 331 30 1, 161●8 , 25882 , 33750 330 30 1, 16138 , 25882 , 33750 330 31 1, 19722 , 26723 34750 329 32 1, 23278 , 2756● , 35750 328 33 1, 26833 , 2840 , 36750 327 34 1, 30305 , 29237 , 37722 326 35 1, 33750 , 30072 , 38694 325 36 1, 37167 , 30901 , 39667 324 37 1, 40556 , 30730 , 40655 323 38 1, 43944 , 32553 , 41555 322 39 1, 47222 , 33380 , 42472 321 40 1, 50500 , 34202 , 43389 320 41 1, 53750 , 35020 , 44378 319 42 1, 56972 , 35836 , 45167 318 43 1, 60139 , 3665● , 46083 317 44 1, 63278 , 37460 , 46889 316 45 1, 66389 , 38268 , 4772● 315 46 1, 69444 , 39073 , 78555 314 47 1, 72444 , 39874 , 49361 313 48 1, 75444 , 40673 , 50167 312 49 1, 78417 , 41469 , 50944 311 50 1, 81●61 , 42262 , 51694 310 51 1, 84278 , 4●051 , 52444 309 52 1, 87139 , 43837 , 53194 308 53 1, 89944 , 44619 , 53916 307 54 1, 92695 , 45●99 , 54611 306 55 1, 95333 , 46174 , 55305 305 56 1, 97917 , 46●47 , 55972 ●04 57 2, 00444 , 47715 , 56611 303 58 2, 0●917 , 4848● , 57250 302 59 2, 05333 , 4924● , 57861 301 60 2, 07694 , 5000● , 58444 300 60 2, 07694 , 50000 , 58444 300 61 2, 10000 , 50753 , 59028 299 62 2, 12250 , 51903 , 59583 298 63 2, 14444 , 52249 , 60139 297 64 2, 16583 , 52991 , 60667 296 65 2, 18667 , 53729 , 61167 295 66 2, 20694 , 54463 , 61667 294 67 2, 22667 , 55193 , 62139 293 68 2, 24583 , 55919 , 62583 292 69 2, 26444 , 56640 , 63000 291 70 2, 28222 , 57357 , 63417 290 71 2, 29917 , 58070 , 63805 289 72 2, 31527 , 58778 , 64167 288 73 2, 33055 , 59482 , 64500 287 74 2, 34527 , 60181 , 64861 286 75 2, 35944 , 60876 , 65194 285 76 2, 36750 , 61566 , 65500 284 77 2, 38611 , 62251 , 65778 283 78 2, 39889 , 62932 , 66028 282 79 2, 41055 , 63607 , 66250 281 80 2, 42222 , 64278 , 66472 280 81 2, 43333 , 64944 , 66667 279 82 2, 44361 , 65605 , 66833 278 83 2, 45278 , 66262 , 67000 277 84 2, 96083 , 66913 , 67139 276 85 2, 46778 , 67559 , 67250 275 86 2, 27417 , 68199 , 67361 274 87 2, 48000 , 68835 , 67417 273 88 2, 48500 , 69465 , 67444 272 89 2, 48944 , 70091 , 67472 271 90 2, 49333 , 70711 , 67500 70 90 2, 49333 70711 , 67500 270 91 2, 49667 , 71325 67472 269 92 2, 49889 , 71933 , 67444 268 93 2, 50000 , 72537 , 67417 267 94 2, 49889 , 73135 , 67361 266 95 2, 49778 , 73727 , 67250 265 96 2, 49639 , 74314 , 67139 264 97 2, 49444 , 74895 , 67000 263 98 2, 49222 , 75471 , 66833 262 99 2, 48972 , 76040 , 66667 261 100 2, 48667 , 76604 , 66472 260 101 2, 48333 , 77162 , 66250 259 302 2, 47944 , 77714 , 66028 258 103 2, 47139 , 78260 , 65778 257 104 2, 46917 , 78801 , 65600 256 105 2, 46278 , 79335 , 65194 255 106 2, 45500 , 79863 , 64861 254 107 2, 44611 , 80385 , 64500 253 108 2, 43611 , 80901 , 64167 252 109 2, 42556 , 81411 , 63805 251 110 2, 41389 , 81915 , 63417 250 111 2, 40139 , 82412 , 63000 249 112 2, 38861 , 82903 , 62583 248 113 2, 37583 , 83388 , 62139 247 114 2, 36194 , 83867 , 61667 246 115 2, 34722 , 84339 , 61167 245 116 2, 32972 , 84805 , 60667 244 117 2, 31222 , 85264 , 60139 243 118 2, 29472 , 85716 , 59583 242 119 2, 27722 , 8616● , 59028 241 120 2, 25972 , 8660● , 58444 240 120 2, 25972 . 86602 , 58444 240 121 ●, 24083 . 87135 , 57861 239 122 2, 22111 . 87462 , 57250 238 123 2, 20038 . 87882 , 56611 237 124 2, 17833 . 88295 , 55972 236 125 2, 15555 . 88701 , 55305 235 126 2, 13167 . 89100 , 54611 234 127 2, 10694 . 89493 , 53916 233 128 2, 08138 . 89879 , 53194 232 129 2, 05500 . 902●8 , 52444 231 130 2, 02805 . 90631 , 51694 230 131 2, 00055 . 90996 , 50944 229 132 1, 97222 . 91354 , 50167 228 133 1, 94333 . 91706 , 49●61 2●7 134 1, 91389 . 92050 , 48555 226 135 1, 88138 . 9●38● , 47722 225 136 1, 85000 . 92718 , 46889 224 137 1, 81889 . 93042 , 46083 223 138 1, 78722 . 93358 , 45167 222 139 1, 75500 . 93667 , 44278 221 140 1, 72222 . 93969 , 43389 220 141 1, 68889 . 94264 , 42472 219 142 1, 65472 . 94552 , 41555 218 143 1, 62000 . 94832 , 40611 217 144 1, 58389 . 95105 , 39667 216 145 1, 54694 . 95371 , 38694 215 146 1, 50944 . 95630 , 37722 214 147 1, 47167 . 95882 , 36750 213 148 1, 43972 . 96126 , 35750 212 149 1, 39417 . 96363 , 34750 211 150 1, 35472 . 9659● , 33750 210 150 1, 35472 , ●6592 , 33750 210 151 1, 31472 , 96814 , 32722 209 152 1, 27417 , 97029 , 31694 208 153 1, 23305 , 97237 , 30638 207 154 1, 19167 , 97437 , 29583 206 155 1, 14972 , 97629 , 28528 205 156 1, 10722 , 97815 , 27444 204 157 1, 06417 , 97992 , 26361 203 158 1, 02056 , 98163 , 25278 202 159 0, 97667 , 98325 , 24194 201 160 0, 93250 , 98481 , 23083 100 161 0, 88778 , 98628 , 21972 199 162 0, 84278 , ●8769 , 20861 198 163 0, 79750 , 98901 , 19750 197 164 0, 75167 , 99027 , 18611 196 165 0, ●0556 , 99144 , 17472 195 166 0, 6●944 , 99254 , 16333 194 167 0, 61305 , 99357 , 15194 193 168 0, 56667 , 99452 , 14055 192 169 0, 52000 , 99535 , 12889 191 170 0, 47333 , 99619 , 11722 190 171 0, 42667 , 99692 , 10555 189 172 0, 37972 , 99756 , 09389 188 173 0, 33278 , 99813 , 08222 187 174 0, 28556 , 99863 , 07055 186 175 0, 23833 , 99905 , 05889 185 176 0, 19083 , 99939 , 04722 184 177 0, 14333 , 99966 , 03555 183 178 0, 09556 , 99985 , 02389 182 179 0, 04778 , 99996 , 01194 181 180 0, 00000 , 00000 , 00000 180 Add Sub: A Compounded Table of the ☽ Evection and Variation. Degrees of Equation. 3 6 9 12 15 18 21 Degrees. Sub Sub: Sub Sub Sub Sub Sub 0 0. 058 0, 116 0, 171 0. 224 0, 273 0, 299 0, 359 360 5 0. 059 0, 120 0, 178 0. 235 0, 290 0, 321 0, 399 355 10 0. 059 0, 120 0, 181 0. 242 0, 301 0, 338 0, 412 350 15 0. 058 0, 119 0, 181 0. 245 0, 308 0, 349 0, 430 345 20 0. 057 0, 117 0, 179 0. 243 0, 309 0, 354 0, 441 340 25 0. 054 0, 112 0, 175 0. 239 0, 306 0, 353 0, 444 335 30 0. 050 0, 106 0, 166 0. 232 0, 300 0, 349 0, 440 330 35 0. 045 0, 097 0, 155 0. 219 0, 287 0, 339 0, 433 325 40 0. 039 0, 087 0, 141 0. 202 0, 270 0, 321 0, 418 320 45 0. 032 0, 074 0, 124 0. 184 0, 248 0, 298 0, 395 315 50 0. 024 0, 059 0, 103 0. 158 0, 221 0, 271 0, 364 310 55 0. 015 0, 042 0, 080 0. 129 0, 188 0, 237 0, 329 305 60 0. 006 0, 024 0, 055 0. 097 0, 150 0, 196 0, 295 300 65 0A004 0, 005 0, 027 0. 054 0, 208 0, 150 0, 234 295 70 0. 015 0A016 0A003 0. 018 0, 063 0, 089 0, 157 290 75 0. 026 0, 038 0, 035 0A028 0, 013 0, 046 0, 116 285 80 0. 038 0, 062 0, 069 0. 062 0A040 0A014 0, 048 280 85 0. 050 0, 086 0, 105 0. 109 0, 096 0, 084 0A024 275 90 0. 063 0, 110 0, 141 0. 157 0, 155 0, 143 0, 101 270 95 0. 075 0, 135 0, 178 0. 205 0, 215 0, 184 0, 182 265 100 0. 087 0, 160 0, 216 0. 265 0, 276 0, 282 0, 265 160 105 0. 100 0, 185 0, 253 0. 304 0, 337 0, 353 0, 349 255 110 0. 112 0, 209 0, 289 0. 353 0, 399 0, 4●5 0, 434 250 115 0. 123 0, 233 0, 326 0. 402 0, 460 0, 496 0, 520 245 120 0. 134 0, 256 0, 361 0. 449 0, 520 0, 566 0, 604 240 125 0. 145 0, 277 0, 394 0. 495 0, 579 0, 636 0, 688 235 130 0. 155 0, 298 0, 426 0. 533 0, 635 0, 793 0, 768 230 135 0. 163 0, 316 0, 456 0. 580 0, 688 0, 767 0, 848 225 140 0. 171 0, 333 0, 483 0. 618 0, 738 0, 829 0, 923 220 145 0. 179 0, 349 0, 507 0. 652 0, 883 0, 883 0, 992 215 150 0. 185 0, 363 0, 537 0. 684 0, 824 0, 934 1, 057 210 155 0. 190 0, 374 0, 549 0. 712 0, 862 0, 981 1, 114 205 160 0. 194 0, 383 0, 564 0. 736 0, 895 0, 022 1, 168 200 165 0. 197 0, 391 0, 577 0. 754 0, 922 0, 058 1, 215 195 180 0. 199 0, 396 0, 588 0. 759 0, 945 0, 086 1, 254 190 175 0. 200 0, 399 0, 594 0 771 0, 962 0, 111 1, 286 185 170 0. 201 ●, 401 0, 597 0. 789 0, 975 0, 129 1, 312 180 Degrees of Equ: Anom. Sub Sub Sub Sub Sub Sub Sub Fe●rees of Equ: Anom. 177 174 171 168 162 162 159 A Compounded Table of the ☽ Evection and Variation. Degrees of Equation. 3 6 9 12 15 18 21 Degrees of Equation. Add Add Add Add Add Add Add 180 0. 201 0, 401 0, 597 0, 789 0, 975 1, 129 1, 312 180 185 0, 200 0, 401 0, 599 0, 794 0, 981 1, 139 1, 331 175 190 0, 198 0, 398 0, 597 0, 794 0, 984 1, 145 1, 341 170 195 0, 195 0, 394 0, 593 0, 794 0, 983 1, 146 1, 346 165 200 0, 192 0, 387 0, 585 0, 782 0, 976 1, 143 1, 346 160 205 0, 187 0, 380 0, 575 0, 770 0, 964 1, 133 1, 338 155 210 0, 182 0, 371 0, 562 0, 755 0, 948 1, 117 1, 323 150 215 0, 176 0, 359 0, 547 0, 736 0, 928 1, 096 1, 300 145 220 0, 169 0, 347 0, 529 0, 715 0, 903 1, 071 1, 275 140 225 0, 162 0, 333 0, 509 0, 690 0, 875 1, 041 1, 242 135 230 0, 154 0, 317 0, 487 0, 663 0, 843 1, 006 1, 204 130 235 0, 145 0, 300 0, 463 0, 633 0, 707 0, 967 1, 161 125 240 0, 136 0, 283 0, 438 0, 600 0, 768 0, 924 1, 112 120 245 0, 127 0, 265 0, 412 0, 566 0, 727 0, 878 1, 059 115 250 0, 117 0, 246 0, 384 0, 530 0, 784 0, 829 1, 002 110 255 0, 107 0, 227 0, 355 0, 493 0, 638 0, 778 0, 943 105 260 0, 097 0, 206 0, 326 0, 454 0, 591 0, 724 0, 880 100 265 0, 087 0, 186 0, 295 0, 414 0, 542 0, 668 0, 815 95 270 0, 076 0, 165 0, 264 0, 374 0, 492 0, 611 0, 748 90 275 0, 066 0, 144 0, 237 0, 331 0, 441 0, 552 0, 679 85 280 0, 055 0, 121 0, 202 0, 291 0, 389 0, 493 0, 609 80 285 0, 045 0, 102 0, 170 0, 249 0, 337 0, 433 0, 538 75 290 0, 035 0, 082 0, 14● 0, 209 0, 286 0, 372 0, 466 70 295 0, 025 0, 062 0, 109 0, 169 0, 234 0, 312 0, 394 65 300 0, 016 0, 042 0, 079 0, 126 0, 183 0, 253 0, 322 60 305 0, 006 0, 023 0, 049 0, 087 0, 133 0, 194 0, 252 55 310 0S002 0, 004 0, 021 0, 048 0, 084 0, 136 0, 176 50 315 0, 011 0S013 0S005 0, 011 0, 037 0, 080 0, 114 45 320 0, 019 0, 030 0, 031 0S025 0S009 0, 026 0, 048 40 325 0, 027 0, 045 0, 056 0, 058 0, 052 0S025 0S015 35 330 0, 034 0, 060 0, 079 0, 091 0, 093 0, 075 0, 072 30 335 0, 040 0, 073 0, 100 0, 120 0, 132 0, 122 0, 134 25 340 0, 045 0, 085 0, 119 0, 147 0, 168 0, 166 0, 187 20 345 0, 050 0, 096 0, 136 0, 171 0, 200 0, 206 0, 238 15 350 0, 054 0, 105 0, 151 0, 192 0, 229 0, 241 0, 284 10 355 0, 057 0, 111 0, 161 0, 210 0, 253 0, 273 0, 325 05 360 0, 059 0, 116 0, 171 0, 224 0, 273 0, 296 0, 359 00 Deg: of Equated Anomaly. Add Add Add Add Add Add Add Degrees of Equated Anomaly. 177 174 171 108 165 162 159 A Compounded Table of the ☽ Evection and Variation. Deg: of Eq▪ Anomaly. 21 24 27 80 33 36 39 Deg. of Eq▪ Anomaly. Sub. Sub Sub Sub Sub Sub: Sub: 0 0, 359 0, 396 0, 427 0, 454 0, 475 0, 491 0. 499 360 5 0, 399 0, 433 0, 473 0, 509 0, 540 0, 565 0. 585 355 10 0, 412 0, 461 0, 511 0, 556 0, 596 0, 632 0. 661 350 15 0, 430 0, 487 0, 542 0, 595 0, 644 0, 689 0. 728 345 20 0, 441 0, 505 0, 567 0, 626 0, 683 0, 737 0. 786 340 25 0, 444 0, 513 0, 581 0, 649 0, 714 0, 775 0. 829 335 30 0, 440 0, 513 0, 588 0, 662 0, 734 0, 805 0. 870 330 35 0, 433 0, 508 0, 585 0, 664 0, 744 0, 822 0. 896 325 40 0, 418 0, 496 0, 575 0, 659 0, 742 0, 827 0. 910 320 45 0, 39● 0, 475 0, 559 0, 647 0, 734 0, 822 0. 910 315 50 0, 364 0, 445 0, 532 0, 622 0, 715 0, 810 0. 002 310 55 0, 329 0, 409 0, 495 0, 589 0, 684 0, 784 0. 884 305 60 0, 295 0, 365 0, 452 0, 545 0, 642 0, 747 0. 850 300 65 0, 234 0, 312 0, 398 0, 493 0, 593 0, 697 0. 805 295 70 0, 157 0, 250 0, 336 0, 430 0, 531 0, 639 0. 749 290 75 0, 116 0, 184 0, 265 0, 356 0, 457 0, 566 0. 681 285 80 0, 048 0, 112 0, 289 0, 277 0, 374 0, 483 0. 598 280 85 0A024 0, 033 0, 107 0, 189 0, 284 0, 389 0. 503 275 90 0, 101 0A051 0, 013 0, 104 0, 184 0, 289 0. 402 270 95 0, 182 0, 140 0A083 0A010 0, 077 0, 178 0. 289 265 100 0, 265 0, 233 0, 185 0, 118 0A037 0, 059 0. 166 260 105 0, 349 0, 327 0, 289 0, 232 0, 157 0A067 0. 036 255 110 0, 43● 0, 424 0, 395 0, 348 0, 290 0, 199 0A102 250 115 0, 520 0, 521 0, 503 0, 465 0, 410 0, 336 0. 246 245 120 0, 604 0, 618 0, 611 0, 584 0, 538 0, 431 0. 392 240 125 0, 688 0, 713 0, 718 0, 703 0, 668 0, 613 0. 540 235 130 0, 768 0, 807 0, 824 0, 821 0, 798 0, 754 0. 690 230 135 0, 848 0, 899 0, 928 0, 937 0, 925 0, 892 0. 839 225 140 0, 923 0, 986 1, 029 1, 051 1, 051 0, 829 0. 987 220 145 0, 992 0, 068 1, 124 1, 159 1, 171 1, 163 1. 133 215 150 1, 057 1, 146 1, 214 1, 273 1, 288 1, 292 1. 274 210 155 1, 114 1, 217 1, 280 1, 358 1, 401 1, 414 1. 410 20● 160 1, 168 1, 280 1, 353 1, 445 1, 499 1, 529 1. 537 200 165 1, 215 1, 337 1, 441 1, 525 1, 590 1, 634 1. 657 195 170 1, 254 1, 387 1, 502 1, 598 1, 675 1, 729 1. 764 190 175 1, 286 1, 427 1, 554 1, 662 1, 750 1, 817 1. 864 185 180 1, 312 1, 462 1, 595 1, 714 1, 815 1, 894 1. 953 180 Deg: of Equated Anomaly. Sub Sub Sub Sub Sub Sub Sub Degree of Equated Aoumaly. 159 156 153 150 147 144 141 A Compounded Table of the ☽ Evection and Variation. Degrees of Eq: Anom. ●2 ●4 27 3● 33 36 39 Degrees of Eq: Anom. Add Add Add Add Add Add Add 180 1, 321 1, 462 1, 595 1, 714 1, 815 1, 894 1, 953 180 185 1, 331 1, 488 1, 530 1, 758 1, 866 1, 959 2, 031 175 190 1, 341 1, 506 1, 656 1, 791 1, 911 2, 011 2, 093 170 195 1, 346 1, 513 1, 671 1, 816 1, 943 2, 053 2, 146 165 200 1, 346 1, 517 1, 678 1, 828 1, 963 2, 084 2, 186 160 205 1, 338 1, 514 1, 680 1, 833 1, 974 2, 101 2, 214 155 210 1, 323 1, 502 1, 672 1, 831 1, 978 2, 109 2, 227 150 215 1, 300 1, 482 1, 66● 1, 818 1, 970 2, 109 2, 232 145 220 1, 275 1, 455 1, 629 1, 795 1, 952 2, 096 2, 226 140 225 1, 242 1, 422 1, 619 1, 765 1, 923 2, 072 2, 208 135 230 1, 204 1, 332 1, 557 1, 725 1, 886 2, 033 2, 177 130 235 1, 161 1, 336 1, 509 1, 67● 1, 840 1, 993 2, 136 125 240 1, 112 1, 285 1, 456 1, 623 1, 785 1, 939 2, 085 120 245 1, 055 1, 227 1, 396 1, 561 1, 722 1, 876 2, 023 115 250 1, 002 1, 165 1, 329 1, 491 1, 651 1, 805 1, 952 110 255 0. 943 ●, 000 1, 258 1, 416 1, 576 1, 725 1, 872 105 260 0, 880 1, 031 1, 184 1, 337 1, 4●9 1, 637 1, 782 100 265 0, 815 0, 959 1, 106 1, 253 1, 401 1, 544 1, 687 95 270 0, 748 0, 884 1, 024 1, 170 1, 307 1, 448 1, 586 90 275 0, 679 0, 807 0, 939 1, 073 1, 210 1, 345 1, 480 85 280 0, 609 0, 718 0, 852 0, 979 1, 108 1, 238 1, 368 80 285 0, 5●8 0, 648 0, 763 0, 8●2 1, 004 1, 128 1, 252 75 290 0, 466 0, 567 0, 674 0, 784 0, 898 1, 015 1, 132 70 295 0, 394 0, 485 0, 564 0, 685 0, 791 0, 899 1, 010 65 300 0, 322 0, 40● 0, 485 0, 584 0, 682 0, 783 0, 887 60 305 0, 252 0, ●23 0, 40● 0, 484 0, 573 0, 665 0, 774 55 310 0, 176 0, 243 0, 312 0, 384 0, 464 0, 547 0, 645 50 315 0, 114 0, 165 0, 223 0, 286 0, 397 0, 430 0, 508 45 320 0, 048 0, 089 0, 1●7 0, 189 0, 250 0, 314 0, 384 40 325 0S015 0, 015 0, 052 0, 094 0, 145 0, 200 0, 260 35 330 0, 072 0S044 0S030 0, 000 0, 043 0, 089 0, 039 30 335 0, 134 0, 123 0, 107 0S084 0S053 0S019 0, 020 . 25 340 0, 187 0, 188 0, 180 0, 168 0, 147 0, 124 0S093 20 345 0, 238 0, 248 0, 250 0, 247 0, 242 0, 223 0, 203 15 350 0, 284 0, 303 0, 316 0, 322 0, 323 0, 318 0, 305 10 355 0, 325 0, 353 0, 386 0, 392 0, 403 0, 407 0, 406 05 360 0, 359 0, 396 0, 427 0, 454 0, 475 0, 491 0, 4●9 00 Deg: of Equated Anomaly. Add Add Add Add Add Add Add Degrees of Equtead Anomaly. 159 156 153 15● 147 144 141 A Compounded Table of the ☽ Evection and Variation. Equated Anomaly. 39 41 45 48 51 54 57 Equated Anomaly. Sub: Sub. Sub Sub Sub Sub Sub: 0 0. 499 0, 502 0, 501 0, 495 0, 481 0, 468 0, 447 360 5 0. 585 0, 599 0, 606 0, 610 0, 609 0, 600 0, 591 355 10 0. 661 0, 686 0, 705 0, 719 0, 726 0, 729 0, 651 350 15 0. 728 0, 763 0, 793 0, 818 0, 837 0, 768 0, 854 345 20 0. 786 0, 83● ●, 870 0, 906 0, 935 0, 959 0, 976 340 25 0. 829 0, 887 0, 938 0, 983 1, 023 1, 057 1, 085 335 30 0. 870 0, 933 0, 992 1, 049 1, 099 1, 144 1, 182 330 35 0. 896 0, 969 ●, 037 1, 102 1, 162 1, 218 1, 266 325 40 0. 910 0, 99● 1, 069 1, 144 1, 213 1, 274 1, 337 320 45 0. 910 1, 001 ●, 087 1, 171 1, 252 1, 327 1, 401 3●5 50 0. 902 0, 996 1, 090 1, 085 1, 274 1, 360 1, 440 310 55 0. 884 0, 982 1, 082 1, 182 1, 282 1, 378 1, 467 305 60 0. 850 0, 958 1, 066 1, 171 1, 275 1, 378 1, 480 300 65 0. 805 0, 918 1, 031 1, 146 1, 259 1, 367 1, 473 295 70 0. 749 0, 863 0, 974 1, 103 1, 225 1, 344 1, 455 290 75 0. 681 0, 800 ●, 922 1, 110 1, 175 1, 301 1, 426 285 80 0. 598 0, 771 0, 84● 0, 979 1, 109 ●, 243 1, 375 280 8● ●. 503 0, 628 ●, 758 0, 894 1, 033 1, 167 1, 307 275 90 0. 402 0, 524 0, 655 0, 794 0, 937 1, 063 1, 228 270 9● 0. 289 0, 412 0, 542 0, 680 0, 827 0, 977 1, 128 265 100 0. 166 0, 292 0, 418 0, 558 0, 704 0, 845 1, 053 260 105 0. 036 0, 153 0, 282 0, 422 0, 568 0, 7●5 1, 88● 255 110 0A102 0, 01● 0, 137 0, 275 0, 423 0, 579 0, 742 250 115 0. 246 0A137 0A016 0, 119 0, 266 0, 442 0, 591 245 120 0. 392 0, 292 0, 177 0A045 0, 091 0, 254 0, 417 240 125 0. 540 0, 449 0, 341 0, 216 0A076 0, 077 0, 239 235 130 0. 690 0, 607 0, 537 0, 389 0, 256 0A108 0, 052 230 135 0. 839 0, 766 0, 675 0, 565 0, 448 0, 296 0A141 225 140 0. 987 0, 925 0, 843 0, 342 0, 623 0, 487 0, 337 220 145 1. 133 1, 081 1, 010 0, 918 0, 808 0, 680 0, 536 215 150 1. 274 1, 235 ●, 174 1, 094 0, 992 0, 872 0, 737 210 155 1. 410 1, 383 1, 234 1, 263 1, 172 1, 062 0, 935 205 160 1. 537 1, 541 1, 488 1, 429 1, 350 1, 249 1, 131 200 165 1. 657 1, 656 1, 633 1, 587 1, 520 1, 431 1, 323 195 170 1. 764 1, 778 1, 768 1, 741 1, 682 1, 605 1, 509 190 175 1. 864 1, 888 1, 892 1, 875 1, 833 1, 769 1, 685 185 180 1. 953 1, 991 2, 005 1, 999 1, 973 1, 923 1, 851 180 Equated Anomaly. Sub Sub Sub Sub Sub Sub Sub Equated Anomaly. 141 138 135 132 129 126 123 A Compounded Table of the ☽ Evection and Variation. Equated Anomaly. 39 42 45 4● 51 54 57 Equated Anomaly. Add Add Add Add Add Add Add 180 1. 953 1, 991 2, 005 1. 999 1, 973 1, 923 1, 851 180 185 2. 031 2, 081 2, 108 2. 103 2, 098 2, 061 2, 004 175 190 2. 093 2, 157 2, 199 2. 218 2, 215 2, 180 2, 142 170 195 ●. 146 2, 218 2, 272 2. 306 2, 317 2, 303 2, 270 165 200 2. 186 2, 269 2, 334 2. 376 2, 402 2, 403 2, 383 160 205 2. 214 2, 307 2, 382 2. 436 2, 471 2, 484 2, 479 155 210 2. 227 2, 330 2, 416 2. 482 2, 526 2, 552 2, 555 150 215 2. 232 2, 340 2, 433 2. 507 2, 568 2, 603 2, 620 145 220 2. 226 2, 34● 2, 441 2. 523 2, 590 2, 639 2, 668 140 225 2. 208 2, 330 2, 4●7 2. 529 2, 600 2, 673 2, 696 135 230 2. 177 2, 300 2, 419 2. 518 2, 600 2, 663 2, 708 130 235 2. 136 2, 267 2, 387 2. 494 2, 583 2, 655 2, 712 125 240 2. 085 2, 220 2, 343 2. 454 2, 551 2, 632 2, 696 120 245 2. 023 2, 161 2, 288 2. 403 2, 500 2, 591 2, 666 115 250 1. 952 2, 091 2, 219 2. 340 2, 446 2, 539 2, 572 110 255 1. 872 2, 012 2, 143 2. 265 2, 375 2, 473 2, 558 105 260 1. 782 1, 923 2, 056 2. 179 2, 292 2, 393 2, 484 100 265 1. 687 1, 825 1, 957 2. 083 2, 198 2, 302 2, 387 95 270 1. 586 1, 721 1, 851 1. 975 2, 094 2, 190 2, 297 90 275 1. 480 1, 611 1, 739 1. 861 1, 975 2, 085 2, 186 85 280 1. 368 1, 496 1, 620 1. 741 1, 853 1, 962 2, 063 80 285 1. 252 1, 375 1, 496 1. 614 1, 726 1, 832 1, 933 75 290 1. 132 1, 250 1, 366 1. 480 1, 490 1, 695 1, 795 70 295 1. 010 1, 111 1, 233 1. 342 1, 449 1, 552 1, 650 65 300 0. 887 0, 991 1, 096 1. 200 1, 303 1, 402 1, 499 60 305 0. 774 0, 884 0, 957 1. 056 1, 153 1, 249 1, 342 55 310 0. 645 0, 725 0, 814 0. 909 1, 001 1, 094 1, 181 50 315 0. 508 0, 590 0, 675 0. 761 0, 872 0, 933 1, 018 45 320 0. 384 0, 457 0, 537 0. 621 0, 691 0, 794 0, 852 40 325 0. 260 0, 325 0, 493 0. 462 0, 516 0, 609 0, 684 35 330 0. 039 0, 195 0, 254 0. 323 0, 380 0, 446 0, 515 30 335 0. 020 0, 067 0, 117 0. 170 0, 227 0, 286 0, 348 25 340 0S093 0S057 0S016 0. 028 0, 076 0, 128 0, 183 20 345 0. 203 0, 177 0, 146 0S110 0S071 0S028 0, 019 15 350 0. 305 0, 291 0, 270 0. 245 0, 214 0, 179 0S141 10 355 0. 406 0, 400 0, 388 0. 373 0, 452 0, 327 0, 296 05 360 0. 499 0, 502 0, 501 0. 495 0, 481 0, 468 0, 447 200 Equated Anomaly. Add Add Add Add Add Add Add Equated Anomaly▪ 141 138 135 ●32 129 126 123 A Compounded Table of the ☽ Evection and Variation. Equated Anomaly. 57 68 63 66 69 72 ●5 Equated Anomaly. Sub Sub: Sub Sub Sub Sub Sub 0 0. 447 0, 421 0, 391 0. 358 0, 320 0, 280 0, 237 360 5 0. 591 0, 574 0, 552 0. 550 0, 496 0, 462 0, 424 355 10 0. 651 0, 719 0, 606 0. 688 0, 665 0, 639 0, 607 350 15 0. 854 0, 856 0, 752 0. 843 0, 828 0, 809 0, 784 345 20 0. 976 0, 986 0, 990 0. 990 0, 981 0, 972 0, 954 340 25 1. 085 1, 107 1, 121 1. 127 1, 129 1, 126 1, 116 335 30 1. 182 1, 214 1, 240 1. 258 1, 268 1, 227 1, 269 330 35 1. 266 1, 309 1, 345 1. 374 1, 396 1, 402 1, 413 325 40 1. 337 1, 392 1, 348 1. 477 1, 508 1, 593 1, 549 320 45 1. 401 1, 459 1, 517 1. 567 1, 608 1, 642 1, 668 315 50 1. 440 ●, 513 1, 580 1. 640 1, 694 1, 739 1, 774 310 55 1. 467 1, 589 1, 631 1. 700 1, 758 1, 820 1, 866 305 60 1. 480 1, 575 1, 663 1. 746 1, 819 1, 885 1, 941 300 65 1. 473 1, 579 1, 680 1. 772 1, 857 1, 936 2, 001 295 70 1. 455 1, 569 1, 676 1. 781 1, 878 1, 966 2, 046 290 75 1. 426 1, 549 1, 663 1. 772 1, 878 1, 981 2, 070 285 80 1. 375 1, 506 1, 63● 1. 754 1, 966 1, 973 2, 074 280 85 1. 307 1, 448 1, 562 1. 713 1, 839 1, 953 2, 074 275 90 1. 228 1, 373 1, 514 1. 655 1, 749 1, 920 2, 035 270 95 1. 128 1, 282 1, 433 1. 578 1, 622 1, 863 1, 993 265 100 1. 013 1, 172 1, 331 1. 487 1, 639 1, 785 1, 929 260 105 0. 882 1, 045 1, 211 1. 375 1, 538 1, 696 1, 845 255 110 0. 742 0, 907 1, 074 1. 246 1, 424 1, 583 1, 744 250 115 0. 591 0, 755 0, 894 1. 101 1, 275 1, 451 1, 621 245 120 0. 417 0, 589 0, 765 0. 945 1, 124 1, 303 1, 479 240 125 0. 239 0, 411 0, 589 0. 772 0, 957 1, 194 1, 325 235 130 0. 052 0, 223 0, 402 0. 587 0, 775 0, 973 1, 156 230 135 0A141 0, 026 0, 204 0. 390 0, 581 0, 776 0, 970 225 140 0. 337 0A175 0, 000 0. 184 0, 377 0, 574 0, 772 220 145 0. 536 0, 378 0A208 0A026 0, 163 0, 361 0, 563 215 150 0. 737 0, 584 0, 419 0. 240 0A063 0, 142 0, 344 210 155 0. 935 0, 790 0, 631 0. 458 0, 273 0A080 0, 119 205 160 1. 131 0, 994 0, 842 0. 675 0, 495 0, 306 0A107 200 165 1. 323 1, 195 1, 051 0. 891 0, 717 0, 533 0, 337 195 170 1. 509 1, 392 1, 257 1. 104 0, 937 0, 683 0, 568 190 175 1. 685 1, 580 1, 455 1. 322 1, 153 0, 979 0, 784 185 180 1. 85● 1, 758 1, 645 1. 513 1, 363 1, 198 1, ●19 180 Equated Anomaly. Sub Sub Sub Sub Sub Sub Sub Equated Anomaly. 123 120 117 ●14 111 108 105 A Compounded Table of the ☽ Evection and Variation▪ Equated Anomaly. 57 60 63 66 69 72 75 Equated Anomaly. Add Add Add Add Add Add Add▪ 180 1, 851 1, 758 1, 645 1, 513 1, 363 1, 198 1, 1●9 180 185 2, 004 1, 924 1, 829 1, 7●2 1, 564 1, 409 1, 2●8 175 190 2, 142 2, 07● 1, 990 1, 880 1, 753 1, 608 1, 448 17● 195 2, 270 2, 214 2, 139 2, 044 1, 930 1, 796 1, 646 165 200 2, 383 2, 341 2, 278 2, 191 2, 090 1, 970 1, 831 160 205 2, 479 2, 451 2, 401 2, 3●9 2, 238 2, 126 2, 001 1●5 210 2, 555 2, 541 2, 507 2, 448 2, 369 2, 272 2, 154 150 215 2, 620 2, 617 2, 591 2, 548 2, 483 2, 400 2, 296 145 220 2, 668 2, 675 2, 663 2, 629 2, 576 2, 509 2, 419 140 225 2, 696 2, 717 2, 717 2, 695 2, 656 2, 596 2, 520 135 230 2, 708 2, 738 2, 748 2, 744 2, 715 2, 668 2, 604 130 235 2, 712 2, 748 2, 767 2, 769 2, 756 2, 723 2, 669 125 240 2, 696 2, 744 2, 774 2, 781 2, 775 2, 755 2, 711 120 245 2, 660 2, 758 2, 760 2, 782 2, 784 2, 129 ●, 739 115 250 2, 572 2, 682 2, 727 2, 761 2, 774 2, 773 2, 750 110 255 2, 558 2, 628 2, 684 2, 724 2, 748 2, 755 2, 746 105 260 2, 484 2, 56● 2, 623 ●, 687 2, 701 2, 7●● 2, 721 100 265 2, 387 2, 478 2, 547 2, 601 2, 640 2, 666 2, 677 95 270 2, 297 2, 383 2, 457 2, 517 2, 56● 2, 600 2, 616 90 275 2, 186 2, 276 2, 354 2, 419 2, 473 2, 514 2, 541 85 280 2, 063 2, 155 2, 238 2, 309 2, 368 2, 415 2, 449 80 285 1, 933 2, 025 2, 109 ●, 185 2, 241 2, 303 2, 343 75 290 1, 795 1, 888 1, 97● 2, 048 2, 117 2, 176 2, 224 70 295 1, 650 1, 743 1, 829 1, 904 1, 975 2, 036 2, 088 65 300 1, 499 1, 590 1, 676 1, 754 1, 798 1, 889 1, 944 60 305 1, 342 1, 431 1, 516 1, 595 1, 663 1, 733 1, 791 55 310 1, 181 1, 268 1, 350 1, 416 1, 502 1, 569 1, 629 50 315 1, 018 1, 100 1, 181 1, 257 1, 329 1, 397 1, 459 45 320 0, 852 0, 930 1, 007 1, 081 1, 152 1, 219 1, 281 40 325 0, 684 0, 758 0, 831 0, 902 0, 971 1, 037 1, 099 35 330 0, 515 0, 584 0, 654 0, 717 0, 787 0, 841 0, 913 30 335 0, 348 0, 410 0, 474 0, 538 0, 602 0, 664 0, 723 25 340 0, 183 0, 238 0, 295 0, 333 0, 424 0, 473 0, 531 20 345 0, 019 0, 067 0, 119 0, 172 0, 226 0, 282 0, 337 15 350 0S141 0S099 0S054 0S006 0, 042 0, 092 0, 144 10 355 0, 296 0, 262 0, 224 0, 184 0S140 0S095 0S048 05 360 0, 447 0, 421 0, 391 0, 358 0, 320 0, 280 0, 237 00 Equated Anomaly. Add Add Add Add Add Add Add Equated Anomaly. 123 12● 117 114 ●11 108 105 A Compounded Table of the ☽ Evection and Variation. Equated Anomaly. 75 78 81 84 ●7 90 Equated Anomaly: Sub: Sub. Sub Sub Sub Sub 0 0. 237 0, 193 0, 146 0, 099 0, 050 0, 000 360 5 0. 424 0, 384 0, 341 0, 295 0, 249 0, 201 355 10 0. 607 0, 571 0, 532 0, 490 0, 446 0, 399 350 15 0. 784 0, 754 0, 720 0, 682 0, 640 0, 596 345 20 0. 954 0, 931 0, 902 0, 869 0, 831 0, 789 340 25 1. 116 1, 100 1, 078 1, 050 1, 016 1, 978 335 30 1. 269 1, 260 ●, 245 1, 224 1, 198 1, 161 330 35 1. 413 1, 412 1, 403 1, 351 1, 366 1, 337 325 40 1. 549 1, 555 1, 553 1, 544 1, 528 1, 505 320 45 1. 668 1, 686 1, 694 1, 692 1, 681 1, 664 315 50 1. 774 1, 801 1, 819 1, 827 1, 826 1, 813 310 55 1. 866 1, 903 1, 930 1, 947 1, 955 1, 953 305 60 1. 941 1, 990 2, 028 2, 054 2, 071 2, 077 300 65 2. 001 2, 059 2, 100 2, 146 2, 172 2, 186 295 70 2. 046 2, 115 2, 171 2, 213 2, 257 2, 282 290 75 2. 070 2, 151 2, 221 2, 279 2, 325 2, 359 285 80 2. 074 2, 170 2, 249 2, 319 2, 378 2, 422 280 85 2. 074 2, 165 2, 259 2, 342 2, 411 2, 467 275 90 2. 035 2, 150 2, 250 2, 342 2, 426 2, 493 270 95 1. 993 2, 118 2, 229 2, 329 2, 418 2, 498 265 100 1. 929 2, 060 2, 186 2, 300 2, 397 2, 487 260 105 1. 845 1, 987 2, 123 2, 242 2, 362 2, 463 255 110 1. 744 1, 897 2, 040 2, 176 2, 302 2, 414 250 115 1. 621 1, 786 1, 942 2, 087 2, 221 2, 347 245 120 1. 479 1, 654 1, 821 1, 979 2, 127 2, 259 240 125 1. 325 1, 504 1, 681 1, 848 2, 008 2, 155 235 130 1. 156 1, 344 1, 524 1, 699 1, 870 2, 000 230 135 0. 970 1, 16● 1, 355 1, 539 1, 714 1, 881 225 140 0. 772 0, 972 1, 168 1, 360 1, 547 1, 722 220 145 0. 563 0, 766 0, 968 1, 166 1, 367 1, 547 215 150 0. 344 0, 550 0, 755 0, 960 1, 161 1, 355 210 155 0. 119 0, 325 0, 533 0, 742 0, 949 1, 149 20● 160 0A107 0, 197 0, 304 0, 515 0, 726 1, 932 200 165 0. 337 0A068 0, 073 0, 283 0, 495 0, 705 195 170 0. 468 0, 367 0A161 0, 049 0, 261 0, 473 190 175 0. 784 0, 599 0, 397 0A188 0, 025 0, 238 185 180 1. 019 0, 828 0, 630 0, 424 0A214 0, 000 180 Equated Anomaly. Sub Sub Sub Sub Sub Sub Equated Anomaly. 105 102 099 96 93 90 A Compounded Table of the ☽ Evection and Variation. Equated Anomaly. 75 7● 81 84 87 90 Equated Anomaly. Add Add Add Add Add Add 180 1, 019 0, 828 0, 630 0, 424 0, 214 0, 000 180 185 1, 238 1, 054 0, 860 0, 658 0, 450 0, 238 175 190 1, 448 1, 271 1, 085 0, 888 0, 684 0, 473 170 195 1, 646 1, 480 1, 302 1, 112 0, 912 0, 705 165 200 1, 831 1, 682 1, 507 1, 326 1, 133 0, 932 160 205 2, 001 1, 858 1, 699 1, 527 1, 343 1, 146 155 210 2, 154 2, 022 1, 886 1, 716 1, 540 1, 355 150 215 2, 296 2, 175 2, 035 1, 886 1, 719 1, 547 145 220 2, 149 2, 310 2, 184 2, 044 1, 887 1, 722 140 225 2, 520 2, 426 2, 313 2, 184 2, 040 1, 881 135 230 2, 604 2, 518 2, 412 2, 307 2, 175 2, 000 130 235 2, 966 2, 598 2, 509 2, 405 2, 294 2, 155 125 240 2, 711 2, 657 2, 580 2, 489 2, 380 2, 259 120 245 2, 739 2, 661 2, 633 2, 553 2, 456 2, 347 115 250 2, 750 2, 712 2, 661 2, 596 2, 513 2, 414 110 255 2, 746 2, 719 2, 674 2, 616 2, 552 2, 463 105 260 2, 721 2, 705 2, 674 2, 626 2, 561 2, 487 100 265 2, 677 2, 673 2, 652 2, 616 2, 566 2, 498 95 270 2, 616 2, 621 2, 611 2, 588 2, 547 2, 493 90 275 2, 541 2, 554 2, 546 2, 538 2, 511 2, 467 85 280 2, 449 2, 471 2, 479 2, 473 2, 453 2, 422 80 285 2, 343 2, 371 2, 388 2, 392 2, 383 2, 359 75 290 2, 224 2, 259 2, 282 2, 294 2, 294 2, 282 70 295 2, 088 2, 132 2, 163 2, 182 2, 190 2, 186 65 300 1, 944 1, 990 2, 028 2, 057 2, 07● 2, 077 60 305 1, 791 1, 840 1, 882 1, 915 1, 939 1, 953 55 310 1, 629 1, 682 1, 725 1, 764 1, 792 1, 813 50 315 1, 459 1, 515 1, 561 1, 605 1, 638 1, 664 45 320 1, 281 1, 335 1, 391 1, 436 1, 474 1, 505 40 325 1, 099 1, 157 1, 21● 1, 260 1, 302 1, 337 35 330 0, 913 0, 971 1, 026 1, 076 1, 124 1, 161 30 335 0, 723 0, 780 0, 835 0, 887 0, 934 0, 978 25 340 0, 531 0, 587 0, 638 0, 694 0, 743 0, 789 20 345 0, 337 0, 392 0, 447 0, 499 0, 548 0, 596 15 350 0, 144 0, 196 0, 248 0, 300 0, 351 0, 399 10 355 0S048 0S000 0S050 0S108 0, 149 0, 201 05 360 0, 273 0, 193 0, 146 0, 099 0S050 0, 000 00 Equated Anomaly. Add Add Add Add Add Add Equated Anomaly. 105 102 99 96 93 90 A Table of the Aequations of Nodes and Moon's Latitude. Eq: Nod: Add Scruples of prop. Latit. ☽ Eccesse Add D. Parts. Parts. D. parts. Parts. 0 180 0. 00000 , 00000 0, 00000 , 00000 180 360 1 181 0, 06389 , 00030 0, 08694 , 00556 179 359 2 182 0, 12750 , 00120 0, 17361 , 01111 178 358 3 183 0, 19083 , 00274 0, 26000 , 01639 177 357 4 184 0, 25389 , 00487 0, 34639 , 02194 176 356 5 185 0, 31667 , 00760 0, 43278 , 02750 175 355 6 186 0, 37944 , 01093 0, 51917 , 03305 174 354 7 187 0, 44139 , 01485 0, 60528 , 03861 173 353 8 188 0, 50250 , 01937 0, 69139 , 04389 172 352 9 189 0, 56305 , 02447 0, 77722 , 04917 171 351 10 190 0, 62305 , 03015 0, 86278 , 05472 170 350 11 191 0, 68222 , 03641 0, 94806 , 06000 169 ●49 12 192 0, 74056 , 04323 1, 03972 , 06528 168 348 13 193 0, 79778 , 05060 1, 11778 , 07083 167 347 14 194 0, 85389 , 05853 1, 20222 , 07611 166 346 15 195 0, 90889 , 06699 1, 28611 , 08139 165 345 16 196 0, 96307 , 07598 1, ●6972 , 08694 164 344 17 197 1, 01556 , 08548 1, 45278 , 09222 163 343 18 198 1, 06●67 , 09549 1, 53556 , 09750 162 342 19 199 1, 11639 , 10599 1, 61778 , 10278 161 341 20 200 1, 16472 , 11698 1, 69944 , 10778 160 340 21 201 1, 21167 , 12843 1, 78083 , 11305 159 339 22 202 1, 25694 , 14033 1, 86139 , 11833 158 338 23 203 1, 30056 , 15267 1, 94167 , 12333 157 337 24 204 1, 34250 , 1654● 2, 02139 , 12833 156 336 25 205 1, 38944 , 17861 2, 10028 , 13333 155 335 26 206 1, 42111 , 19217 2, 17861 , 13833 154 334 27 207 1, 45778 , 20611 2, 25639 , 14●06 153 333 28 208 1, 39278 , 22287 2, 33333 , 14806 152 332 29 209 1, 52611 , 23504 2, 40944 , 15306 151 331 30 210 1, 55778 , 25000 2, 48500 , 15778 150 330 30 210 1. 55778 , 25000 2, 48500 , 15778 150 330 31 211 1, 58667 , 26526 2, 56000 , 16250 149 329 32 212 1, 61306 , 28081 2, 63417 , 16722 148 328 33 213 1, 63667 , 29663 2, 70722 , 17●67 147 327 34 214 1, 65861 , 31270 2, 77944 , 17639 146 326 35 215 1, 67833 , 32899 2, 85111 , 18083 145 325 36 216 1, 69583 , 34549 2, 92194 , 18528 144 324 37 217 1, 71222 , 36218 2, 99167 , 18972 143 323 38 218 1, 72722 , 37904 3, 06056 , 19417 142 322 39 219 1, 74139 , 39640 3, 12861 , 19861 141 321 40 220 1, 75222 , 41318 3, 19556 , 20306 140 320 41 221 1, 75944 , 43041 3, 26167 , 20732 139 319 42 222 1, 76389 , 44774 3, 32667 , 21139 138 318 43 223 1, 76556 , 46512 3, 39056 , 21556 137 317 44 224 1, 76639 , 48255 3, 45361 , 21944 136 316 45 225 1, 76667 , 50000 3, 51564 , 22346 135 315 46 226 1, 76472 , 51744 3, 57639 , 22722 134 314 47 227 1, 76000 , 53487 3, 63611 , 23111 133 313 48 228 1, 75361 , 55226 3, 69500 , 23472 132 312 49 229 1, 74472 , 56953 3, 75194 , 23833 131 311 50 230 1, 733●3 , 58682 3, 80833 , 24194 130 310 51 231 1, 71944 , 60395 3, 86444 , 24556 129 309 52 232 1, 70389 , 62096 3, 91917 , 24917 128 308 53 233 1, 68611 , 63781 3, 97194 , 25250 127 307 54 234 1, 66639 , 65451 4, 02306 , 25583 126 306 55 235 1, 64500 , 67101 4, 07333 , 25917 125 305 56 236 1, 62167 , 68730 4, 12250 , 26194 124 304 57 237 1, 59611 , 70336 4, 17083 , 26500 123 303 58 238 1, 56889 , 71918 4, 21806 , 26806 120 302 59 239 1, 5397● , 7347● 4, 26306 , 27083 101 301 60 240 1, 50889 , 75000 4, 30722 , 27361 120 300 60 240 1, 50889 , 75000 4, 30722 , 27361 120 300 61 241 1, 47611 , 76496 4, 34972 , 27639 119 299 62 242 1, 44167 , 77959 4, 39111 , 27917 118 298 63 243 1, 40583 , 79389 4, 43139 , 28194 117 297 64 244 1, 36833 , 80783 4, 47028 , 28444 116 296 65 245 1, 32917 , 82439 4, 50778 , 28667 115 295 66 246 1, 28833 , 83456 4, 54389 , 28889 114 294 67 247 1, 24667 , 84732 4, 57861 , 29111 113 293 68 248 1, 20250 , 85967 4, 61194 , 29333 112 292 69 249 1, 15750 , 87152 4, 64389 , 29528 111 291 70 250 1, 11139 , 88302 4, 67417 , 29750 110 290 71 251 1, 06361 , 89400 4, 70306 , 29944 109 289 72 252 1, 01417 , 90450 4, 73056 , 30139 108 288 73 253 0, 96389 , 91451 4, 75639 , 30333 107 287 74 254 0, 91306 , 92402 4, 78111 , 30500 106 286 75 255 0, 86167 , 93301 4, 80500 , 30639 105 285 76 256 0, 80889 , 94147 4, 32639 , 30750 104 284 77 257 0, 75500 , 94939 4, 84694 , 30861 103 283 78 258 0, 70000 , 95177 4, 86611 , 30944 102 282 79 259 0, 64444 , 96359 4, 88333 , 31056 101 281 80 260 0, 58833 , 96984 4, 89917 , 31167 100 280 81 261 0, 53139 , 97552 4, 91●61 , 31250 99 279 82 262 0, 47389 , 98063 4, 92667 , 31333 98 278 83 263 0, 41583 , 98514 4, 9●806 , 31417 97 277 84 264 0, 35722 , 98907 4, 94778 , 31472 96 276 85 265 0, 29833 , 99240 4, 95611 , 31528 95 275 86 266 0, 23917 , 99513 4, 96278 , 31556 94 274 87 267 0, 17944 , 99726 4, 96833 , 31583 93 273 88 268 0, 11972 , 99878 4, 97167 , 31611 92 272 89 269 0, 06000 , 99964 4, 97389 , 31639 91 271 90 270 0, 00000 , 00000 4, 97500 , 31667 90 270 Subst. A Table of the Moon's Reductions to the Ecliptic. Reduct. Subst. D. parts. 0 180 , 00000 180 360 1 181 , 00417 179 359 2 182 , 00833 178 358 3 183 , 01250 177 357 4 184 , 01639 176 356 5 185 , 02028 175 355 6 186 , 02417 174 354 7 187 , 02833 173 353 8 188 , 03222 172 352 9 189 , 03611 171 351 10 190 , 04000 170 350 11 191 , 04389 169 349 12 192 , 04778 168 348 13 193 , 05●67 167 347 14 194 , 05528 166 346 15 195 , 05889 165 345 16 196 , 06194 164 344 17 197 , 06556 163 343 18 198 , 06●89 162 342 19 199 , 07194 161 341 20 200 , 07500 160 340 21 201 , 07806 159 339 22 202 , 08111 158 338 23 203 , 08389 157 337 24 204 , 08694 156 336 25 205 , 08944 155 335 26 206 , 09194 154 334 27 207 , 09444 153 333 28 208 , 09694 152 332 29 209 , 09944 151 331 ●0 210 , 10278 150 330 30 210 , 10167 150 330 31 211 , 10333 149 329 32 212 , 10500 148 328 33 213 , 10667 147 327 34 214 , 10806 146 326 35 215 , 10972 145 325 36 216 , 11111 144 324 37 217 , 11222 143 323 38 218 , 11306 142 322 39 219 , 11417 141 321 40 220 , 11500 140 320 41 221 , 11556 139 219 42 222 , 11583 138 318 43 223 , 11611 137 317 44 224 , 11639 136 316 45 225 , 11667 135 315 46 226 , 11639 134 314 47 227 , 11611 133 313 48 228 , 11583 132 212 49 229 , 11556 131 311 50 230 , 11500 130 310 51 231 , 11417 129 309 52 232 , 11306 128 308 53 233 , 11222 127 307 54 234 , 11111 126 306 55 235 , 10972 125 305 56 236 , 10778 124 304 57 237 , 10639 12● 303 58 238 , 10472 122 302 59 239 , 10306 121 391 60 240 , 10139 120 300 60 240 , 10139 120 300 61 241 , 09917 119 299 62 242 , 09667 118 298 63 243 , 09417 117 297 64 244 , 09167 116 296 65 245 , 08917 115 295 66 246 , 08667 114 294 67 247 , 08361 113 293 68 248 , 08083 112 292 69 249 , 07778 111 291 70 250 , 07472 110 290 71 251 , 07167 109 289 72 252 , 06833 108 288 73 253 , 06528 107 287 74 254 , 06167 106 286 75 255 , 05861 105 285 76 256 , 05500 104 284 77 257 , 05139 103 283 78 258 , 04750 102 282 79 259 , 04389 101 281 80 260 , 03972 100 280 81 261 , 03583 99 279 82 262 , 03194 98 278 83 263 , 02806 97 277 84 264 , 02389 96 276 85 265 , 02000 95 275 86 266 , 01611 94 274 87 267 , 01250 93 273 88 268 , 00833 92 272 89 269 , 00417 91 271 90 270 , 00000 90 270 Add The difference of the true ☌ or ☍ from the middle of the Obscuration. Lat. ☽ Differ. D. par Parts. 0, 10 , 00861 0, 20 , 01722 0, 30 , 02611 0, 40 , 03500 0, 50 , 04361 0, 60 , 05222 0, 70 , 06083 0, 80 , 06972 0, 90 , 07833 1, 00 , 08722 1, 10 , 09583 1, 20 , 10472 1, 30 , 11361 1, 40 , 12222 1, 50 , 13083 1, 60 , 13944 Latitude. ☽ North Desc. Add South Asc. Add North Asc. Subst. South Desc. Subst. A Table of the Mean Lunations. Years Hours: Parts Months. Common. Bissextile. Days Hours 1 255, 18944 complea. Hours: parts. Hours: Parts. 2 510, 37889 January 0035, 26556 0035, 26556 1 24 3 056, 83417 Februa. 0707, 26556 0022, 531●9 2 48 B4 336, 02361 March. 0043, 7972● 0057 79722 3 72 5 591, 21306 April. 0045, 06306 0069, 06306 4 96 6 137, 66833 May. 0080, 32889 0104, 32889 5 120 7 392, 85778 June. 0091, 59472 0115, 59472 6 144 B8 673, 04722 July. 0126, 86028 0150, 86028 7 168 9 218, 50250 August 0162, 12611 0186, 12611 8 192 10 473, 69194 Septem. 0173, 39194 0197, 39194 9 216 11 020, 14722 October 0208, 65778 0232, 65778 10 240 B12 299, 33667 Novem 0219, 92361 0243, 92361 11 264 13 554, 52611 Decem. 0255, 18944 0279, 18944 12 288 14 100, 98139 13 312 15 356, 17083 Canonion Syzygiarum. 14 336 B16 635, 36028 ☌ ☍ 15 360 17 181, 81556 16 384 18 437, 00500 Hours: Parts Hours: Parts. 17 408 19 692, 19444 I 0708, 73417 0354, 36722 18 432 B20 262, 64972 TWO 1417, 46833 1063, 10139 19 456 40 525, 29944 III 2126, 20250 1771, 83556 20 480 60 079, 21528 IV 2834, 03667 2480, 56972 21 504 80 341, 86500 V 3543, 67083 3189, 30361 22 528 100 604, 51472 VI 4252, 40500 3898, 03806 23 552 200 500, 29556 VII 4961, 13944 4606, 77222 24 576 300 396, 07639 VIII 5669, 87361 5315, 50667 25 600 400 291, 85694 26 624 500 187, 63778 Epochaes. 27 648 600 083, 41861 Years Complete. Hours: Parts. 28 672 700 687, 93361 29 696 800 583, 71417 Christi. 0425, 70667 30 720 900 479, 49500 1600 0176, 06694 1000 375, 27583 1620 0439, 31667 2000 041, 81750 1640 0701, 96639 3000 417, 09333 1660 0255, 88194 The Horizontal Parallaxes, Semidiameters, and Hourly motions of the Sun and Moon. Degrees Horiz. Paral. ☉ Semidiam. ☉ Hourly motion. ☉ Semia. Cone Shad. Horizon. Paralax. ☽ Semidiam. ☽ Hourly motion ☽ Degrees Parts. Parts. Parts. Parts. Parts. Parts. Parts. 0 , 03855 , 26936 , 03972 , 22948 , 92692 . 25964 , 49444 360 6 , 03859 , 26968 , 03981 , 22980 , 92982 . 26043 , 49916 354 12 , 03863 , 27001 , 03990 , 23013 , 93273 . 26122 , 50388 348 18 , 03868 , 27033 , 03999 , 23046 , 93564 . 26201 , 50860 342 24 , 03872 , 27066 , 04008 , 23078 , 93854 . 26280 , 51332 336 30 , 03876 , 27099 , 04017 , 23111 , 94145 . 26359 , 51804 330 36 , 03881 , 27131 , 04026 , 2●144 , 94436 . 26438 , 52276 324 42 , 03885 , 27164 , 04035 , 23176 , 94727 . 26517 , 52748 318 48 , 03889 , 27196 , 04044 , 23209 , 95018 . 26596 , 53220 312 54 , 03894 , 27239 , 04052 , 23242 , 95308 . 26679 , 53682 306 60 , 03898 , 27271 , 04061 , 23274 , 95599 . 26754 , 54164 300 66 , 03902 , 27304 , 04070 , 23307 , 95889 . 26833 , 54636 294 72 , 03907 , 27337 , 04079 , 23340 , 96180 . 26912 , 55108 288 78 , 03911 , 27369 , 04088 , 23372 , 96471 . 26991 , 55581 282 84 , 03915 , 27401 , 04097 , 23405 , 96762 . 27069 , 55953 276 90 , 03919 , 27433 , 04106 , 23438 , 97052 . 27148 , 56425 270 96 , 03924 , 27466 , 04115 , 23470 , 97343 . 27227 , 56897 264 102 , 03928 , 27498 , 04124 , 23503 , 97634 . 27306 , 57369 258 108 , 03932 , 27531 , 04132 , 23536 , 97925 . 27385 , 57841 252 114 , 03937 , 27564 , 04141 , 23568 , 98215 . 27464 , 58313 246 120 , 03941 , ●7596 , 04150 , 23601 , 98506 . 27543 , 58785 240 126 , 03945 , 27629 , 04159 , 23634 , 98797 . 27622 , 59257 234 132 , 03950 , 27661 , 04168 , 23666 , 99087 . 27701 , 59729 228 138 , 03954 , 27694 , 04177 , 23699 , 99378 . 27780 , 60201 222 144 , 03958 , 27727 , 04186 , 23732 , 99669 . 27859 , 60673 216 150 , 03963 , 27759 , 04195 , 23764 , 99960 . 27938 , 61145 210 156 , 03967 , 27792 , 04204 , 23797 1, 00250 . 28017 , 61617 2●4 162 , 03971 , 27824 , 04213 , 23830 1, 00541 . 28096 , 62089 198 168 , 03976 , 27857 , 04222 , 23863 1, 00832 . 28175 , 62461 192 174 , 03981 , 27889 , 04231 , 23896 1, 01123 . 28254 , 6●933 186 180 , 03988 , ●7916 , 04250 , 23928 1, 01414 . 28333 , ●3611 180 Dist▪ 4 32 9 33 291 79 472 erenc The Declination and Meridian Angles. ♈ ♎ ♉ ♏ ♊ ♐ Declina. Ang. Declina. Ang. Declina. Ang. D. parts D. P. D. Parts. D. P. D. Parts. D. P. 0 0, 00000 66. 47 11, 51167 69, 33 20, 22278 77. 70 30 1 0, 39889 66. 47 11, 86333 69, 52 20, 43917 78. 07 29 2 0, 79806 56. 48 12, 21111 69, 72 20, 63583 78. 43 28 3 1, 19694 66. 50 12, 55583 69, 92 20, 83278 78. 80 27 4 1, 59528 66. 52 12, 89694 70, 13 21, 02361 79. 18 26 5 1, 99361 66. 55 13, 23472 70, 35 21, 20806 79. 57 25 6 2, 39111 66. 58 13, 56861 70, 58 21, 38528 79. 95 24 7 2, 78778 66. 63 13, 89917 70, 81 21, 55611 80. 33 23 8 3, 18444 66. 68 14, 22556 71, 05 21, 72083 80. 72 22 9 3, 57972 66. 73 14, 54806 71, 30 21, 87833 81. 12 21 10 3, 97444 66. 78 14, 86639 71, 55 22, 02917 81. 51 20 11 4, 36778 66. 85 15, 18056 71, 80 22, 17278 81. 92 19 12 4, 76028 66. 92 15, 49056 72, 07 22, 30972 82. 31 18 13 5, 15139 67. 00 15, 79639 72, 33 22, 43944 82. 73 17 14 5, 54139 67. 08 16, 09750 72, 60 22, 56222 83. 15 16 15 5, 92972 67, 18 16, 39417 72, 88 22, 67750 83. 57 15 16 6, 31611 67. 28 16, 68861 73, 17 22, 78611 83. 98 14 17 6, 70167 67. 40 16, 97278 73, 45 22, 88694 84. 40 13 18 7, 08500 67. 52 17, 25500 73, 75 22, 98083 84. 83 12 19 7, 46667 67. 63 17, 53167 74, 05 23, 06750 85. 25 11 20 7, 84611 67. 75 17, 80389 74, 35 23, 14639 85. 68 10 21 8, 22389 67. 88 18, 07056 74, 67 23, 21806 86. 10 09 22 8, 59944 68 02 18, 33250 74, 98 23, 28222 86. 53 08 23 8, 97222 68 15 18, 58833 75, 30 23, 33889 86. 97 07 24 9, 34278 68 30 18, 83917 75, 63 23, 38833 87. 40 06 25 9, 71139 68 47 19, 08444 75, 97 23, 4300● 87. 83 05 26 10, 07722 68 63 19, 32389 76, 30 23, 46417 88 26 04 27 10, 44000 68 80 19, 55750 76, 65 23, 49083 88 70 03 28 10, 80056 68 97 19, 78528 77, 00 23, 50972 89. 13 02 29 11, 15750 69. 15 20, 00722 77, 35 23, 52139 89. 57 01 30 11, 51167 69. 33 20, 22278 77, 70 23, 52500 90. 00 00 ♓ ♍ ♒ ♌ ♈ ♋ Tycho's Table of Refractions. Altitude ☉ ☽ ✴ ✴ Parts. Parts. Parts. 0 , 56667 , 55000 , 50000 1 , 43333 , 41667 , 35833 2 , 33333 , 33333 , 25833 3 , 28333 , 28333 , 20833 4 , 25833 , 25556 , 18333 5 , 24167 , 23889 , 16667 6 , 22500 , 23056 , 15000 7 , 21250 , 21250 , 13750 8 , 18750 , 20000 , 11250 9 , 17500 , 18889 , 10000 10 , 16667 , 17917 , 09167 11 , 15833 , 16944 , 08333 12 , 15000 , 15972 , 07500 13 , 14167 , 15000 , 06667 14 , 13333 , 14167 , 05833 15 , 12500 , 13333 , 05000 16 , 11667 , 12500 , 04167 17 , 10833 , 11667 , 03333 18 , 09583 , 10833 , 02083 19 , 08333 , 10000 , 00833 20 , 07500 , 09167 , 00000 21 , 06667 , 08333 , 00000 22 , 05833 , 07639 , 00000 23 , 05278 , 06944 24 , 04722 , 06250 25 , 04167 , 05556 26 , 03750 , 05000 27 , 03333 , 04444 28 , 02917 , 03889 29 , 02639 , 03333 30 , 02361 , 02778 31 , 02083 , 02500 32 , 01806 , 0222● 33 , 01528 , 01944 34 , 01250 , 01667 35 , 00972 , 01389 36 , 00833 , 01250 37 , 00694 , 01111 38 , 00556 , 00972 39 , 00417 , 00833 40 , 00278 , 00694 41 , 00250 , 00556 42 , 00222 , 00417 43 , 00194 , 00278 44 , 00167 , 00139 45 , 00139 , 00000 Satur's Mean Motions. Epochae Longit. ♄ Aphelion. ♄ Node ♄ Deg. parts Deg. parts Deg. Parts. Christi. 73. 13056 215. 25722 98. 98861 1600 208. 43944 265. 99722 110. 51389 1620 93. 13083 266. 63139 110. 65778 1640 337. 81722 267. 26583 110. 80194 1660 222. 50111 267. 88333 110. 94583 1 12. 22611 0. 03167 0. 00722 2 24. 45250 0. 06333 0. 01444 3 36. 67861 0. 09500 0. 02167 B 4 48. 93833 0. 12694 0. 02889 5 61. 16444 0. 15861 0. 03611 6 73. 39056 0. 19078 0. 04306 7 85. 61694 0. 22194 0. 05028 B 8 97. 87667 0. 25361 0. 05750 9 110. 10278 0. 28528 0. 06472 10 122. 32889 0. 31694 0. 07194 11 134. 55500 0. 34889 0. 07917 B 12 146. 81472 0. 38056 0. 08639 13 159. 04111 0. 41222 0. 09361 14 171. 26722 0. 44389 0. 10083 15 183. 49333 0. 47556 0. 10806 B 16 195. 75306 0. 50722 0. 11528 17 207. 97917 0. 53917 0. 12250 18 220. 20556 0. 57083 0. 12944 19 232. 43167 0. 60250 0. 13667 B 20 244. 69139 0. 63417 0. 14389 40 129. 38278 1 26861 0. 28806 60 14. 07417 1. 90278 0. 43222 80 258. 76528 2. 53694 0. 57611 100 143. 45667 3. 17111 0. 72028 Satur's mean Motions. Years. Longit. ♄ Aphel. ♄ Node ♄ Deg. parts. Deg. parts. Deg. parts. 100 143, 45667 3, 27111 0, 72028 200 286, 91361 6, 34250 1, 44056 300 80, 37056 9, 51361 2, 16111 400 21●, 82722 12, 68500 2, 88139 500 357, 28417 15, 85611 3, 60 67 600 140, 74083 19, 02750 4, 32194 700 284, 19778 22, 19861 5, 04222 800 67, 65444 25, 37001 5, 76278 900 211, 11139 28, 5411 6, 48306 1000 354, 56086 31, 71250 7, 20333 2000 349, 13639 63, 42500 14, 40667 3000 343, 70444 95, 13750 21, 61000 4000 338, 27278 126, 85000 28, 81333 5000 332, 84083 158, 56250 36, 01667 January 1, 03833 0, 00278 0, 00056 February 1, 97639 0, 00528 0 00139 March 3, 01472 0, 00778 0, 00194 April 4, 01944 0, 01028 0, 00250 May 5, 05806 0, 01333 0, 00333 June 6, 06278 0, 01556 0, 00389 July 7, 10111 0, 01833 0, 00444 August 8, 13972 0, 02139 0, 00500 September 9, 14444 0, 02361 0, 00556 October 10, 18278 0, 02639 0, 00611 November 11, 18778 0, 02917 0, 00667 December 12, 22611 0, 03167 0, 00722 Satur's Mean Motions. In Days. In Hours. Long. ♄ Aphel. ♄ N●d. ♄ Long. ♄ D. parts Parts. Parts. Parts. 1 0, 03361 , 00000 , 00002 1 , 00139 2 0, 06694 , 00000 , 00003 2 , 00278 3 0, 10056 , 00028 , 00005 3 , 00417 4 0, 13389 , 00028 , 00007 4 , 00556 5 0, 16750 , 00056 , 00009 5 , 00694 6 0, 20111 , 00056 , 00011 6 , 00833 7 0, 23444 , 00056 , 00013 7 , 00972 8 0, 26806 , 00083 , 00015 8 , 01111 9 0, 30139 , 00083 , 00017 9 , 01250 10 0, 33500 , 00083 , 00019 10 , 01389 11 0, 36861 , 00111 , 00020 11 , 01528 12 0, 40194 , 00111 , 00022 12 , 01667 13 0, 43556 , 00111 , 00024 13 , 01806 14 0, 46889 , 00139 , 00026 14 , 01944 15 0, 50250 , 00139 , 00028 15 , 02083 16 0, 53583 , 00139 , 00030 16 , 02222 17 0, 56944 , 00167 , 00032 17 , 02361 18 0, 60306 , 00167 , 00034 18 , 02500 19 0, 63639 , 00167 , 00036 19 02639 20 0, 67000 , 00194 , 00038 20 , 02778 21 0, 70333 , 00194 , 00040 21 , 02917 22 0, 73694 , 00194 , 00041 22 , 03083 23 0, 77056 , 00222 , 00042 23 , 03222 24 0, 80389 , 00222 , 00043 24 , 03361 25 0, 83750 , 00222 , 00045 26 0, 87083 , 00250 , 00047 27 0, 90444 , 00250 , 00049 28 0, 93806 , 00250 , 00051 29 0, 97139 , 00278 , 00053 30 1, 00500 , 00278 , 00055 31 1, 03833 , 00278 , 00057 32 1, 07194 , 00306 , 00059 Saturn's mean Motions in the parts of an Hour. Long. ♄ Parts. 1 , 00001 2 , 00002 3 00004 4 , 00005 5 , 00006 6 , 00008 7 , 00009 8 , 00011 9 , 00012 10 , 00013 11 , 00015 12 , 00016 13 , 00018 14 , 00019 15 , 00020 16 , 00022 17 , 00023 18 , 00025 19 , 00026 20 , 00027 21 , 00029 22 , 00030 23 , 00032 24 , 00033 25 , 00035 26 , 00036 27 , 00037 28 , 00039 29 , 00040 30 , 00042 31 , 00043 32 , 00044 33 , 00046 34 , 00047 35 , 00048 36 , 00050 37 , 00051 38 , 00052 39 , 00054 40 , 00055 41 , 00056 42 , 00058 43 , 00059 44 , 00061 45 , 00062 46 , 00063 47 , 00065 48 , 00066 49 , 00068 50 , 00069 51 , 00070 52 , 00072 53 , 00074 54 , 00075 55 , 00076 56 , 00078 57 , 00079 58 , 00081 59 , 00082 60 , 00083 61 , 00085 62 , 00086 63 , 00087 64 , 00089 65 , 00090 66 , 00091 67 , 00093 68 , 00094 69 , 00095 70 , 00097 71 , 00098 72 , 00099 73 , 00101 74 , 00102 75 , 00103 76 , 00105 77 , 00106 78 , 00107 79 , 00109 80 , 00111 81 , 00112 82 , 00113 83 , 00115 84 , 00116 85 , 00118 86 , 00119 87 , 00120 88 , 00122 89 , 00123 90 , 00125 91 , 00126 92 , 00127 93 , 00129 94 , 00130 95 , 00131 96 , 00133 97 , 00134 98 , 00136 99 , 00137 Jupiter's mean Motions. Epochae Longit. ♃ Aphel. ♃ Node ♃ Deg. parts. Deg. Parts. Deg. Parts. Christi. 179, 91583 148, 42389 87, 67722 1600 160, 80556 188, 02333 98, 62306 1620 48, 06667 188, 51833 98, 76000 1640 295, 32778 189, 01333 98, 89667 1660 182, 58889 189, 50833 99, 03333 1 30, 34222 0, 02472 0, 00694 2 60, 68444 0, 04944 0, 01361 3 91, 02667 0, 07417 0, 02056 B 4 121, 45222 0, 09889 0, 02722 5 151, 79444 0, 12361 0, 03417 6 182, 13667 0, 14833 0, 04111 7 212, 47889 0, 17333 0, 04778 B 8 242, 90444 0, 19806 0, 05472 9 273, 24667 0, 22278 0, 06167 10 303, 58889 0, 24750 0, 06833 11 333, 93139 0, 27222 0, 07528 B 12 4, 35667 0, 29694 0, 08194 13 34, 69889 0, 32167 0, 08889 14 65, 04111 0, 34639 0, 09583 15 95, 38361 0, 37111 0, 10250 B 16 125, 80889 0, 39611 0, 10944 17 156, 15111 0, 42083 0, 11639 18 186, 49361 0, 44556 0, 12306 19 216, 83583 0, 47028 0, 13000 B 20 247, 26111 0, 49500 0, 13694 40 134, 52222 0, 99000 0, 27361 60 21, 78333 1, 48500 0, 41056 80 269, 04444 1, 98000 0, 54722 100 156, 30556 2, 47500 0, 68417 Jupiter's mean Motions. Years. Longit. ♃ Aphelion. ♃ Node. ♃ Deg. parts. Deg. Parts. Deg. Parts. 100 156, 30556 2, 47500 0, 68417 200 312, 61111 4, 95000 1, 36833 300 108, 91694 7, 42500 2▪ 05222 400 265, 22250 9, 89972 2, 73639 500 61, 52806 12, 37472 3, 42056 600 217, 83361 14, 84972 4, 10472 700 14, 13944 17, 32472 4, 78861 800 170, 44500 19, 79972 5, 47278 900 326, 75056 22, 27472 6, 15694 1000 123, 05611 24, 74972 6, 84111 2000 246, 11250 49, 49972 13, 68222 3000 9, 16861 74, 24889 20, 52306 4000 132, 22500 98, 99833 27, 36417 5000 255, 28111 123, 74806 34, 20500 January. 2. 57694 0, 00194 0, 00056 February. 4. 90472 0, 00417 0, 00111 March. 7. 48167 0, 00611 0, 00167 April. 9 97556 0, 00806 0, 00222 May. 12. 55250 0, 01028 0, 00278 June. 15. 04639 0, 01222 0, 00333 July. 17. 62333 0, 01444 0, 00389 August. 20. 20056 0, 01667 0, 00444 Septemb. 22. 69444 0, 01861 0, 00500 October. 25. 27139 0, 02083 0, 00556 Novemb. 27. 76528 0, 02278 0, 00611 Decemb. 30. 34222 0, 02472 0, 00694 Jupiter's mean Motions. In Days. In Hours. Long. ♃ Aphel. ♃ Nod. ♃ Long. ♃ D. parts Parts. Parts. Parts. 1 0, 08306 , 00006 , 00002 1 , 00333 2 0, 16611 , 00013 , 00003 2 , 00722 3 0, 24944 , 00020 , 00005 3 , 01028 4 0, 33250 , 00026 , 00007 4 , 01389 5 0, 41556 , 00033 , 00009 5 , 01722 6 0, 49861 , 00039 , 00011 6 , 02083 7 0, 58194 , 00046 , 00013 7 , 02417 8 0, 66500 , 00053 , 00015 8 , 02722 9 0, 74816 , 00059 , 00017 9 , 03111 10 0, 83141 , 00066 , 00019 10 , 03472 11 0, 914●4 , 00072 , 00020 11 , 03806 12 0, 99750 , 00079 , 00022 12 , 04167 13 1, 08056 , 00085 , 00024 13 , 04500 14 1, 16361 , 00091 , 00026 14 , 04861 15 1, 24694 , 00098 , 00028 15 , 05194 16 1, 33000 , 00104 , 00030 16 , 05556 17 1, 41306 , 00111 , 00032 17 , 05889 18 1, 49611 , 00117 , 00034 18 , 06222 19 1, 57944 , 00123 , 00036 19 ▪ 06583 20 1, 66250 , 00130 , 00038 20 , 06917 21 1, 74556 , 00136 , 00039 21 , 07278 22 1, 82861 , 00142 , 00041 22 , 07611 23 1, 91194 , 00149 , 00043 23 , 07972 24 1, 99500 , 00155 , 00045 24 , 08306 25 2, 07806 , 00162 , 00047 26 2, 16111 , 00168 , 00049 27 2, 24444 , 00174 , 00051 28 2, 32750 , 00181 , 00053 29 2, 41056 , 00197 , 00055 30 2, 49389 , 00203 , 00057 31 2, 57694 , 00●09 , 00059 32 ●, 66000 , 00216 , 00061 Jupiter's mean Motions in the parts of an Hour. Long. ♃ Parts. 1 , 00003 2 , 00007 3 , 00010 4 , 00013 5 , 00017 6 , 00020 7 , 00024 8 , 00027 9 , 00031 10 , 00034 11 , 00038 12 , 00041 13 , 00045 14 , 00048 15 , 00052 16 , 00055 17 , 00058 18 , 00062 19 , 00065 20 , 00069 21 , 0007● 22 , 00076 23 , 00079 24 , 00083 25 , 00086 26 , 00090 27 , 00093 28 , 00097 29 , 0010● 30 , 00104 31 , 00107 32 , 00111 33 , 00114 34 , 00117 35 , 00121 36 , 00124 37 , 00128 38 , 00131 39 , 00135 40 , 00138 41 , 00142 42 , 00145 43 , 00149 44 , 00152 45 , 00156 46 , 00159 47 , 00162 48 , 00166 49 , 00169 50 , 00173 51 , 00176 52 , 00180 53 , 00183 54 , 00187 55 , 00190 56 , 00194 57 , 00197 58 , 00201 59 , 00204 60 , 00208 61 , 00211 62 , 00214 63 , 00218 64 , 00221 65 , 00225 66 , 00228 67 , 00232 68 , 00235 69 , 00238 70 , 00241 71 , 00245 72 , 00248 73 , 00251 74 , 00255 75 , 00258 76 , 00262 77 , 00265 78 , 00269 79 , 00272 80 , 00276 81 , 00279 82 , 00283 83 , 00286 84 , 00290 85 , 00293 86 , 00297 87 , 00300 88 , 00303 89 , 00307 90 , 00311 91 , 00314 92 , 00318 93 , 00321 94 , 00325 95 , 00328 56 , 00332 97 , 00335 98 , 00339 99 , 00342 The Mean Motions of Mars. Epochae Longit. ♂ Aphelion. ♂ Node ♂ Deg. parts Deg. parts Deg. Parts. Christi. 40. 71611 113. 97083 25. 30583 1600 307. 27611 148. 99833 46. 74222 1620 175. 60778 149. 43611 47. 01028 1640 43. 94000 149. 87389 47. 27806 1660 272. 27194 150. 21167 47. 54639 1 191. 28556 0. 02194 0. 01333 2 22. 57111 0. 04389 0. 02667 3 213. 85667 0. 06556 0. 04028 B 4 45. 66639 0. 08750 0. 05361 5 236. 95167 0. 10944 0. 06694 6 68 23750 0. 13139 0. 08028 7 259. 52278 0. 15306 0. 09361 B 8 91. 33278 0. 17500 0. 10722 9 282. 61833 0. 19722 0. 12056 10 113. 90389 0. 21889 0. 13389 11 305. 18944 0. 24056 0. 14722 B 12 136. 99917 0. 26250 0. 16056 13 328. 28472 0. 28444 0. 17417 14 159. 57028 0. 30639 0. 18778 15 350. 85583 0. 32806 0. 20111 B 16 182. 66556 0. 35028 0. 21444 17 13. 95111 0. 37222 0. 22778 18 205. 23667 0. 39417 0. 24139 19 36. 52222 0. 41583 0. 25472 B 20 228. 33194 0. 43778 0. 26806 40 96. 66389 0. 47556 0. 53583 60 324. 99●11 1. 31333 0. 80389 80 193. 32778 1. 75139 1. 07194 100 61. 66000 2. 18917 1. 33972 The mean Motions of Mars. Years. Longit. ♂ Aphel. ♂ Node ♂ Deg. parts. Deg. parts. Deg: parts. 100 61, 66000 2, 18917 1, 17306 200 123, 32000 4, 37833 2, 67944 300 184, 98000 6, 56778 4, 01944 400 246, 64000 8, 75694 5, 35917 500 308, 30000 10, 94611 6, 69889 600 9, 96000 13, 13528 8, 03861 700 71, 62000 15, 32444 9, 37833 800 133, 28000 17, 51361 10, 71806 900 194, 94000 19, 70306 12, 05806 1000 256, 60000 21, 89222 13, 39778 2000 153, 20028 43, 78444 26, 79528 3000 49, 80028 65, 67639 40, 19306 4000 306, 40056 8●, 56889 53, 59056 5000 203, 00056 109, 46083 66, 98833 January 16, 24611 0, 00194 0, 00111 February 30, 92028 0, 00361 0, 00222 March 47, 16639 0, 00556 0, 00333 April 62, 88833 0, 00722 0, 00444 May 79, 13472 0, 00917 0, 00556 June 94, 85667 0, 01083 0, 00667 July 111, 10306 0, 01250 0, 00778 August 127, 34917 0, 01444 0, 00889 September 143, 07111 0, 01639 0, 01000 October 159, 31750 0, 01833 0, 01111 November 175, 03944 0, 02028 0, 01222 December 191, 28556 0, 02194 0, 01333 The mean Motions of Mars. In Days. In Hours. Long. ♂ Apha. ♂ Node ♂ Long. ♂ D. Parts. Parts. Parts. Parts. 1 0, 52417 . 00006 , 00003 1 , 02194 2 1, 04806 , 00012 , 00007 2 , 04361 3 1, 57222 , 00018 , 00010 3 , 06556 4 2, 09611 , 00024 , 00014 4 , 08722 5 2, 62111 , 00030 , 00018 5 , 10917 6 3, 14444 , 00036 , 00021 6 , 13111 7 3, 66833 , 00042 , 00025 7 , 15278 8 4, 19250 , 00048 , 00028 8 , 17472 9 4, 71667 , 00054 , 00032 9 , 19667 10 5, 24083 , 00060 , 00036 10 , 21833 11 5, 76472 , 00066 , 00039 11 , 24028 12 6, 28889 , 00072 , 00043 12 , 26194 13 6, 81278 , 00078 , 00046 13 , 28389 14 7, 33694 , 00084 , 00050 14 , 30583 15 7, 86111 , 00090 , 00054 15 , 32750 16 8, 38500 , 00096 , 00057 16 , 34944 17 8, 90917 , 00102 , 00061 17 , 37111 18 9, 43333 , 00108 , 00064 18 , 39306 19 9, 95750 , 00114 , 00068 19 , 41500 20 10, 48139 , 00120 , 00072 20 , 43667 21 11, 00556 , 00126 , 00075 21 , 45861 22 11, 52944 , 00132 , 00079 22 , 48028 23 12, 05361 , 00138 , 00082 23 , 50222 24 12, 57778 , 00144 , 00086 24 , 52417 25 13, 10167 , 00150 , 00090 26 13, 62583 , 00156 , 00093 27 14, 15000 , 00162 , 00097 28 14, 67417 , 00168 , 00100 29 15, 19861 , 00174 , 00104 30 15, 72222 , 00180 , 00108 31 16, 24611 , 00186 , 00111 32 16, 77028 , 00192 , 00115 The mean Motions of Mars in parts of an Hour. Long. ♂ Parts. 1 , 00022 2 , 00043 3 , 00065 4 , 00087 5 , 00109 6 , 00131 7 , 00152 8 , 00174 9 , 00196 10 , 002●8 11 , 00240 12 , 00262 13 , 00284 14 , 00306 15 , 00327 16 , 00349 17 , 00371 18 , 00393 19 , 00415 20 , 00436 21 , 00458 22 , 00480 23 , 00502 24 , 00524 25 , 00545 26 , 00567 27 , 00589 28 , 00611 29 , 00633 30 , 00655 31 , 00676 32 , 00698 33 , 00720 34 , 00742 35 , 00764 36 , 00785 37 , 00807 38 , 00829 39 , 00851 40 , 00873 41 , 00894 42 , 00916 43 , 00938 44 , 00960 45 , 00982 46 , 01003 47 , 01025 48 , 01047 49 , 01069 50 , 01091 51 , 01112 52 , 01134 53 , 01156 54 , 01178 55 , 01200 56 , 01221 57 , 01243 58 , 01265 59 , 01287 60 , 01309 61 , 01330 62 , 01352 63 , 01374 64 , 01396 65 , 01418 66 , 01439 67 , 01461 68 , 01483 69 , 01505 70 , 01527 71 , 01548 72 , 01570 73 , 01592 74 , 01614 75 , 01636 76 , 01657 77 , 01679 78 , 01701 79 , 01723 80 , 01746 81 , 01768 82 , 01789 83 , 01811 84 , 01833 85 , 01855 86 , 01877 87 , 01898 88 , 01920 89 , 01942 90 , 01966 91 , 01988 92 , 02009 93 , 02031 94 , 02053 95 , 02075 56 , 02097 97 , 02118 98 , 02140 99 , 02162 The mean Motions of Venus. Epochae Longit. ♀ Aphel. ♀ Node ♀ Deg. parts. Deg. Parts. Deg. Parts. Christi. 42, 77917 282, 84556 60, 72111 1600 352, 47278 305, 38500 74, 12722 1620 176, 34389 305, 66667 74, 29472 1640 0, 21500 305, 94833 74, 46222 1660 184, 08611 306, 23000 74, 62972 1 224, 79306 0, 01417 0. 00833 2 89, 58611 0, 02806 0, 01667 3 324, 37917 0, 04222 0, 02500 B 4 180, 77417 0, 05639 0, 03361 5 45, 56722 0, 07028 0, 04194 6 270, 36028 0, 08444 0, 05028 7 135, 15333 0, 09861 0, 05861 B 8 1, 54833 0, 11250 0, 06694 9 226, 34139 0, 12667 0, 07528 10 91, 13444 0, 14083 0, 08361 11 315, 92750 0, 15472 0, 09222 B 12 182, 32278 0, 16889 0, 10056 13 47, 11583 0, 18306 0; 10889 14 271, 90861 0, 19722 0, 11722 15 136, 70167 0, 21111 0, 12556 B 16 3, 09694 0, 22528 0 13389 17 227, 89000 0, 23944 0, 14222 18 92, 68306 0, 25333 0, 15083 19 317, 47611 0, 26750 0, 15917 B 20 183, 87111 0, 28167 0, 16750 40 7, 74222 0, 56361 0, 33528 60 191, 61361 0, 84528 8, 50278 80 15, 48472 1, 12694 0, 67028 100 199, 35583 1, 40861 0, 83778 The mean Motions of Venus. Years. Longit. ♀ Aphelion. ♀ Node. ♀ Deg. parts. Deg. Parts. Deg. Parts. 100 199, 35583 1, 40861 0, 83778 200 38, 71167 2, 81750 1, 67583 300 238, 06750 4, 22611 2, 51361 400 77, 42333 5, 63500 2, 35167 500 276, 77917 7, 04361 4, 18944 600 116, 13500 8, 45222 5, 02750 700 315, 49083 9, 86111 5, 86528 800 154, 84639 11, 26972 6, 70333 900 354, 20250 12, 67833 7, 54111 1000 193, 55833 14, 08722 8, 37889 2000 27, 11639 28, 17444 16, 75778 3000 220, 67472 42, 86139 28, 13694 4000 54, 23278 46, 34889 33, 51611 5000 247, 79111 61, 43583 41, 89500 January. 49. 66750 0, 00111 0, 00083 February. 94. 52833 0, 00222 0, 00139 March. 144. 19556 0, 00361 0, 00222 April. 192. 26083 0, 00472 0, 00278 May. 241. 92833 0, 00583 0, 00361 June. 289. 99361 0, 00694 0, 00417 July. 339. 65833 0, 00806 0, 00500 August. 29. 32833 0, 00917 0, 00556 Septemb. 77. 39361 0, 01056 0, 00611 October. 127. 06083 0, 01167 0, 00694 Novemb. 171. 12611 0, 01278 0, 00750 Decemb. 224. 79306 0, 01417 0, 00833 The mean Motions of Venus. In Days. In Hours. Long. ♀ Aphel. ♀ Node ♀ Long. ♀ D. Parts. Parts. Parts. Parts. 1 1, 6022● , 00004 , 00002 1 0, 06667 2 3, 20444 , 00007 , 00004 2 0, 13361 3 4, 80639 , 00011 , 00006 3 0, 20028 4 6, 40861 , 00015 , 00009 4 0, 26722 5 8, 01083 , 00019 , 00011 5 0, 33389 6 9, 61306 , 00023 , 00013 6 0, 40056 7 10, 21528 , 00027 , 00016 7 0, 46750 8 12, 81750 , 00031 , 00018 8 0, 53417 9 14, 41944 , 00035 , 00020 9 0, 60083 10 16, 02167 , 00038 , 00023 10 0, 66778 11 17, 62389 , 00042 , 00025 11 0, 73444 12 19, 22611 , 00046 , 00027 12 0, 80139 13 20, 8●833 , 00050 , 00030 13 0, 86806 14 22, 43056 , 00054 , 00032 14 0, 93472 15 24, 03250 , 00058 , 00034 15 1, 00167 16 25, 63472 , 00062 , 00037 16 1, 06833 17 27, 23694 , 00066 , 00039 17 1, 13500 18 28, 83917 , 00069 , 00041 18 1, 20194 19 30, 44139 , 00073 , 00044 19 1, 26861 20 32, 04361 , 00077 , 00046 20 1, 33556 21 33, 64556 , 00081 , 00048 21 1, 40222 22 35, 24778 , 00085 , 00051 22 1, 46889 23 36, 85000 , 00089 , 00053 23 1, 53583 24 38, 45222 , 00093 , 00055 24 1, 60250 25 40, 05444 , 00097 , 00058 26 41, 65639 , 00100 , 00060 27 43, 25861 , 00104 , 00062 28 44, 86083 , 00108 , 00065 29 46, 4630● , 00112 , 00067 30 48, 06528 , 00116 , 00069 31 49, 66750 , 00120 , 00072 32 51, 26972 , 00124 , 00074 The mean Motions of Venus in parts of an Hour. Long. ♀ Parts. 1 , 00067 2 , 00133 3 , 00200 4 , 00267 5 , 00334 6 , 00401 7 , 00468 8 , 00534 9 , 00601 10 , 00667 11 , 00734 12 00801 13 , 00868 14 , 00935 15 , 01002 16 , 01068 17 , 01135 18 , 01202 19 , 01268 20 , 01335 21 , 01402 22 , 01469 23 , 01536 24 , 01603 25 , 01669 26 , 01736 27 , 01803 28 , 01869 29 , 01936 30 , 02003 31 , 02070 32 , 02137 33 , 02204 34 , 02270 35 , 02337 36 , 02404 37 , 02470 38 , 02537 39 , 02604 40 , 02671 41 , 02738 42 , 02805 43 , 02871 44 , 02938 45 , 03005 46 , 03071 47 , 03138 48 , 03205 49 , 03272 50 , 03339 51 , 03406 52 , 03472 53 , 03539 54 , 03606 55 , 03672 56 , 03739 57 , 03806 58 , 03873 59 , 03940 60 , 04007 61 , 04073 62 , 04140 63 , 04207 64 , 04273 65 , 04340 66 , 04407 67 , 04474 68 , 04541 69 , 04608 70 , 04674 71 , 04741 72 , 04808 73 , 04874 74 , 04941 75 , 05008 76 , 05075 77 , 05142 78 , 05209 79 , 05276 80 , 05342 81 , 05408 82 , 05475 83 , 05542 84 , 05609 85 , 05676 86 , 05743 87 , 05810 88 , 05876 89 , 05943 90 , 06009 91 , 06076 92 , 06143 93 , 06210 94 , 06277 95 , 06344 96 , 06410 97 , 06477 98 , 06544 99 , 06610 Mercuries mean Motion. Epochae Longit. ☿ Aphelion. ☿ Node ☿ Deg. parts Deg. parts Deg. Parts. Christi. 316. 26111 205. 31361 000. 0●000 1600 66. 95583 251. 63028 42. 51139 1620 81. 83944 252. 20611 43. 04250 1640 96. 72306 252. 78806 43. 57361 1660 111. 6●694 253. 35028 44. 10472 1 53. 72111 0. 02889 0. 02667 2 107. 44222 0. 05778 0. 05306 3 161. 16333 0. 08667 0. 07972 B 4 218. 97667 0. 11583 0. 10611 5 272. 69778 0. 14472 0. 13278 6 326. 41889 0. 17361 0. 15917 7 20. 14000 0. 20250 0. 18583 B 8 77. 95361 0. 23167 0. 21250 9 131. 67444 0. 26056 0. 23889 10 185. 39556 0. 28944 0. 26556 11 239. 11667 0. 31833 0. 29194 B 12 296. 92694 0. 34750 0. 31861 13 350. 65139 0. 37639 0. 34528 14 44. 37250 0. 40527 0. 37167 15 98. 09361 0. 43417 0. 39833 B 16 155. 90694 0. 46333 0. 42472 17 209. 62806 0. 49222 0. 45139 18 263. 34917 0. 52111 0. 47778 19 317. 07028 0. 55000 0. 50444 B 20 14. 88361 0. 57889 0. 53111 40 29. 76722 1. 15778 1. 06194 60 44. 65083 1. 73667 1. 59306 80 59 53472 2. 31611 2. 12417 100 74. 41833 2. 89472 2. 65500 Mercuries mean Motions Years. Longit. ☿ Aphel. ☿ Node ☿ Deg. parts. Deg. parts. Deg: parts. 100 74, 41833 2, 89472 2, 65500 200 148, 83694 5, 78972 5, 31028 300 223, 25527 8, 68444 7, 96528 400 297, 67361 11, 57917 10, 62028 500 12, 09222 14, 47389 1●, 27556 600 86, 510●6 17, ●6889 15, 93056 700 160, 92889 20, 26361 18, 58556 800 235, ●4750 23, 1583● 21, 24083 900 309, 78250 26, 05333 23, 89583 1000 24, 18417 ●8, 94806 26, 55083 2000 48, 36861 5●, 89611 4●, 10194 3000 72, 55278 86, 84417 79, 65278 4000 96, 73694 115, 79222 106, 20333 5000 120, 9●47● 144, 74861 132, 75472 January 126, 86●89 0, 00250 0, 00222 February 241, 45083 0, 00472 0, 00444 March 8, 31472 0, 00722 0, 00667 April 131, 08639 0, 00972 0, 00861 May 257, 95028 0, 01222 0, 01083 June 20, 72194 0, 01444 0, 01306 July 147, 58583 0, 01694 0, 01528 August 274, 44972 0, 01917 0, 01778 September 37, 22139 0, 02167 0, 02000 October 164, 08556 0, 02417 0, 02222 November 286, 85722 0, 02639 0, 02417 December 53, 72139 0, 02889 0, 02667 The Mean Motions of Mars. In Days. In Hours. Long. ☿ Aphel. ☿ Node. ☿ Long. ☿ Deg. parts. Parts. Parts. Parts. 1 4, 09222 , 00008 , 00007 1 0, 17056 2 8, 18472 , 00015 , 00014 2 0, 34111 3 12, 27722 , 00023 , 00021 3 0, 51167 4 16, ●6944 , 00031 , 00029 4 0, 68222 5 20, 46194 , 00039 , 00036 5 0, 85250 6 24, 55444 , 00047 , 00043 6 1, 02306 7 28, 64667 , 00055 , 00051 7 1, 19361 8 32, 73917 , 00063 , 00058 8 1, 36417 9 36, 83193 , 00071 , 00065 9 1, 53472 10 40, 92389 , 00079 , 00073 10 1, 70528 11 45, 01611 , 00086 , 00080 11 1, 87556 12 49, 1086● , 00094 , 00087 12 2, 04611 13 53, 20111 , 00102 , 00095 13 2, 21667 14 57, 29333 , 00110 , 00102 14 2, 37822 15 61, 38583 , 00118 , 00109 15 2, 55778 16 65, 47806 , 00126 , 00117 16 2, 72806 17 69, 57056 , 00134 , 00124 17 2, 89861 18 73, 66306 , 00142 , 00131 18 3 06917 19 77, 75528 , 00150 , 00139 19 3, 23972 20 81, 84778 , 00158 , 00146 20 3, 41028 21 85, 94000 , 00165 , 00153 21 3, 58083 22 90, 03250 , 00173 , 00161 22 3, 75111 23 94, 12500 , 00181 , 00168 23 3, 92167 24 98, 21722 , 00189 , 00175 24 4, 09222 25 102, 30972 , 00197 , 00182 26 106, 40194 , 00205 , 00190 27 110, 49444 , 00213 , 00197 28 114, 58694 , 00221 , 00204 29 118, 67917 , 00229 , 00212 30 122, 77167 , 00237 , 00219 31 126, 86389 , 00243 , 00226 32 130, 95611 , 00251 , 00233 Mercuries mean Motions in parts of an Hour. Long. ☿ Parts. 1 , 00170 2 , 00341 3 , 00511 4 , 00682 5 , 00852 6 , 01023 7 , 01193 8 , 01364 9 , 01534 10 , 01705 11 , 01875 12 , 02046 13 , 02217 14 , 02387 15 , 02557 16 , 02728 17 , 02898 18 , 03069 19 , 03239 20 , 03410 21 , 03580 22 , 03751 23 , 03921 24 , 04092 25 , 04262 26 , 04433 27 , 04603 28 , 04774 29 , 04944 30 , 05115 31 , 05285 32 , 05456 33 , 05626 34 , 05797 35 , 05967 36 , 06138 37 , 06●08 38 , 06479 39 , 06649 40 , 06820 41 , 06990 42 , 07161 43 , 07331 44 , 07502 45 , 07672 46 , 07843 47 , 08013 48 , 08184 49 , 08354 50 , 08525 51 , 08695 52 , 08866 53 , 09036 54 , 09207 55 , 09377 56 , 09548 57 , 09718 58 , 09889 59 , 10059 60 , 10230 61 , 10400 62 , 10571 63 , 10741 64 , 10912 65 , 11082 66 , 11253 67 , 11423 68 , 11594 69 , 11764 70 , 11935 71 , 12106 72 , 12276 73 , 12446 74 , 12617 75 , 12787 76 , 12958 77 , 13128 78 , 13299 79 , 13469 80 , 13640 81 , 13811 82 , 13981 83 , 14152 84 , 14322 85 , 14493 86 , 14663 87 , 14834 88 , 15004 89 , 15175 90 , 15345 91 , 15516 92 , 15687 93 , 15857 94 , 16028 95 , 16198 96 , 16369 97 , 16540 98 , 167●1 99 , 16882 A Table of Declinations. ♈ North Latitude. ♎ South Latitude. 0 1 2 3 4 5 6 0 0, 00 0, 92 1, 83 2, 75 3, 67 4. 58 6. 00 30 1 0, 40 1, 32 2, 23 3, 15 4, 07 4. 98 6. 20 29 2 0, 80 1, 72 2, 63 3, 55 4, 47 5. 38 6. 30 28 3 1, 20 2, 12 3, 03 3, 95 4, 87 5. 78 6. 70 27 4 1, 60 2, 51 3, 43 4, 35 5, 27 6. 18 7. 10 26 5 2, 00 2, 91 3, 83 4, 75 5, 83 6. 58 7. 50 25 6 2, 40 3, 31 4, 23 5, 15 6, 06 6. 98 7. 88 24 7 2, 78 3, 71 4, 63 5, 55 6, 46 7. 38 8. 28 23 8 3, 18 4, 11 5, 03 5, 95 6, 86 7. 78 8. 68 22 9 3, 58 4, 50 5, 42 6, 33 7, 25 8. 17 9 08 21 10 3, 97 4, 90 5, 80 6, 73 7, 65 8. 57 9 48 20 11 4, 37 5, 30 6, 20 7, 13 8, 05 8. 97 9 88 19 12 4, 77 5, 70 6, 60 7, 53 8, 45 9 36 10. 27 18 13 5, 15 6, 08 7, 00 7, 92 8, 83 9 76 10. 67 17 14 5, 55 6, 48 7, 40 8, 32 9, 23 10. 16 11. 07 16 15 5, 93 6, 87 7, 78 8, 70 9, 62 10. 55 11. 45 15 16 6, 32 7, 23 8, 15 9, 08 10, 00 10. 93 11. 85 14 17 6, 70 7, 62 8, 53 9, 47 10, 38 11. 32 12. 23 13 18 7, 08 8, 00 8, 93 9, 85 10, 68 11. 70 1●. 62 12 19 7, 47 8, 38 9, 30 10, 23 11, 15 12. 08 13. 00 11 20 7, 85 8, 77 9, 70 10, 63 11, 55 12. 47 13. 38 10 21 8, 22 9, 08 10, 15 11, 0● 11, 93 12. 85 13. 80 9 22 8, 60 9, 53 10, 47 11, 38 12, 32 13. 23 14. 15 8 23 8, 97 9, 92 10, 85 11, 77 12, 70 13. 62 14. 53 7 24 9, 35 10, 28 11, 22 12, 13 13, 07 14. 00 14. 90 6 25 9, 72 10, 65 11, 58 12, 50 13, 43 14. 37 15. 28 5 26 10, 08 11, 02 11, 95 12, 87 13, 80 14. 73 15. 65 4 27 10, 43 11, 38 12, 32 13, 23 14, 17 15. 10 16. 02 3 28 10, 80 11, 75 12, 68 13, 60 14, 53 15. 47 16. 38 2 29 11, 15 12, 08 13, ●3 13, 95 14, 88 15. 82 16. 75 1 30 11, 51 12, 45 13, 38 14, 31 15, 25 16. 18 17. 10 0 ♓ North Latitude. ♍ South Latitude. A Table of Declinations. ♈ South Latitude. ♎ North Latitude 0 1 2 3 4 5 6 0 0, 92 1, 83 2, 75 3, 67 4, 58 5, 50 30 1 0, 52 1, 45 2, 35 3, 27 4, 18 5, 10 29 2 0, 12 1, 05 1, 95 2, 87 3, 78 4, 70 28 3 0▪ 28 0, 65 1, 57 2, 48 3, 40 4, 32 27 4 0, 68 0, 25 1, 17 2, 08 3, 00 3, 92 26 5 1, 08 0, 15 0, 77 1, 68 2, 60 3, 52 25 6 1, 47 0, 55 0, 37 1, 28 2, 03 3, 12 24 7 1, 87 0, 95 0, 03 0, 8● 1, 80 2, 72 23 8 2, 27 1, 35 0, 43 0, 48 1, 42 2, 33 22 9 2, 48 1, 73 0, 82 0, 10 1, 03 1, 95 21 10 3, 05 2, 13 1, 22 0, 30 0, 63 1, 55 20 11 3, 45 2, 53 1, 61 0, 68 0, 23 1, 15 19 12 3, 85 2, 93 2, 01 1, 07 0, 17 0, 77 18 13 4, 23 3, 32 2, 40 1, 47 0, 55 0, 38 17 14 4, 62 3, 68 2, 95 1, 87 0, 93 0, 00 16 15 5, 00 4, 08 3, 17 2, 25 1, 32 0, 38 15 16 5, 38 4, 47 3, 53 2, 63 1, 68 0, 77 14 17 5, 77 4, 85 3, 92 3, 00 2, 07 1, 15 13 18 6, 15 5, 23 4, 30 3, 38 2, 45 1, 53 12 19 6, 53 5, 62 4, 68 3, 77 2, 83 1, 92 11 20 6, 92 5, 98 5, 07 4, 13 3, 20 2, 28 10 21 7, 28 6, 35 5, 45 4, 50 3, 57 2, 65 9 22 7, 67 6, 73 5, 83 4, 88 3, 95 3, 02 8 23 8, 05 7, 12 6, 20 5, 25 4, 32 3, 38 7 24 8, 42 7, 50 6, 57 5, 63 4, 70 3, 75 6 25 8, 78 7, 87 6, 93 6, 00 5, 07 4, 12 5 26 9, 15 8, 23 7, 30 6, 37 5, 43 4, 48 4 27 9, 51 8, 58 7, 83 6, 72 5, 78 4, 83 3 28 9, 88 8, 95 8, 02 7, 07 6, 13 5, 18 2 29 10, 23 9, 30 8, 37 7, 42 6, 48 5, 53 1 30 10, 58 9, 65 8, 72 7, 77 6, 83 5, 88 0 ♓ North Latitude. ♍ South Latitude. A Table of Declinations. ♉ North Latitude. ♏ South Latitude. 0 1 2 3 4 5 6 0 11, 51 12, 45 13, 38 14, 31 15, 25 16, 18 17, 10 30 1 11, 87 12, 80 13, 73 14, 67 15, 60 16, 55 17, 47 29 2 12, 22 13, 15 14, 08 15, 02 15, 95 16, 19 17, 82 28 3 12, 55 13, 48 14, 42 15, 35 16, 30 17, 23 18, 17 27 4 12, 90 13, 83 14, 78 15, 70 16, 65 17, 58 18, 52 26 5 13, 23 14, 18 15, 12 16, 05 17, 00 17, 93 18, 87 25 6 13, 57 14, 52 15, 45 16, 40 17, 33 18, 28 19, 20 24 7 13, 90 14, 85 15, 78 16, 73 17, 67 18, 58 19, 53 23 8 14, 23 15, 18 16, 12 17, 07 18, 00 18, 95 19, 87 22 9 14, 55 15, 50 16, 43 17, 38 18, 33 19, 28 20, 20 21 10 14, 87 15, 82 16, 75 17, 70 18, 65 19, 60 20, 53 20 11 15, 18 16, 13 17, 07 18, 02 18, 97 19, 92 20, 85 19 12 15, 48 16, 43 17, 38 18, 33 19, 23 20, 23 21, 17 18 13 15, 80 16, 75 17, 70 18, 65 19, 60 20, 55 21, 48 17 14 16, 10 17, 05 18, 00 18, 95 19, 90 20, 87 21, 80 16 15 16, 40 17, 35 18, 30 19, 25 20, 20 21, 17 22, 10 15 16 16, 68 17, 63 18, 60 19, 55 20, 50 21, 63 22, 40 14 17 16, 97 17, 92 18, 88 19, 85 20, 80 21, 77 22, 70 13 18 17, 25 18, 20 19, 17 20, 13 21, 08 22, 05 22, 98 12 19 17, 53 18, 48 19, 45 20, 42 21, 37 22, 33 23, 27 11 20 17, 80 18, 77 19, 7● 20, 68 21, 65 22, 62 23, 55 10 21 18, 07 19, 0● 20, 00 20, 95 21, 92 22, 88 23, 83 9 22 18, 3● 19, 30 20, 27 21, 22 22, 18 23, 15 24, 10 8 23 18, 58 19, 57 20, 53 21, 48 22, 45 23, 42 24, 37 7 24 18, 83 19, 82 20, 78 21, 75 22, 72 2●, 68 24, 63 6 25 19, 08 20, 05 21, 03 22, 00 22, 97 23, 93 24, 88 5 26 19, 32 20, 28 21, 27 22, 23 23, 20 24, 18 25, 13 4 27 19, 55 20, 52 21, 50 22, 47 23, 43 24, 42 25, 37 3 28 19, 78 20, 75 21, 73 22, 70 23, 67 24, 65 25, 60 2 29 20, 00 20, 98 21, 95 22, 93 23, 90 24, 88 25, 83 1 30 20, 22 21, 20 22, 17 23, 15 24, 12 25, 10 26, 05 0 ♌ North Latitude. ♒ South Latitude. A Table of Declinations. ♉ South Latitude. ♏ North Latitude 0 1 2 3 4 5 6 0 10, 58 09, 65 8, 72 7, 77 6, 83 5, 88 30 1 10, 93 10, 00 9, 07 8, 12 7, 18 6, 23 29 2 11, 28 10, 33 9, 40 8, 47 7, 52 6, 57 28 3 11, 62 10, 67 9, 73 8, 80 7, 85 6, 90 27 4 11, 97 11, 02 10, 07 9, 13 8, 18 7, 23 26 5 12, 30 11, 35 10, 40 9, 47 8, 52 7, 57 25 6 12, 63 11, 68 10, 73 9, 80 8, 87 7, 83 24 7 12, 97 12, 01 11, 07 10, 12 9, 17 8, 20 23 8 13, 28 12, 33 11, 38 10, 47 9, 48 8, 52 22 9 13, 60 12, 65 11, 70 10, 75 9, 80 8, 83 21 10 13, 92 12, 97 12, 02 11, 07 10, 12 9, 15 20 11 14, 23 13, 28 12, 33 11, 38 10, 48 9, 45 19 12 14, 53 13, 58 12, 63 11, 68 10, 72 9, 75 18 13 14, 83 13, 88 12, 93 11, 98 11, 02 10, 05 17 14 15, ●3 14, 18 1●, 23 12, 28 11, 32 10, 35 16 15 15, 43 14, 48 13, 53 12, 57 11, 60 10, 6● 15 16 15, 72 14, 77 13, 80 12, 85 11, 88 10, 92 14 17 16, 00 15, 05 14, 08 13, 13 12, 17 11, 20 13 18 16, 28 15. 33 14, 37 13, 40 12, 43 11, 47 12 19 16, 57 15. 60 14, 63 13, 67 12, 70 11, 73 11 20 16, 83 15. 87 14, 90 13, 93 12, 97 12, 00 10 21 17, 10 16. 13 15, 17 14, 20 13, 23 12, 25 9 22 17, 37 16. 40 15, 43 14, 47 13, 48 1●, 50 8 23 17, 62 16. 65 15, 68 14, 72 13, 73 12, 75 7 24 17, 87 16. 90 15, 93 14, 97 13, 98 13, 00 6 25 18, 12 17. 15 16, 17 15, 20 14, 22 13, 23 5 26 18, 35 17. 38 16, 42 15, 43 14, 45 13, 48 4 27 18, 58 17. 60 16, 63 15, 65 14, 68 13, 68 3 28 18, 80 17. 83 16, 85 15, 87 14, 90 13, 90 2 29 19, 02 18. 05 17, 07 16, 08 15, 12 14, 12 1 30 19, 23 18. 27 17, 28 16, 30 15, 33 14, 35 0 ♌ South Latitude. ♏ North Latitude. A Table of Declinations. ♊ North Latitude. ♐ South Latitude. 0 1 2 3 4 5 6 0 20, 22 21, 20 22, 17 23, 15 24, 12 25, 10 26, 05 30 1 20, 43 21, 42 22, 38 23, 37 24, 33 25, 32 26, 27 29 2 20, 63 21, 62 22, 60 23, 58 24, 55 25, 53 26, 48 28 3 20, 83 21, 82 22, 80 23, 78 24, 75 25, 73 26, 70 27 4 21, 02 22, 00 22, 98 23, 97 24, 95 25, 92 26, 90 26 5 21, 22 22, 18 23, 17 24, 15 25, 13 26, 12 27, 08 25 6 21, 38 22, 37 23, 35 24, 35 25, 32 26, 30 27, 35 24 7 21, 55 22, 53 23, 52 24, 52 25, 50 26, 48 27, 45 23 8 21, 72 22, 70 23, 68 24, 68 25, 67 26, 65 27, 62 22 9 21, 88 22, 87 23, 85 24, 85 25, 83 26, 82 27, 78 21 10 22, 03 23, 02 24, 00 25, 00 25, 98 26, 97 27, 93 20 11 22, 17 23, 17 24, 15 25, 15 26, 13 27, 12 28, 08 19 12 22, 32 23, 32 24, 30 25, ●0 26, 28 27, 27 28, 23 18 13 22, 45 23, 45 24, 43 25, 43 26, 42 27, 40 28, 37 17 14 22, 57 23, 57 24, 55 25, 55 26, 53 27, 52 28, 50 16 15 22, 68 23, 68 24, 67 25, 65 26, 65 27, 63 28, 62 15 16 23, 78 23, 72 24, 77 25, 75 26, 75 27, 75 28, 72 14 17 22, 88 23, 88 24, 88 25, 87 26, 87 27, 87 28, 82 13 18 22, 98 23, 98 14, 98 25, 97 26, 97 27, 97 28, 92 12 19 2●, 07 24, 07 25, 07 26, 05 27, 05 28, 05 29, 03 11 20 23, 15 24, 15 25, 15 26, 13 27, 13 28, 13 29, 12 10 21 23, 22 24, 22 25, 22 26, 22 27, 20 28, 20 29, 20 9 22 23, 28 24, 28 25, 28 26, 28 27, 27 28, 27 29, 25 8 23 23, 33 24, 33 25, 3● 26, 33 27, 32 28, 32 29, 30 7 24 23, 38 24, 38 25, 38 26, 38 27, 37 28, 37 29, 37 6 25 23, 43 24, 43 25, 43 26, 43 27, 42 28, 42 29, 42 5 26 23, 47 24, 47 25, 47 26, 47 27, 47 28, 47 29, 47 4 27 23, 49 24, 50 25, 50 26, 50 27, 50 28, 50 29, 50 3 28 23, 50 24, 51 25, 51 26, 51 27, 51 28, 51 29, 51 2 29 23, 51 24, 52 25, 52 26, 52 27, 52 28, 52 29, 52 1 30 23, 52 24, 52 25, 52 26, 52 27, 52 28, 52 29, 52 0 ♑ South Latitude. ♋ North Latitude. A Table of Declinations. ♊ South Latitude. ♐ North Latitude. 0 1 2 3 4 5 6 0 19, 23 18, 27 17, 28 16, 30 15, 33 14. 35 30 1 19, 45 18, 47 17, 48 16, 50 15, 53 14. 55 29 2 19, 52 18, 67 17, 68 16, 70 15, 73 14. 75 28 3 19, 85 18, 87 17, 88 16, 90 15, 92 14. 95 27 4 20, 03 19, 05 18, 05 17, 10 16, 12 15. 1● 26 5 20, 22 19, 25 18, 27 17, ●8 16, 30 15. 30 25 6 20, 40 19, 42 18, 43 17, 45 16, 47 15. 47 24 7 20, 57 19, 58 18, 60 17, 62 16, 63 15. 63 23 8 20, 73 19, 75 18, 77 17, 78 16, 78 15. 80 22 9 20, 90 19, 92 18, 93 17, 93 16, 93 15. 95 21 10 21, 05 20, 07 19, 08 18, 08 17, 10 16. 08 20 11 21, 18 20, 18 19, 22 18, 22 17, 23 16. 22 19 12 21, 32 20, 33 19, 35 18, 35 17, 37 16. 35 18 13 21, 45 20, 47 19, 47 18, 48 17, 48 16. 47 17 14 21, 58 20, 58 19, 58 18, 60 17, 60 16. 58 16 15 21, 68 20, 68 19, 68 18, 70 17, 70 16. 70 15 16 21, 78 20, 78 19, 78 18, 80 17, 80 16. 80 14 17 21, 88 20, 88 19, 88 18, 90 17, 90 16. 90 13 18 21, 98 20, 98 19, 98 19, 00 18, 00 16. 98 12 19 22, 07 21, 07 20, 07 19, 08 18, 08 17. 07 11 20 22, 15 21, 15 20, 15 19, 17 18, 17 17. 15 10 21 22, 22 21, 22 20, 22 19, 23 18, 23 17. 23 9 22 22, 28 21, 28 20, 28 19, 28 18, 28 17. 2● 8 23 22, 33 21, 33 20, 33 19, 33 18, 33 17. 33 7 24 22, 38 21, 38 20, 38 19, 38 18, 38 17. 38 6 25 22, 4● 21, 43 20, 43 19, 43 18, 43 17. 43 5 26 22, 47 22, 47 20, 47 19, 47 18, 47 17. 47 4 27 22, 50 21, 50 20, 50 19, 50 18, 50 17. 50 3 28 22, 51 21, 51 20, 51 19, 51 18, 51 17. 51 2 29 22, 52 21, 52 20, 52 19, 52 18, 52 17. 52 1 30 22, 52 21, 52 20, 52 19, 52 18, 52 17. 52 0 ♑ North Latitude. ♋ South Latitude. A Table of Declinations. ♈ North Latitude. ♌ South Latitude. 0 1 2 3 4 5 6 0 0, 00 359, 62 359, 22 358, 82 358, 42 358. 02 357. 62 1 0, 92 0, 53 0, 13 359, 73 359, 33 358. 93 358. 53 2 1, 83 1, 45 1, 05 0, 65 0, 25 359. 85 359. 45 3 2, 75 2, 37 1, 97 1, 57 1, 17 0. 77 0. 37 4 3, 67 3, 28 2, 88 2, 48 2, 08 1. 68 1. 28 5 4, 58 4, 20 3, 80 4, 40 3, 00 2. 60 2. 20 6 5, 50 5, 12 4, 72 4, 32 3, 9● 3. 52 3. 12 7 6, 42 6, 03 5, 63 5, 23 4, 83 4. 43 4. 03 8 7, 35 6, 95 6, 55 6, 15 5, 75 5. 35 4. 95 9 8, 27 7, 87 7, 47 7, 07 6, 67 6. 27 5. 87 10 9, 18 8, 78 8, 38 7, 98 7, 58 7. 18 6. 78 11 10, 10 9, 70 9, 30 8, 92 8, 52 8. 12 7. 72 12 11, 03 10, 63 10, 23 9, 85 9, 45 9 05 8. 65 13 11, 95 11, 55 11, 15 10, 77 10, 37 9 97 9 57 14 12, 88 12, 48 12, 08 11, 70 11, 30 10. 90 10. 50 15 13, 80 13, 42 13, 02 12, 63 12, 23 11. 67 11. 43 16 14, 7● 14, 3● 13, 95 13, 57 13, 17 12. 77 12. 37 17 15, 67 15, 27 14, 88 14, 50 14, 10 13. 70 13. 30 18 16, 58 16, 20 15, 82 15, 43 15, 03 14. 65 14. 25 19 17, 52 17, 13 16, 75 16, 37 15, 97 15. 58 15. 18 20 18, 45 18, 07 17, 68 17, 30 16, 90 16. 52 16. 12 21 19, 38 19, 00 18, 62 18, 23 17, 85 17. 47 17. 07 22 20, 33 19, 93 19, 55 19, 18 18, 80 18. 42 18. 01 23 21, 27 20, 88 20, 50 20, 13 19, 75 19 37 19 97 24 22, 20 21, 83 21, 45 21, 08 20, 70 20. 32 20. 92 25 23, 15 22, 78 22, 40 22, 03 21, 65 11. 27 21. 87 26 24, 10 23, 73 23, 35 22, 98 22, 60 22. 22 22. 83 27 25, 03 24, 68 44, 32 23, 95 23, 57 23. 18 23. 80 28 25, 98 25, 63 25, 27 24, 90 24, 52 24. 15 24. 77 29 26, 95 26, 58 26, 22 25, 85 25, 48 25. 12 25. 73 30 27, 90 27, 55 27, 18 26, 82 26, 45 26. 08 26. 70 A Table of Right Ascensions. ♈ South Latitude ♎ North Latitude. 180. Add. 0 1 2 3 4 5 6 0 0. 38 0, 78 1, 18 1, 58 1, 98 2, 38 1 1. 30 1, 70 2, 10 2, 50 2, 90 3, 30 2 2. 22 2, 62 3, 02 3, 42 3, 82 4, 22 3 3. 13 3, 53 3, 93 4, 33 4, 73 5, 13 4 4. 05 4, 45 4, 85 5, 25 5, 65 6, 05 5 4. 97 5, 37 5, 77 6, 17 6, 57 6, 97 6 5. 90 6, 30 6, 70 7, 10 7, 50 7, 88 7 6. 82 7, 22 7, 62 8, 02 8, 42 8, 80 8 7. 73 8, 13 8, 53 8, 93 9, 33 9, 72 9 8. 66 9, 07 9, 47 9, 85 10, 25 10, 63 10 9 58 9, 98 10, 38 10, 77 11, 17 11, 55 11 10. 50 10, 90 11, 30 11, 68 12, 08 12, 47 12 11. 42 11, 82 12, 22 12, 60 13, 00 13, 38 13 12. 33 12, 73 13, 13 13, 52 13, 92 14, 30 14 13. 27 13, 65 14, 05 14, 43 14, 83 15, 22 15 14. 20 14, 58 14, 97 15, 35 15, 75 16, 13 16 15. 12 15, 50 15, 88 16, 27 16, 67 17, 05 17 16. 03 16, 42 16, 80 17, 18 17, 58 17, 97 18 16. 97 17, 35 17, 73 18, 12 18, 50 18, 88 19 17. 90 18, 28 18, 67 19, 03 19, 42 19, 80 20 18. 83 19, 22 19, 60 19, 97 20, 35 20, 72 21 19 76 20, 15 20, 53 20, 90 21, 28 21, 65 22 20. 70 21, 08 21, 47 21, 83 22, 20 22, 57 23 21. 63 22, 01 22, 40 22, 77 23, 13 23, 50 24 22. 58 22, 95 23, 33 23, 70 24, 07 24, 43 25 23. 52 23, 88 24, 27 24, 63 25, 00 25, 35 26 24. 47 24, 83 25, 20 25, 57 25, 93 26, 28 27 25. 42 25, 78 26, 15 26, 50 26, 87 27, 22 28 26. 37 26, 72 27, 08 27, 43 27, 80 28, 15 29 27. 32 27, 67 28, 02 28, 37 28, 73 29, 08 30 28. 27 28, 63 28, 97 29, 32 29, 67 30, 02 A Table of Right Ascensions. ♉ North Latitude. ♏ South Latitude. 180 Add. 0 1 2 3 4 5 6 0 27, 90 27, 55 27, 18 26, 82 26, 45 26, 08 25, 70 1 28, 85 28, 50 28, 13 27, 78 27, 42 27, 05 26, 67 2 29, 82 29, 45 29, 10 28, 75 28, 38 28, 02 27, 63 3 30, 77 30, 42 30, 07 29, 72 29, 35 28, 98 28, 62 4 31, 72 31, 38 31, 03 30, 68 30, 32 29, 97 29, 60 5 32, 70 32, 37 32, 00 31, 65 31, 30 30, 95 30, 58 6 33, 67 33, 33 32, 97 32, 63 32, 28 31, 93 31, 57 7 34, 63 34, 30 33, 96 33, 62 33, 27 32, 92 32, 56 8 35, 60 35, 28 34, 95 34, 61 34, 26 33, 91 33, 55 9 36, 57 36, 27 35, 93 35, 60 35, 25 34, 90 34, 55 10 37, 55 37, 25 36, 92 36, 59 36, 25 35, 90 35, 55 11 38, 55 38, 23 37, 91 37, 58 37, 25 36, 91 36, 56 12 39, 53 39, 23 38, 90 38, 58 38, 25 37, 92 37, 57 13 40, 52 40, 22 39, 90 39, 58 39, 26 38, 93 38, 58 14 41, 51 41, 21 40, 90 40, 59 40, 27 39, 95 39, 60 15 42, 51 42, 21 41, 90 41, 60 41, 28 40, 97 40, 63 16 43, 51 43, ●1 42, 91 42, 61 42, 30 41, 98 41, 65 17 44, 51 44, 22 43, 92 43, 62 43, 32 43, 00 4●, 67 18 45, 52 45, 23 44, 93 44, ●3 44, 33 44, 02 43, 70 19 46, 53 46, 24 45, 95 45, 65 45, 35 45, 05 44, 73 20 47, 53 47, 25 46, 97 46, 67 46, 38 46, 08 45, 77 21 48, 55 48, 27 47, 98 47, 70 47, 42 47, 12 46, 82 22 49, 57 49, 28 49, 00 48, 73 48, 45 48, 15 47, 87 23 50, 58 50, 30 50, 03 49, 77 49, 48 49, 20 48, 92 24 51, 60 51, 33 51, 07 50, 80 50, 53 50, 25 49, 97 25 52, 63 52, 37 52, 10 51, 85 51, 58 51, 30 51, 03 26 53, 67 5●, 40 53, 15 52, 90 52, 63 52, 37 52, 10 27 54, 70 54, 45 54, 20 53, 95 53, 70 53, 43 53, 17 28 55, 7● 55, 48 55, 25 55, 00 54, 75 54, 50 54, 23 29 56, 77 56, 53 56, 30 56, 05 55, 82 55, 57 55, 30 30 57, 80 57, 58 57, 35 57, 12 56, 88 56, 63 56, 38 A Table of Right Ascensions. ♉ South Latitude. ♏ North Latitude. 180. Add. 0 1 2 3 4 5 6 0 28, 27 28. 62 28, 97 29, 32 29, 67 30, 02 1 29, 22 29. 57 29, 92 30, 27 30, 62 30, 95 2 30, 17 30. 52 30, 87 31, 22 31, 57 31, 90 3 31, 12 31. 47 31, 82 32, 17 32, 52 32, 85 4 32, 08 32. 4● 32, 77 33, 12 33, 45 33, 78 5 33, 05 33. 38 33, 72 34, 07 34, 40 34, 73 6 34, 02 34. 35 34, 68 35, 02 35, 35 35, 68 7 34, 98 35. 32 35, 65 35, 97 36, 30 36, 63 8 35, 95 36. 28 36, 62 56, 93 37, 25 37, 5● 9 36, 93 37. 25 37, 58 37, 90 38, 22 38, 5● 10 37, 90 38. 22 38, 55 38, 87 39, 18 39, 48 11 38, 88 39, 20 39, 52 39, 83 40, 15 40, 45 12 39, 87 40. 18 40, 50 40, 80 41, 12 41, 42 13 40, 85 41. 17 41, 47 41, 77 42, 08 42, 38 14 41, 83 42, 15 42, 45 42, 75 43, 05 43, 35 15 42, 82 43, 13 43, 43 43, 73 44, 03 44, 32 16 43, 81 44, 12 44, 42 44, 72 45, 00 45, 28 17 44, 81 45, 11 45, 40 45, 70 45, 98 46, 25 18 45, 81 46, 10 46, 39 46, 68 46, 97 47, 23 19 46, 82 47, 10 47, 38 47, 67 47, 95 48, 22 20 47, 82 48, 10 48, 38 48, 66 48, 93 49, 20 21 4●, 83 49, 10 49, 38 49, 65 49, 92 50, 18 22 49, 84 50, 10 50, 38 50, 64 50, 90 51, 17 23 50, 85 51, 11 51, 38 51, 63 51, 89 52, 15 24 51, 87 52, 12 52, 39 52, 63 52, 88 53, 14 25 52, 88 53, 13 53, 39 53, 63 5●, 88 54, 13 26 53, 92 54, 15 54, 40 54, 64 54, 88 55, 12 27 54, 93 55, 18 55, 42 55, 65 55, 89 56, 12 28 55, 97 56, 20 56, 43 56, 67 56, 90 57, 11 29 57, 00 57, 22 57, 45 57, 68 57, 91 58, 12 30 58, 03 58, 25 58, 48 58, 70 58, 92 59, 12 A Table of Right Ascensions. ♊ North Latitude ♐ South Latitude. 180 Add. 0 1 2 3 4 5 6 0 57, 80 57 58 57, 35 57, 12 56, 88 56, 63 56, 38 1 58, 85 58. 63 58, 40 58, 17 57, 95 57, 70 57, 47 2 59, 88 59 68 59, 45 59, 23 59, 02 58, 78 58, 55 3 60, 93 60. 73 66, 52 60, 30 60, 08 59, 87 59, 63 4 61, 98 61. 78 61, 58 61, 37 61, 17 60, 95 60, 73 5 63, 05 62. 85 62, 65 62, 45 62, 25 62, 03 61, 83 6 64, 10 63. 92 63, 72 63, 53 63, 33 63, 13 62, 93 7 65, 15 64. 98 64, 78 64, 62 64, 42 64, 22 64, 03 8 66, 22 66. 05 65, 87 65, 70 65, 50 65, 32 65, 13 9 67, 28 67. 12 66, 95 66, 78 66, 60 66, 42 66, 23 10 68, 35 68 18 68, 03 67, 87 67, 70 67, 52 67, 35 11 69, 42 69. 27 69, 12 68, 95 68, 80 68, 63 68, 47 12 70, 48 70. 35 70, 20 70, 05 69, 90 69, 75 69, 58 13 71, 7 71. 43 71, 28 71, 15 71, 00 70, 85 70, 70 14 72, 63 72. 52 72, 37 72, 25 72, 10 71, 97 71, 82 15 73, 70 73. 60 73, 47 73, 35 73, 22 73, 08 72, 95 16 74, 78 74. 68 74, 55 74, 45 74, 32 74, 20 74, 07 17 75, 87 75. 77 75, 65 75, 55 75, 43 75, 32 75, 20 18 76, 95 76. 85 76, 75 76, 65 76, 55 76, 45 76, 33 19 78, 03 77. 93 77, 85 77, 75 77, 67 77, 57 77, 47 20 79, 12 79. 03 78, 95 78, 87 78, 78 78, 68 78, 60 21 80, 20 80. 13 80, 05 79, 98 79, 90 79, 82 79, 73 22 81, 28 81. 22 81, 15 81, 08 81, 02 80, 93 80, 87 23 82, 37 82. 30 82, 25 82, 18 82, 13 82, 07 82, 00 24 83, 47 83. 40 83, 35 83, 30 83, 25 83, 20 83, 15 25 84, 55 84. 50 84, 45 84, 42 84, 37 84, 33 84, 28 26 85, 63 84. 60 85, 55 85, 53 85. 48 85, 47 85, 38 27 86, 73 86. 70 86, 67 86, 65 86. 6● 86, 60 86, 57 28 87, 82 87. 80 87, 77 87, 73 87. 78 87, 73 87, 70 29 88, 92 88 90 88, 88 88, 88 88: 87 88, 87 88, 85 30 90, 00 90. 00 90, 00 90, 00 90. 00 90, 00 90, 00 A Table of Right Ascensions. ♊ South Latitude. ♐ North Latitude. 180 Add. 0 1 2 3 4 5 6 0 58, 03 58, 25 58, 48 58, 70 58, 92 59, 12 1 59, 07 59, 28 59, 50 59, 72 59, 92 60, 13 2 60, 10 60, 32 60, 52 60, 73 60, 93 61, 13 3 61, 15 61, 35 61, 55 61, 77 61, 95 62, 14 4 62, 18 62, 38 62, 58 62, 80 62, 97 63, 15 5 63, 23 63, 42 63, 62 63, 83 63, 98 64, 17 6 64, 28 64, 47 64, 65 64, 87 65, 02 65, 18 7 65, 33 65, 52 65, 68 65, 90 66, 03 66, 20 8 66, 38 66, 57 66, 73 66, 93 67, 07 67, 22 9 67, 45 67, 52 67, 77 67, 97 68, 10 68, 25 10 68, 50 68, 67 68, 82 68, 98 69, 12 69, 27 11 69, 57 69, 72 69, 87 70, 01 70, 15 70, 28 12 70, 63 70, 77 70, 92 17, 05 71, 18 71, 32 13 71, 70 71, 82 71, 97 72, 08 72, 22 72, 35 14 72, 77 72, 88 73, 02 73, 13 73, 25 73, 38 15 73, 83 73, 95 74, 07 74, 18 74, 30 74, 42 16 74, 90 75, 02 75, 12 75, 23 75, 33 75, 45 17 75, 97 76, 08 76, 18 76, 28 76, 38 76, 48 18 77, 05 77, 15 77, 25 77, 33 77, 43 77, 52 19 78, 12 78, 22 78, 30 78, 38 78, 47 78, 55 20 79, 20 79, 28 79, 35 79, 43 79, 52 79, 58 21 80, 28 80, 35 80, 42 80, 48 80, 57 80, 63 22 81, 35 81, 42 81, 47 81, 53 81, 60 81, 67 23 82, 42 82, 48 82, 53 82, 58 82, 65 82, 70 24 83, 50 83, 55 83, 60 83, 65 83, 70 83, 75 25 84, 58 84, 62 84, 67 84, 70 84, 75 84, 78 26 85, 67 85, 68 85, 73 85, 75 85, 80 85, 82 27 86, 75 86, 77 86, 80 86, 82 86, 85 86, 87 28 87, 83 87, 83 87, 87 87, 87 87, 90 87, 90 29 88, 92 88, 92 88, 93 88, 93 88, 95 88, 95 30 90, 00 90, 00 90, 00 90, 00 90, 00 90, 00 A Table of Right Ascensions. ♋ North Latitude ♑ South Latitude. 180 Add. 0 1 2 3 4 5 6 0 90, 00 90, 00 90, 00 90. 00 90, 00 90, 00 90, 00 1 91, 08 91, 10 91, 12 91. 12 91, 13 91, 13 91, 15 2 92, 18 92, 20 92, 23 92. 23 92, 27 92, 27 92, 30 3 93, 27 93, 30 93, 33 93. 35 93, 38 93, 40 93, 43 4 94, ●7 94, 40 94, 45 94. 47 94, 52 94, 53 94, 62 5 95, 45 95, 50 95, 55 95. 58 95, 63 95, 67 95, 72 6 96, 53 96, 60 96, 65 96. 70 96, 75 96, 80 96, 85 7 97, 63 97, 70 97, 75 97. 82 97, 87 97, 93 98, 00 8 98, 72 98, 78 98, 85 98. 92 99, 98 99, 07 99, 13 9 99, ●0 99, 87 99, 95 100 02 100, 10 100, 18 100, 27 10 100, ●8 100, 97 101, 05 101. 13 101, 22 101, 32 101, 40 11 101, 97 102, 07 102, 15 102. 25 102, 33 102, 43 102, 53 12 103, 05 103, 15 103, 25 103. 35 103, 45 103, 55 103, 67 13 104, 13 104, 2● 104, 35 104. 45 104, 57 104, 68 104, 80 14 105, 22 105, 32 105, 45 105. 55 105, 68 105, 80 105, 93 15 106, 30 106, 40 106, 53 106. 65 106, 78 106, 92 107, 05 16 107, 37 107, 48 107, 63 107. 75 107, 90 108, 0● 108, 18 17 108, 43 108, 57 108, 72 108. 85 108, 00 109, 15 109, 30 18 109, 52 109, 65 109, 80 109. 95 110, 10 110, 25 110, 42 19 110, 58 110, 73 110, 88 111. 05 111, 20 111, 37 111, 53 20 111, 65 111, 82 111 97 112. 13 112, 30 112, 48 112, 65 21 112, 72 112, 88 113, 05 113. 22 113, 40 113, 58 113, 77 22 113, 78 113, 95 114, 13 114. 30 114, 50 114, 68 114, 87 23 114, 85 115, 02 115, 22 115. 38 115, 58 115, 78 115, 97 24 115, 90 116, 08 116, 28 116 47 116, 67 116, 87 117, 07 25 116, 95 117, 15 117, 35 117. 55 117, 75 117, 97 118. 17 26 118, 02 118, 22 118, 42 118. 63 118, 83 119, 05 119. 27 27 119, 07 119, 27 119, 48 119. 70 119, 92 120, 13 120. 37 28 120, 12 120, 32 120, 55 120. 77 120, 98 122, 22 121. 45 29 121, 15 121, 37 121, 60 121. 83 122, 05 122, 30 122. 53 30 122, 20 122, 42 122, 65 122. 88 123, 12 123, 37 123. 62 A Table of Right Ascensions. ♋ South Latitude. ♑ North Latitude. 180 Add. 0 1 2 3 4 5 6 0 90, 00 90, 00 90, 00 90, 00 90, 00 90, 00 1 91, 08 91, 08 91, 07 91, 07 91, 05 91, 05 2 92, 17 92, 17 92, 13 92, 13 92, 10 92, 10 3 93, 25 93, 23 93, 20 93, 18 93, 15 93, 13 4 94, 3● 94, 32 94, 27 94, 25 94, 20 94, 18 5 95, 42 95, 38 95, 33 95, 30 95, 25 95, 22 6 96, 50 96, 45 96, 40 96, 35 96, 30 96, 25 7 97, 58 97, 52 97, 47 97, 42 97, 35 97, 30 8 98, 65 98, 58 98, 53 98, 47 98, 40 98, 33 9 99, 72 99, 65 99, 58 99, 52 99, 43 99, 37 10 100, 80 100, 72 100, 65 100, 57 100, 48 100, 42 11 101, 88 101, 78 101, 70 101, 62 101, 53 101, 45 12 102, 95 102, 85 102, 75 102, 67 102, 57 102, 48 13 104, 03 103, 92 103, 82 103, 72 103, 62 103, 52 14 105, 10 104, 98 104, 88 104, 77 104, 67 104, 55 15 106, 17 106, 05 105, 93 105, 82 105, 70 105, 58 16 107▪ 23 107, 12 106, 98 106, 87 106, 75 106, 62 17 108, ●0 108, 18 108, 0● 107, 92 107, 78 107, 65 18 109, 37 109, 23 109, 08 108, 95 108, 82 108, 68 19 110, 43 110, 28 110, 13 110, 99 110, 85 109, 72 20 111, 50 111, 33 111, 18 111, 02 111, 88 110, 73 21 112, 55 112, 38 112, 2● 112, 03 112, 90 111, 75 22 113, 62 113, 4● 113, 27 113, 07 113, 93 112, 78 23 114, 67 114, 48 114, 32 114, 10 114, 97 113, 80 24 115, 72 115, 53 115, 35 115, 13 115, 98 114, 82 25 116, 77 116, 58 116, 38 116, 17 116, 02 115, 83 26 117, 82 117, 62 117, 42 117, 20 117, 03 116, 85 27 118, 85 118, 65 118, 45 118, 23 118, 05 117, 86 28 119, 90 119, 68 119, 48 119, 27 119, 07 118, 87 29 120, 93 120, 72 120, 50 120, ●8 120, 08 119, 88 30 121, 97 121, 75 121, 52 121, 30 121, 08 120, 88 A Table of Right Ascensions. ♌ North Latitude ♒ South Latitude. 180 Add. 0 1 2 3 4 5 6 0 122, ●0 122, 42 122, 65 122, 88 123, ●2 123. 37 123. 62 1 123, ●3 123, 47 123, 70 123, 95 124, ●8 124. 43 124. 70 2 124, 27 124, 52 124, 75 125, 00 125, 25 125. 50 125. 77 3 125, 30 125, 55 125, 80 126, ●5 126, 30 126. 57 126. 83 4 126, 33 126, 60 126, 85 127, 10 127, 37 127. 63 127. 90 5 127, 37 127, 63 127, 90 128, 15 128, 42 128. 70 128. 97 6 128, 40 128, 67 128, 93 129, 20 129, 47 129. 75 130. 03 7 129, 42 129, 70 129, 97 130, 23 130, 52 130. 80 131. 08 8 130, 43 130, 72 131, 00 131, 27 131, 55 131. 85 232. 13 9 131, 45 131, 73 132, 02 132, 30 132, 58 132. 88 133. 18 10 132, 46 132, 75 133, 03 133, 33 133, 62 133. 92 134. 23 11 133, 47 133, 77 134, 05 134, 35 134, 65 134. 95 135. 27 12 134, 48 134, 78 135, 07 135, 37 135, 67 135. 98 136. 30 13 135, 48 135, 78 136, 08 136, 38 136, 68 137. 00 137. 33 14 136, 49 136, 79 137, 09 137, 39 137, 70 138. 02 138. 35 15 137, 4● 237, 79 138, 09 138, 40 138, 72 139. 03 139. 37 16 138, 48 138, 78 139, 10 139, 41 139, 73 140. 05 140. 40 17 139, 47 139, 78 140, 10 040, 41 140, 74 141. 07 141. 42 18 140, 46 140, 77 141, 09 141, 42 141, 74 142. 08 142. 43 19 141, 45 141, 76 142, 09 142, 41 142, 75 143. 09 143. 44 20 142, 43 142, 75 143, 08 143, 41 143, 75 144. 10 144. 44 21 143, 41 143, 73 144, 07 144, 40 144, 74 145. 10 145. 45 22 144, 38 144, 72 145, 05 145, 39 145, 74 146. 09 146. 45 23 145, 36 145, 70 146, 03 146, 38 146, 73 147. 08 147. 44 24 146, 33 146, 67 147, 02 147, 37 147, 72 148. 07 148. 43 25 147, 30 147, 65 148, 00 148, 35 148, 70 149. 05 149. 42 26 148, 27 148, 62 148, 97 149, 32 149, 68 150. 03 150. 40 27 149, 23 149, 58 149, 93 150, 28 150, 65 151. 01 151. 38 28 150, 18 150, 55 150, 90 151, 25 151, 62 151. 98 152. 37 29 151, 15 551, 50 151, 87 152, 22 152, 52 152. 95 153. 33 30 152, 10 152, 45 152, 82 153, 18 153, 55 153. 92 154. 30 A Table of Right Ascensions. ♌ South Latitude ♒ North Latitude. 180. Add. 0 1 2 3 4 5 6 0 121, 97 121, 75 121, 52 121, 30 121, 08 120. 88 1 123, 00 122, 78 122, 55 122, 32 122, 09 121. 88 2 124, 03 123, 80 123, 57 123, 33 123, 10 122. 89 3 125, 07 124, 82 124, 58 124, 35 124, 11 123. 88 4 126, 08 125, 85 125, 60 125, 36 125, 12 123. 88 5 127, 12 126, 87 126, 61 126, 37 126, 12 125. 87 6 128, 13 127, 88 127, 61 127, 37 127, 12 126. 86 7 129, 15 128, 89 128, 62 128, 37 128, 11 127. 85 8 130, 16 129, 90 129, 62 129, 36 129, 10 128. 83 9 131, 17 130, 90 130, 62 130, 35 130, 08 129. 82 10 132, 18 131, 90 131, 62 131, 34 131, 07 130. 80 11 133, 18 132, 90 132, 62 132, 33 132, 05 131. 78 12 134, 19 133, 90 133, 61 133, 32 133, 03 132. 77 13 135, 19 134, 89 134, 60 134, 30 134, 02 133. 75 14 136, 19 135, 88 135, 58 135, 28 135, 00 134. 72 15 137, 18 136, 87 136, 57 136, 27 135, 97 135. 68 16 138, 17 237, 85 137, 55 137, 25 136, 95 136. 65 17 139, 15 138, 83 138, 53 138, 23 137, 92 137. 6● 18 140, 13 139, 82 139, 50 139, 20 138, 88 138. 5● 19 141, 12 140, 80 140, 48 140, 17 139, 85 139. 55 20 142, 10 141, 78 141, 45 141, 13 140, 82 140. 52 21 143, 07 142, 75 142, 42 142, 10 141, 78 141. 47 22 144, 05 143, 72 143, 38 143, 07 142, 75 142. 4● 23 145, 02 144, 68 144, 35 144, 03 143, 50 143. 37 24 145, 98 145, 65 145, 32 144, 98 144, 65 144. 3● 25 146, 95 146, 62 146, 28 145, 93 145, 60 145. ●7 26 147, 92 147, 58 147, 23 146, 88 146, 55 146. 22 27 148, 88 148, 53 148, 18 147, 83 147, 48 147. 15 28 149, 83 149, 48 149, 13 148, 78 148, 43 148. 1● 29 150, 77 150, 43 150, 08 149, 73 149, 38 149. ●● 30 151, 73 551, 38 151, 03 150, 68 150, 33 149. 9● A Table of Right Ascensions. ♈ North Latitude. ♓ South Latitude. 180 Add. 0 1 2 3 4 5 6 0 152, 10 152, 45 152, 82 153. 18 153, 55 153, 92 154, 30 1 153, 05 153, 42 153, 78 154. 15 154, 52 154, 88 155, 27 2 154, 02 154, 37 154, 73 155. 10 155, 48 155, 85 156, 23 3 154, 97 155, 32 155, 68 156, 0● 156, 43 156, 82 157, 20 4 155, 90 156, 27 156, 65 157. 02 157, 40 157, 78 158, 17 5 156, 85 157, 22 157, 60 157. 97 158, 35 158, 73 159, 13 6 157, 80 258, 17 158, 55 158. 92 159, 30 159, 68 160, 08 7 158, 73 159, 12 159, 50 159. 87 160, 25 160, 63 161, 03 8 159, 67 160, 07 160, 45 160. 82 161, 20 161, 58 161, 99 9 160, 62 161, 00 161, 38 161. 77 162, 15 162, 53 162, 93 10 161, 55 161, 93 162, 32 162. 70 163, 10 163, 48 163, 88 11 162, 48 162, 87 163, 25 163. 63 164, 03 164, 42 164, 82 12 163, 42 163, 80 164, 18 164. 57 164, 97 165, 35 165, 75 13 164, 33 164, 73 165, 21 165. 50 165, 90 166, 30 166, 70 14 165, 27 165, 67 166, 05 166. 43 166, 83 167, 23 167, 63 15 166, 20 166, 58 166, 98 167. 37 167, 77 168, 33 168, 57 16 167, 12 167, 52 167, 92 168. 30 168, 70 169, 10 169, 50 17 168, 05 168, 45 168, 85 569. 23 169, 62 170, 03 170, 43 18 168, 97 169, 37 169, 77 170. 15 170, 55 170, 95 171, 35 19 169, 90 170, 30 170, 70 171. 08 171, 48 171, 88 172, 28 20 170, 82 171, 22 171, 62 172. 02 172, 42 172, 82 173, 22 21 171, 73 172, 13 172, 53 172. 93 173, 33 173, 73 174, 13 22 172, 65 173, 05 173, 45 173. 85 174, 25 174, 65 175, 05 23 173, 58 173, 97 174, 37 174. 77 175, 17 175, 57 175, 97 24 174, 50 174, 88 175, 28 175. 68 176, 08 176, 48 176, 88 25 175, 42 175, 80 176, 20 176. 60 177, 00 177, 40 177. 80 26 176, 33 176, 72 177, 12 177. 52 177, 92 178, 32 178. 72 27 177, 25 177, 63 178, 03 178. 43 178, 83 179, 23 179. 63 28 178, 17 178, 55 178, 95 179. 35 579, 75 180, 15 180. 55 29 179, 08 179, 47 179, 87 180 27 180, 67 181, 07 181. 47 30 180, 00 180, 38 180, 78 181. 18 181, 58 181, 98 182. 38 A Table of Right Ascensions. ♍ South Latitude ♓ North Latitude. 180 Add. 0 1 2 3 4 5 6 0 152 151, 73 151, 37 151, 03 150, 68 150, 33 149, 98 1 153 152, 68 152, 33 151, 98 551, 63 151, 27 150, 92 2 154 153, 62 153, 28 152, 92 152, 57 152, 20 151, 85 3 154 154, 58 154, 22 153, 85 153, 50 153, 13 152, 78 4 155 155, 52 155, 17 154, 80 154, 43 154, 07 153, 72 5 156 156, 48 156, 12 155, 73 155, 37 155, 00 154, 65 6 157 157, 42 157, 05 156, 67 156, 30 155, 93 155, 57 7 158 158, 37 157, 99 157, 60 157, 23 156, 87 156, 50 8 159 159, 30 158, 92 158, 53 158, 17 157, 80 157, 43 9 160 160, 23 159, 85 159, 47 159, 10 158, 72 158, 35 10 161 161, 17 160, 78 160, 40 160, 03 159, 65 159, 28 11 162 162, 10 161, 72 161, 33 160, 97 160, 58 160, 20 12 163 163, 03 162, 65 162, 27 161, 88 161, 50 161, 12 13 164 163, 97 163, 58 163, 20 162, 82 162, 42 162, 03 14 165 164, 88 164, 50 164, 12 163, 73 163, 33 163, 95 15 166 165, 80 165, 42 165, 03 164, 65 164, 25 163, 87 16 167 166, 73 166, 35 165, 95 165, 57 165, 17 164, 78 17 168 167, 67 167, 27 166, 87 166, 48 166, 08 165, 70 18 168 168, 58 168, 18 167, 78 167, 40 167, 00 166, 62 19 169 169, 50 169, 10 168, 70 168, 32 167, 92 167, 53 20 170 170, 42 170, 02 169, 62 169, 23 168, 83 168, 45 21 171 171, 34 170, 93 170, 53 170, 15 169, 75 169, 37 22 172 172, 27 171, 87 171, 47 171, 07 170, 67 170, 28 23 173 173, 18 172, 78 172, 38 171, 98 171, 58 171, 20 24 174 174, 10 173, 70 173, 30 172, 90 172, 50 172, 12 25 175 175, 03 174, 63 174, 23 173, 83 173, 43 173, 03 26 176 175, 95 175, 55 175, 15 174, 75 174, 35 173, 95 27 177 176, 87 176, 47 176, 07 175, 67 175, 27 174, 87 28 178 177, 78 177, 38 176, 98 176, 58 176, 18 175, 78 29 179 178, 70 178, 30 177, 90 177, 50 177, 10 176, 70 30 179 179, 62 179, 32 178, 82 178, 42 178, 02 177, 62 A Table of Ascensional Differences. Poles. 1 2 3 4 5 6 7 Degrees of Declination. 1 00. 01 00. 0● 00, 05 00, 07 00, 08 00, 10 00, 12 2 0. 03 0. 06 0, 10 0, 13 0, 17 00, 22 0, 25 3 0. 05 0. 10 0, 15 0, 22 0, 27 0, 32 0, 37 4 0. 06 0. 13 0, 22 0, 28 0, 35 0, 42 0, 50 5 0. 08 0. 16 0, 27 0, 35 0, 43 0, 53 0, 62 6 0. 10 0. 21 0, 32 0, 42 0, 53 0, 63 0, 73 7 0. 11 0. 25 0, 37 0, 50 0, 62 0, 73 0, 87 8 0. 13 0. 28 0, 42 0, 57 0, 70 0, 85 0, 98 9 0. 15 0. 32 0, 48 0, 63 0, 80 0, 95 1, 12 10 0. 18 0. 35 0, 53 0, 70 0, 88 1, 07 1, 23 11 0. 20 0. 38 0, 58 0, 78 0, 97 1, 17 1, 37 12 0. 21 0. 42 0, 63 0, 85 1, 07 1, 28 1, 50 13 0. 23 0. 47 0, 70 0, 93 1, 15 1, 38 1, 62 14 0. 25 0. 50 0, 75 1, 00 1, 25 1, 50 1, 75 15 0. 26 0. 53 0, 80 1, 07 1, 35 1, 62 1, 88 16 0. 28 0. 57 0, 87 1, 15 1, 43 1, 73 2, 01 17 0. 30 0. 62 0, 92 1, 23 1, 53 1, 83 2, 15 18 0. 32 0. 65 0, 98 1, 30 1, 63 1, 95 2, 28 19 0. 35 0. 68 1, 03 1, 38 1, 73 2, 07 2, 42 20 0. 36 0. 73 1, 10 1, 45 1, 82 2, 20 2, 57 21 0. 38 0. 77 1, 15 1, 53 1, 92 2, 32 2, 70 22 0. 40 0. 82 1, 22 1, 62 2, 03 2, 43 2, 85 23 0. 42 0. 85 1, 28 1, 70 2, 13 2, 55 2, 98 24 0. 44 0. 88 1, 33 1, 78 2, 23 2, 68 3, 03 25 0. 46 0. 93 1, 40 1, 87 2, 33 2, 82 3, 28 26 0. 48 0. 98 1, 47 1, 95 2, 45 2, 93 3, 43 27 0. 51 1. 02 1, 53 2, 05 2, 55 3, 07 3, 58 28 0. 53 1. 07 1, 60 2, 13 2, 67 3, 20 3, 75 29 0. 55 1. 13 1, 67 2, 22 2, 78 3, 33 3, 90 30 0. 58 1. 15 1, 73 2, 32 2, 90 3, 48 4, 07 31 0. 60 1. 20 1, 80 2, 40 3, 01 3, 62 4, 23 32 0. 62 1. 25 1, 88 2, 50 3. 13 3, 77 4, 40 A Table of Ascensional Differences. Height. 8 9 10 11 12 13 14 Degrees of Declination. 1 00, 13 00. 15 00, 18 00, 20 00, 22 00, 23 00, 25 2 0, 28 0. 32 0, 35 0, 38 0, 42 0, 47 0, 50 3 0, 42 0. 48 0, 53 0, 58 0, 63 0, 70 0, 75 4 0, 57 0. 63 0, 70 0, 78 0, 85 0, 93 1, 00 5 0, 70 0. 80 0, 88 0, 97 1, 07 1, 15 1, 25 6 0, 85 0. 95 1, 07 1, 17 1, 28 1, 38 1, 50 7 0, 98 1. 12 1, 23 1, 37 1, 50 1, 62 1, 73 8 1, 13 1. 27 1, 42 1, 57 1, 72 1, 87 2, 00 9 1, 27 1. 43 1, 60 1, 77 1, 93 2, 10 2, 27 10 1, 42 1. 60 1, 78 1, 97 2, 15 2, 33 2, 52 11 1, 57 1. 77 1, 97 2, 17 2, 37 2, 57 2, 78 12 1, 72 1. 93 2, 15 2, 37 2, 58 2, 82 3, 03 13 1, 87 2. 10 2, 33 2, 57 2, 82 3, 05 3, 30 14 2, 00 2. 27 2, 5● 2, 78 3, 03 3, 30 3, 57 15 2, 17 2. 43 2, 70 2, 98 3, 27 3, 55 3, 83 16 2, 32 2. 60 2, 90 3, 20 3, 50 3, 80 4, 10 17 2, 47 2. 78 3, 08 3, 40 3, 73 4, 05 4, 37 18 2, 62 2. 95 3, 28 3, 62 3, 97 4, 30 4, 65 19 2, 77 3. 13 ●, 48 3, 83 4, 28 4, 57 4, 92 20 2, 93 3. 30 3, 68 4, 05 4, 43 4, 82 5, 20 21 3, 10 3. 48 3, 88 4, 28 4, 68 5, 08 5, 50 22 3, 25 3. 67 4, 08 4, 50 4, 93 5, 35 5, 78 23 3, 42 3. 85 4, 30 4, 7● 5, 18 5, 62 6, 12 24 3, 58 4. 05 4, 50 4, 63 5, 43 5, 90 6, 37 25 3, 75 4. 23 4, 72 5, 20 5, 68 6, 18 6, 68 26 3, 93 4. 43 4, 93 5, 43 5, 95 6, 47 6, 98 27 4, 10 4. 63 5, 15 5, 68 6. 22 6, 75 7, 30 28 4, 28 4. 83 5, 38 5, 93 6. 48 7, 05 7, 62 29 4, 47 5. 03 5, 62 6, 18 6. 77 7, 35 7, 95 30 4, 65 5. 25 5, 85 6, 45 7: 05 7, 67 8, 28 31 4, 85 5. 47 6, 08 6, 70 7. 33 7, 97 8, 62 32 5, 03 5. 68 6, 33 6, 98 7. 63 8, 30 8, 97 A Table of Ascensional Differences. Poles. 15 16 17 18 19 20 21 Degrees of Declination. 1 00, 27 00, 28 00; 30 00, 32 00, 35 00, 37 00, 38 2 0, 53 0, 57 0, 62 0, 65 0, 68 0, 73 0, 77 3 0, 80 0, 87 0, 92 0, 98 1, 03 1, 10 1, 15 4 1, 07 1, 15 1, 23 1, 30 1, 38 1, 45 1, 53 5 1, 35 1, 27 1, 53 1, 63 1, 73 1, 82 1, 92 6 1, 62 1, 73 1, 83 1, 95 2, 07 2, 20 2, 32 7 1, 95 2, 01 2, 15 2, 28 2, 42 2, 57 2, 70 8 2, 15 2, 32 2, 47 2, 62 2, 77 2, 93 3, 10 9 2, 43 2, 60 2, 78 2, 95 3, 13 3, 30 3, 48 10 2, 70 2, 90 3, 08 3, 28 3, 48 3, 68 3, 88 11 2, 98 3, 20 3, 40 3, 62 3, 83 4, 05 4, 28 12 3, 27 3, 50 3, 73 3, 97 4, 20 4, 43 4, 68 13 3, 55 3, 80 4, 05 4, 30 4, 57 4, 82 5, 08 14 3, 83 4, 10 4, 37 4, 65 4, 92 5, 20 5, 50 15 4, 12 4, 40 4, 70 5, 00 5, 30 5, 60 5, 90 16 4, 40 4, 72 5, 03 5, 35 5, 67 5, 98 6, 32 17 4, 70 5, 03 5, 37 5, 70 6, 03 6, 38 6, 73 18 5, 00 5, 35 5, 70 6, 07 6, 42 6, 78 7, 17 19 5, 30 5. 67 6, 05 6, 42 6, 82 7, 20 7, 60 20 5, 60 5. 98 6, 38 6, 78 7, 20 7, 62 8, 03 21 5, 90 6. 32 6, 73 7, 17 7, 60 8, 03 8, 47 22 6, 22 6. 65 7, 10 7, 55 8, 00 8, 45 8, 92 23 6, 5● 6. 98 7, 45 7, 93 8, 40 8, 88 9, 37 24 6, 85 7. 33 7, 82 8, 32 8, 82 9, 32 9, 83 25 7, 18 7. 68 8, 20 8, 72 9, 23 9, 77 10, 32 26 7, 52 8. 03 8, 58 9, 12 9, 67 10, 23 10, 78 27 7, 85 8. 40 8, 97 9, 53 10, 10 10, 68 11, 28 28 8, 18 8. 77 9, 35 9, 95 10, 55 11, 15 11, 78 29 8, 53 9 15 9, 75 10, 38 11, 17 11, 63 12, 28 30 8, 90 9 53 10, 17 10, 82 11, 47 12, 13 12, 80 31 9, 27 9 92 10, 58 11, 27 11, 93 12, 63 13, 33 32 9, 63 10. 32 11, 01 11, 72 12, 42 13, 15 13, 88 A Table of Ascensional Differences. Height. 22 23 24 25 26 27 28 Degrees of Declination. 1 00, 40 00. 42 00, 45 00, 47 00, 48 00, 51 00, 53 2 0, 82 0. 85 0, 88 0, 93 0, 98 1, 02 1, 07 3 1, 22 1. 28 1, 33 1, 40 1, 47 1, 53 1, 60 4 1, 62 1. 70 1, 78 1, 87 1, 95 2, 05 2, 13 5 2, 03 2. 13 2, 23 2, 33 2, 45 2, 55 2, 67 6 2, 43 2. 55 2, 68 2, 82 2, 93 3, 07 3, 20 7 2, 85 2. 98 3, 13 3, 28 3, 43 3, 58 3, 75 8 3, 25 3. 42 3, 58 3, 75 3, 93 4, 10 4, 28 9 3, 67 3. 85 4, 05 4, 23 4, 43 4, 63 4, 83 10 4, 08 4. 30 4, 50 4, 72 4, 93 5, 15 5, 38 11 4, 50 4. 73 4, 97 5, 20 5, 45 5, 68 5, 93 12 4, 93 5. 18 5, 43 5, 68 5, 95 6, 22 6, 48 13 5, 35 5. 63 5, 90 6, 18 6, 47 6, 75 7, 05 14 5, 78 6. 08 6, 37 6, 68 6, 98 7, 30 7, 62 15 6, 22 6. 53 6, 85 7, 18 7, 53 7, 85 8, 18 16 6, 65 6. 98 7, 33 7, 68 8, 05 8, 40 8, 77 17 7, 10 7. 45 7, 82 8, 20 8, 58 8, 97 9, 35 18 7, 55 7. 93 8, 32 8, 72 9, 12 9, 53 9, 85 19 8, 00 8. 40 8, 82 9, 23 9, 67 10, 10 10, 55 20 8, 45 8. 88 9, 32 9, 77 10, 23 10, 68 11, 15 21 8, 92 9 38 9, 83 10, 32 10, 78 11, 28 11, 77 22 9, 40 9 88 10, 37 10, 87 11, 37 11, 88 12, 40 23 9, 88 10. 38 10, 90 11, 42 11, 95 12, 48 13, 05 24 10, 37 10. 90 11, 43 11, 98 12, 55 13, 12 13, 70 25 10, 87 11. 42 11, 98 12, 57 13, 15 13, 80 14, 35 26 11, 37 11. 95 12, 55 13, 15 14, 77 14, 38 15, 03 27 11, 88 12. 48 13, 12 13, 73 14, 38 15, 05 15, 72 28 12, 40 13. 05 13, 70 14, 35 15, 03 15, 72 16, 42 29 12, 93 13. 62 14, 28 14, 48 15. 68 16, 40 17, 13 30 13, 48 14. 18 14, 90 15, 62 16. 35 17, 12 17, 88 31 14, 05 14. 78 15, 52 16, 27 17, 03 17, 83 18, 63 32 14, 62 15. 38 16, 15 16, 93 17, 75 18, 57 19, 40 A Table of Ascensional Differences. Poles. 29 30 31 32 33 34 35 Degrees of Declination. 1 00, 5● 00, 58 00, 60 00, 62 00, 65 00, 67 00, 70 2 1, 12 1, 15 1, 20 1, 25 1, 30 1, 35 1, 40 3 1, 67 1, 73 1, 80 1, 88 1, 95 2, 03 2, 10 4 2, 22 2, 32 2, 40 2, 50 2, 60 2, 70 2, 80 5 2, 78 2, 90 3, 01 3, ●3 3, 25 3, 38 3, 52 6 3, 33 3, 48 3, 62 3, 77 3, 92 4, 07 4, 22 7 3, 90 4, 07 4, 23 4, 40 4, 57 4, 75 4, 93 8 4, 47 4, 65 4, 85 5, 03 5, 23 5, 43 5, 65 9 5, 03 5, 25 5, 47 5, 68 5, 90 6, 13 6, 37 10 5, 62 5, 85 6, 0● 6, 33 6, 58 6, 83 7, 10 11 6, 18 6, 45 6, 70 6, 98 7, 25 7, 53 7, 82 12 6, 77 7, 05 7, 33 7, 63 7, 93 8, 25 8, 57 13 7, 35 7, 67 7, 97 8, 30 8, 62 8, 97 9, 30 14 7, 93 8, 28 8, 62 8, 97 9, 32 9, 68 10, 05 15 8, 53 8, 90 9, 27 9, 63 10, 02 10, 42 10, 82 16 9, 13 9, 53 9, 92 10, 32 10, 7● 11, 15 11, 58 17 9, 75 10, 17 10, 58 11, 02 11, 45 11, 90 12, 37 18 10, 38 10, 8● 11, 27 11, 72 12, 18 12, 67 13, 15 19 11, 00 11, 47 11, 93 12, 42 12, 92 13, 43 13, 85 20 11, 63 12, 13 12, 63 13, 15 13, 67 14, 22 14, 77 21 12, 28 12, 80 13, 33 13, 88 14, 43 15, 00 15, 65 22 12, 93 13, 48 14, 05 14, 62 15, 22 15, 82 16, 45 23 13, 62 14, 18 14, 78 15, 38 16, 00 16, 63 17, 28 24 14, 28 14, 90 15, 52 16, 15 16, 80 17, 48 18, 17 25 14, 98 15, 62 16, 27 16, 93 17, 63 18, 33 19, 05 26 15, 68 16, 35 17, 03 17, 75 18, 47 19, 20 19, 97 27 16, 40 17, 10 17, 83 18, 57 19, 32 20, 10 20, 90 28 17, 13 17, 88 18, 63 19, 40 20, 20 21, 01 21, 85 29 17, 90 18, 67 19, 45 20, 27 21, 10 21, 95 22, 83 30 18, 67 19, 47 20, 30 21, 15 22, 02 22, 92 23, 85 31 19, 45 20, 30 21, 17 22, 05 22, 97 23, 92 24, 88 32 20, 27 21, 15 22, 05 23, 98 23, 93 24, 93 25, 95 A Table of Ascensional Differences. Height. 36 37 38 39 40 41 42 Degrees of Declination. 1 00, 73 00, 75 00, 78 00, 82 00, 83 00, 87 00, 90 2 1, 45 1, 53 1, 57 1, 62 1, ●8 1, 73 1, 80 3 2, 18 2, 27 2, 35 2, 43 2, 52 2, 62 2, 70 4 2, 92 3, 01 3, 13 3, 25 3, 37 3, 48 3, 62 5 3, 65 3, 78 3, 92 4, 07 4, 22 4, 37 4, 52 6 4, 38 4, 55 4, 72 4, 87 5, 07 5, 25 5, 43 7 5, 12 5, 32 5, 50 5, 70 5, 92 6, 13 6, 35 8 5, 87 6, 08 6, 30 6, 53 6, 77 7, 02 7, 27 9 6, 60 6, 85 7, 10 7, 47 7, 63 7, 88 8, 20 10 7, 37 7, 63 7, 92 8, 22 8, 50 8, 82 9, 1● 11 8, 12 8, 42 8, 73 9, 05 9, 38 9, 73 10, 08 12 8, 88 9, 22 9, 57 9, 92 10, 27 10, 65 11, 0● 13 9, 65 10, 02 10, 40 10, 77 11, 17 11, 58 12, 00 14 10, 43 10, 83 11, 23 11, 65 12, 08 12, 53 12, 97 15 11, 23 11, 65 12, 08 12, 53 13, 00 13, 47 13, 97 16 12, 03 12, 48 12, 95 13, 43 13, 92 14, 43 14, 97 17 12, 83 13, 32 13, 82 14, 33 14, 87 15, 42 15, 98 18 13, 65 14, 17 14, 70 15. 25 15, 82 16, 40 17, 01 19 14, 48 15, 03 15, 60 16. 18 16, 80 17, 42 18, 07 20 15, 33 15, 92 16, 32 17. 13 17, 78 18, 45 19, 13 21 16, 18 16, 82 17, 45 18. 12 18, 78 19, 50 20, 22 22 17, 08 17, 73 18, 40 19 10 19, 82 20, 57 21, 33 23 17, 97 18, 65 19, 37 20. 10 20, 87 21, 65 22, 47 24 18, 87 19, 60 20, 35 21. 13 21, 93 22, 77 23, 63 25 19, 80 20, 57 21, 35 22. 18 23, 03 23, 92 24, 83 26 20, 75 21, 57 22, 40 23. 27 24, 17 25, 08 26, 05 27 21, 73 22, 58 23, 47 24. 37 25, 32 26, 28 27, 30 28 22, 72 23, 61 24, 55 25. 50 26, 50 27, 52 28, 60 29 23, 75 24, 68 25, 67 26. 67 27, 72 28, 80 29, 95 30 24, 80 25, 78 26, 82 27. 87 28, 98 30, 12 31, 32 31 25, 80 26, 92 28, 00 29. 12 30, 28 31, 48 3●, 75 32 27, 00 28, 08 29, 22 30. 90 31, 52 32, 90 34, 23 A Table of Ascensional Differences. Poles. 43 44 45 46 47 48 49 Degrees of Declination. 1 00, 93 00, 97 01, 00 01, 03 01, 07 01, 12 01, 15 2 1, 87 1, 93 2, 00 2, 07 2, 15 2, 22 2, 30 3 2, 80 2, 90 3, 00 3, 12 3, 22 3, 33 3, 45 4 3, 7● 3, 87 4, 01 4, 15 4, 30 4, 45 4, 62 5 4, 68 4, 85 5, 02 5, 20 5, 38 5, 58 5, 78 6 5, 62 5, 83 6, 03 6, 25 6, 47 6, 70 6, 95 7 6, 57 6, 82 7, 05 7, 30 7, 57 7, 83 8, 12 8 7, 53 7, 80 8, 08 8, 37 8, 67 8, 98 9, 30 9 8, 50 8, 80 9, 12 9, 43 9, 78 10, 13 10, 50 10 9, 47 9, 80 10, 15 10, 53 10, 90 11, 30 11, 70 11 10, 45 10, 82 11, 22 11, 62 12, 03 12, 47 12, 92 12 11, 43 11, 85 12, 27 12, 72 13, 18 13, 65 14, 15 13 12, 43 12, 88 13, 35 13, 83 14, 33 14, 85 15, 40 14 13, 45 13, 93 14, 43 14, 97 15, 50 16, 08 16, 67 15 14, 47 15, 00 15, 53 16, 12 16, 70 17, 32 17, 95 16 15, 51 16, 08 16, 67 17, 27 17, 90 18, 57 19, 27 17 16, 57 17, 17 17, 80 18, 45 19, 13 19, 85 20, 60 18 17, 63 18, 28 18, 97 19, 67 20, 38 21, 15 21, 95 19 18, 73 19, 42 20, 15 20, 88 21, 67 22, 48 23, 33 20 19, 83 20, 58 21, 35 22, 13 22, 97 23, 85 24, 75 21 20, 98 21, 77 22, 57 23, 42 24, 30 25, 23 26, 20 22 22, 13 22, 97 23, ●3 24, 73 25, 67 26, 67 27, 70 23 23, 32 24, 20 24, 12 26, 08 27, 08 28, 13 29, 23 24 24, 53 25, 47 26, 43 27, 45 28, 52 29, 63 30, 80 25 25, 78 26, 77 27, 80 28, 87 30, 00 31, 20 32, 43 26 27, 03 28, 10 29, 18 30, 33 31, 53 32, 80 34, 13 27 28, 37 29, 48 30, 63 31, 85 33 12 34, 47 35, 88 28 29, 73 30, 90 32, 12 33, 42 34, 77 36, 20 37, 70 29 31, 13 32, 37 33, 67 35, 03 36, 47 38, 00 39, 62 30 32, 58 33, 88 35, 27 36, 72 38, 25 39, 88 41, 62 31 33, 97 35, 47 36, 93 38, 48 40, 12 41, 87 43, 73 32 35, 63 37, 12 38, 67 40, 32 42, 07 43, 95 45, 9● A Table of Ascensional Differences. Height. 50 51 52 53 54 55 56 Degrees of Declination. 1 01. 20 01. 23 01, 28 01, 33 01, 38 01, 43 01, 48 2 2. 38 2. 47 2, 57 2, 65 2, 75 2, 87 2, 97 3 3. 58 3. 72 3, 85 3, 98 4, 13 4, 28 4, 45 4 4. 78 4. 95 5, 13 5, 32 5, 52 5, 73 5, 95 5 5. 98 6. 20 6, 43 6, 67 6, 92 7, 18 7, 45 6 7. 20 7. 45 7, 73 8, 01 8, 32 8, 63 8, 97 7 8. 42 8. 72 9, 03 9, 38 9, 73 10, 27 10, 48 8 9 63 10. 00 10, 37 10, 75 11, 15 11, 58 12, 02 9 10. 88 11. 28 11, 70 12, 13 12, 58 13, 07 13, 58 10 12. 13 12. 58 13, 05 13, 53 14, 05 14, 58 15, 15 11 13. 40 13. 88 14, 40 14, 95 15, 52 16, 12 16, 75 12 14. 67 15. 22 15, 78 16, 38 17, 02 17, 67 18, 37 13 15. 63 16. 57 17, 18 17, 08 18, 53 19, 25 20, 01 14 17. 28 17. 93 18, 62 19, 32 20, 07 20, 87 21, 70 15 18. 62 19 32 20, 07 20, 83 21, 63 22, 50 23, 40 16 19 98 20. 73 21, 53 22, 37 23, 25 24, 17 25, 15 17 21. 37 22. 18 23, 03 23, 93 24, 88 25, 88 26, 95 18 22. 78 23. 65 24, 57 25, 55 26, 57 27, 65 28, 80 19 24. 23 25. 17 26, 15 27, 18 28, 28 29, 45 30, 68 20 25. 72 26. 72 27, 77 28, ●8 30, 07 31, 32 32, 65 21 27. 23 28. 30 29, 43 30, 62 31, 90 33, 25 34, 68 22 28. 80 29. 93 31, 13 32, 42 33, 78 35, 23 36, 80 23 30. 40 31. 62 32, 90 34, 28 35, 75 37, 32 39, 00 24 32. 05 33. 35 34, 73 36, 22 37, 80 39, 48 41, ●0 25 33. 77 35. 17 36, 65 38, 23 39, 93 41, 75 43, 73 26 35. 53 37. 05 38, 63 40, 33 40, 17 44, 15 4●, 30 27 37. 38 39 00 40, 70 42, 55 44, 70 46, 68 49, 07 28 39 32 41. 03 42, 88 44, 88 47, 03 49, 40 52, 02 29 41. 35 43. 20 45, 20 47, 35 49, 73 52, 33 55, 27 30 43. 48 45. 48 47, 65 50, 02 52, 62 55, 53 58, 87 31 45. 73 47. 90 50, 27 52, 88 55, 80 59, 10 62, 97 32 48. 13 50. 50 53, 12 56, 02 59, 32 63, 17 67, ●8 A Table of oblique Ascensions. S. D. 1 2 3 4 5 6 ♈ 0 000, 00 000, 00 000, 00 000, 00 000, 00 000, 00 4 3, 63 3, 60 3, 58 3, 55 3, 53 3. 48 8 7, 28 7, 23 7, 17 7, 12 7, 07 7, 00 12 10, 95 10, 87 10, 77 10, 68 10, 60 10, 53 16 14, 62 14, 50 14, 38 14, 28 14, 17 14, 07 20 18, 32 18, 17 18, 03 17, 90 17, 77 17, 62 24 22, 05 21, 87 21, 70 21, 55 21, 38 21, 22 28 25, 80 25, 62 25, 42 25, 23 25, 05 24, 83 ♉ 2 29, 60 29, 38 29, 17 28, 95 28, 73 28, 50 6 33, 43 33, 18 32, 95 32, 72 32, 45 32, 22 10 37, 32 37, 05 36, 78 36, 52 36, ●5 35, 98 14 41, 23 40, 95 40, 65 40, 37 40, 08 39, 78 18 45, 22 44, 90 44, 60 44, 28 43, 98 43, 67 22 49, 25 48, 90 48, 58 48, 25 47, 92 47, 58 26 53, 30 52, 95 52, 62 52, 27 51, 90 51, 55 ♊ 0 57, 43 57, 07 56, 70 56, 33 55, 95 55, 58 4 61, 62 61, 22 60, 83 60, 47 60, 07 59, 68 8 65, 83 65, 42 65, 03 64, 63 64, 22 63, 83 12 70, 08 69, 67 69, 27 68, 85 68, 43 68, 03 16 74, 37 73, 95 73, 53 73, 12 72, 68 72, 27 20 78, 68 78, 27 77, 83 77, 40 76, 98 76, 55 24 83, 02 82, 60 82, 17 81, 73 81, ●0 80, 87 28 87, 38 86, 95 86, 52 86, 07 85, 63 85, 20 ♋ 2 91, 75 91, 32 90, 88 90, 45 90, 03 89, 58 6 96, 12 95, 68 95, 25 94, 80 94, 38 93, 95 10 100, 45 100, 03 99, 60 99, 17 98, 75 98, 32 14 104, 78 104, 37 103, 95 103, 53 103, 10 102, 68 18 109, 10 108, 68 108, 28 107, 87 107, 45 107, 05 22 113, 38 112, 97 112, 58 112, 18 111, 78 111, 38 26 117, 63 117, 2● 116, 85 116, 47 116, 08 115, 70 30 121, 83 121, 47 121, 10 120, 73 120, 35 119, 98 A Table of oblique Ascensions. S. D 1 2 3 4 5 6 ♌ 0 121, 83 121, 47 121. 10 120, 73 120, 35 119, 98 4 125, 98 125, 63 125. 30 124, 93 124, 58 124, 23 8 130, 10 129, 75 129. 4● 129, 10 128, 77 128, 43 12 134, 17 133, 85 133. 53 133, 23 132, 92 132, 60 16 138, 18 137, 90 137. 62 137, 32 137, 0● 136, 75 20 142, 15 141, 88 141. 62 141, 35 141, 08 140, 82 24 146, 08 145, 85 145. 62 145, 37 145, 12 144, 85 28 149, 97 149, 77 149. 53 149, 32 149, 10 148, 87 ♍ 2 153, 82 153, 63 153. 43 153, 25 153, 05 152, 85 6 157, 63 157, 47 157. 30 157, ●3 156, 93 156, 80 10 161, 42 161, 27 161. 13 161, 00 160, 87 160, 72 14 165, 17 165, 07 164. 93 164, 83 164, 73 164, 62 18 168, 90 168, 82 168. 72 168, 63 168, 57 168, 48 22 172, 62 172, 55 172. 50 172, 43 172, 38 172, 33 26 176, 32 176, 28 176. 27 176, 23 176, 20 176, 17 ♎ 0 180, 00 180, 00 180. 00 180, 00 180, 00 180, 00 4 183, 68 183, 72 183. 73 183, 77 183, 80 183, 83 8 187, 38 187, 45 187. 50 187, 57 187, 62 187, 67 12 191, 10 191, 18 191. 28 191, 37 191, 43 191, 52 16 194, 83 194, 93 195. 07 195, 17 195, 27 195, 38 20 198, 58 198, 73 198. 87 199, 00 199, 13 199, 28 24 202, 37 202, 53 202. 70 202, 87 20●, 02 203, 20 28 206, 18 206. 37 206. 57 206, 75 206, 95 207, 15 ♏ 2 210, 03 210. 23 210. 47 210, 68 210, 90 211, 13 6 213, 92 214. 15 214. 38 214, 63 214, 88 215, 15 10 217, 85 218. 12 218. 38 218, 58 218, 92 219, 18 14 221, 82 222. 10 222. 38 222, 53 222, 97 223, 25 18 225, 83 226. 15 226. 47 226, 38 227, 08 227, 40 22 229, 90 230. 25 230. 57 230, 90 231, 23 231, 57 26 234, 02 234. 37 234. 70 235, 07 235, 42 235, 77 30 238, 17 238. 53 238. 90 239, 27 239, 65 240, 02 A Table of oblique Ascensions. S. D. 1 2 3 4 5 6 ♐ 0 238, 17 238, 53 238, 90 239, 27 239, 65 240. 02 4 242, 37 242, 77 243, 15 243, 53 243, 92 244. 30 8 246, 62 247, 03 247, 42 247, 82 248, 22 248. 62 12 250, 90 251, 32 251, 72 252, 13 252, 55 252. 95 16 255, 22 255, 63 256, 05 256, 47 256, 90 257. 32 20 259, 55 259, 97 260, 40 260, 83 261, 25 261. 68 24 263, 88 264, 32 264, 75 265, 20 265, 62 266. 05 28 26●, 25 268, 68 269, 12 269, 55 269, 97 270. 42 ♑ 2 272, 62 273, 05 273, 48 273, 93 274, 37 274. 80 6 276, 98 277, 40 277, 83 278, 27 278, 70 279. 13 10 281, 32 281, 73 282, 17 282, 60 283, 02 283. 45 14 285, 63 286, 05 286, 47 286, 88 287, 32 287. 73 18 289, 92 290, 33 290, 73 291, 15 291, 57 291. 97 22 294, 17 294, 58 294, 97 295, 37 295, 78 296. 17 26 298, 38 298, 78 299, 17 299, 53 299, 93 300. 32 ♒ 0 302, 57 302, 93 303, 30 303, 67 304, 05 304. 42 4 306, 70 307, 05 307, 38 307, 73 308, 10 308. 45 8 310, 75 311, 10 311, 42 311, 75 312, 08 312. 42 12 314, 78 315, 10 315, 40 315, 72 316, 02 316. 33 16 318, 77 319, 05 319, 35 319, 63 319, 92 320. 22 20 322, 68 322, 95 323, 22 323, 48 323, 75 324. 02 24 326, 57 326, 82 327, 05 327, 28 327, 55 327. 78 28 330, 40 330, 62 330, 83 331, 05 331, 27 331. 50 ♓ 2 334, 20 334, 38 334, 58 334, 77 334, 95 335. 17 6 337, 95 338, 13 338, 30 338, 45 338, 62 338. 78 10 341, 68 341, 83 341, 97 342, 10 342, 23 342. 38 14 345, 38 345, 50 345, 62 345, 72 345, 83 345. 93 18 349, 05 349, 13 349, 23 349, 32 349, 40 349. 47 22 352, 72 352, 77 352, 83 352, 88 352, 93 353. 00 26 356, 37 356, 40 356, 42 356, 45 356, 47 356. 52 30 360, 00 360, 00 360, 00 360, 00 360, 00 360. 00 A Table of oblique Ascensions. S. D. 7 8 9 10 11 12 ♈ 0 000, 00 000. 00 000, 00 000, 00 000, 00 000, 00 4 03, 47 03. 43 03, 40 03, 38 03, 35 03, 33 8 06, 95 06. 88 06, 83 06, 78 06, 72 06, 67 1● 10, 4● 10. 35 10, 27 10, 18 10, 10 10, 00 16 13, 95 13. 83 13, 72 13, 60 13, 50 13, 37 20 17, 48 17. 33 17, 20 17, 05 16, 92 16, 77 24 21, 05 20. 87 20, 72 20, 53 20, ●8 20, 20 28 24, 65 24. 47 24, 27 24, 07 23, 87 23, 67 ♉ 2 28, 30 28. 07 27, 85 27, 63 27, 40 27, 18 6 31, 98 31. 72 31, 48 31, 23 30, 82 30, 73 10 35, 72 35. 45 35, 18 34, 90 34, 63 34, 35 14 39, 50 39 20 38, 92 38, 62 38, 32 38, 02 18 43, 35 43. 03 42, 72 42, 40 42, 08 41, 75 22 47, ●5 46. 92 46, 57 46, 23 45, ●0 45, 53 26 51, 20 50. 83 50, 48 50, 12 49, 77 49, 38 ♊ 0 55, 20 54. 83 54, 47 54, 08 53, 70 53, 32 4 59, 28 58. 90 58, 52 58, 12 57, 72 57, 32 8 63, 42 63. 03 62, 62 62, ●0 61, 80 61, 37 12 67, 60 67. 20 66, 78 66, 35 65, 93 65, 50 16 71, 85 71. 42 70, 98 70, 53 70, 12 69, 68 20 76, 12 75. 68 75, 22 74, 80 74, 35 73, 92 24 80, 42 79. 98 79, 53 79, 08 78, 63 78, 18 28 84, 75 84. 32 83, 87 83, 42 82, 97 82, 52 ♋ 2 89, 12 88 68 88, 23 87, 78 87, 33 86, 88 6 93, 48 93. 05 92, 60 92, 17 91, 72 91, 27 10 97, 88 97. 45 97, 00 96, 57 96, 12 95, 68 14 102, 27 101. 83 101, 40 100, 95 100, 52 100, 10 18 106, 63 106. 22 105, 80 105, 37 104, 95 104, 52 22 110, 97 110. 58 110, 17 109, 77 109, 35 108, 92 26 115, 30 114. 92 114, 53 114, 13 113, 73 113, 32 30 119, 60 119, 23 118, 87 118, 48 118, 10 117, 72 A Table of oblique Ascensions. S. D 7 8 9 10 11 12 ♌ 0 119, 60 119, 23 118, 87 118, 48 118, 10 117, 72 4 123, 87 123, 52 123, 17 122, 80 122, 43 122, 07 8 128, 10 127, 77 127, 42 127, 07 126, 75 126, 38 12 132, 30 131, 97 131, 65 131, 33 131, 02 130, 68 16 136, 45 136, 15 135, 87 135, 57 135, 27 134, 97 20 140, 55 140, 28 140, 02 139, 75 139, 47 139, 18 24 144, 63 144, 38 144, 15 143, 90 143, 65 143, 38 28 148, 67 148, 45 148, 22 148, 02 147, 78 147, 55 ♍ 2 152, 67 152, 47 152, 28 142, 08 151, 88 151, 68 6 156, 65 156, 47 156, 30 156, 13 155, 97 155, 80 10 160, 58 160, 43 160, 30 160, 15 160, 02 159, 87 14 164, 50 164, 38 164, 27 164, 15 164, 05 163, 93 18 168, 40 168, 30 168, 22 168, 13 168, 05 167, 97 22 172, 27 172, 22 172, 15 172, 10 172, 05 171, 98 26 176, 13 176, 12 176, 08 176, 07 176, 03 176, 00 ♎ 0 180, 00 180, 00 180, 00 180, 00 180, 00 180, 00 4 183, 87 183, 88 183, 92 183, 93 183, 97 184, 00 8 187, 73 187, 78 187, 85 187, 90 187, 95 188, 02 12 191, 60 191, 70 191, 78 191, 87 191, 95 192, 03 16 195, 50 195, 62 195, 73 195, 85 195, 95 196, 07 20 199, 42 199, 57 199, 70 199, 85 199, 98 200, 13 24 200, 35 203, 53 203, 70 203, 87 204, 03 204, 20 28 207, 33 207, 53 207, 72 207, 92 208, 12 208, 32 ♏ 2 211, 33 211, 55 211, 78 211, 98 212, 22 212, 45 6 215, 37 215, 62 215, 85 216, 10 216, 35 216, 62 10 219, 45 219, 72 219, 98 220, 25 220, 53 220, 82 14 223, 55 223, 85 224, 13 224, 43 224, 73 225, 03 18 227, 70 228, 03 228, 35 228, 67 228, 98 229, 32 22 231, 90 232, 23 232, 58 232, 93 233, 25 233, 62 26 236, 13 236, 48 236, 83 237, 20 237, 57 237, 93 30 240, 40 240, 77 241, 13 241, 52 242, 90 242, 28 A Table of oblique Ascensions. S. D. 7 8 9 10 11 12 ♐ 0 240, 40 240, 77 241, 13 241. 52 241. 90 242. 28 4 244, 70 245, 08 245, 47 245. 87 246. 27 246. 68 8 249, 03 249, 42 249, 83 250. 23 250. 65 251. 08 12 253, 37 253, 78 254, 20 254. 63 255. 05 255. 48 16 257, 73 258, 17 258, 60 259. 05 259. 48 259. 90 20 262, 12 262, 55 263, 00 263. 43 263. 88 264. 32 24 266, 52 266, 95 267, 40 267. 83 268. 28 268. 73 28 270, 88 271, 32 271, 77 272. 22 272. 67 273. 12 ♑ 2 275, 25 275, 68 276, 13 276. 58 277. 03 277. 48 6 279, 58 280, 02 280, 47 280. 92 281. 37 281. 82 10 283, 88 284, 32 284, 78 285. 20 285. 65 286. 08 14 288, 15 288, 58 289, 02 289. 47 289. 88 290. 32 18 292, 40 292, 80 293, 22 293. 65 294. 07 294. 50 22 296, 58 296, 97 297, 38 297. 80 298. 20 298. 63 26 300, 72 301, 10 301, 48 301. 88 302. 28 302. 68 ♒ 0 304, 80 305, 17 305, 53 305. 92 306. 30 306. 68 4 308, 80 309, 17 309, 52 309. 88 310. 23 313. 62 8 312, 75 313, 08 313, 43 313. 77 314. 10 314. 47 12 316, 65 316, 97 317, 28 317. 60 317. 92 318. 25 16 320, 50 320, 80 321, 08 321. 38 321. 68 321. 98 20 324, 28 324, 55 324▪ 82 325. 10 325. 37 325. 65 24 328, 02 328, 28 328, 52 328. 77 329. 18 329. 27 28 331, 70 331, 93 332, 15 332. 37 332. 60 332. 82 ♓ 2 335, 35 335, 53 335, 73 335. 93 336. 13 336. 33 6 338, 95 339, 13 339, 28 339. 47 339. 62 339. 80 10 342, 52 342, 67 342, 80 342. 95 343. 08 343. 23 14 346, 05 346, 17 346, 28 346. 40 346. 50 346. 63 18 349, 57 349, 65 349, 73 349. 82 349. 90 350. 00 22 353, 05 353, 12 353, 13 353. 22 353. 28 353. 33 26 356, 53 356, 57 356, 60 356. 62 356. 65 356. 67 30 360, 00 360, 00 360, 00 360. 00 360. 00 360. 00 A Table of oblique Ascensions. S. D. 13 14 15 16 17 18 ♈ 0 000, 00 000, 00 000, 00 000, 00 000, 00 000, 00 4 03, 28 03, 27 03, 23 03, 20 03, 17 03, 13 8 06, 60 06, 55 06, 48 06, 43 06, 37 06, 30 12 09, 93 09, 83 09, 75 09, 67 09, 57 09, 47 16 13, 27 13, 15 13, 02 12, 92 12▪ 78 12, 67 20 16, 63 16, 48 16, 33 16, 18 16, 03 15, 88 24 20, 03 19, 85 19, 67 19, 50 19, 32 19, 15 28 23, 47 23, 27 23, 07 22, 85 22, 65 22, 45 ♉ 2 26, 95 26, 72 26, 48 26, 25 26, 03 25, 78 6 30, 47 30, 22 29, 97 29, 70 29, 45 29, 17 10 34, 07 33, 80 33, 52 33, 22 32, 98 32, 63 14 37, 72 37, 40 37, 10 36, 78 36, 47 36, 15 18 41, 43 41, 10 40, 77 40, 43 40, 08 39, 73 22 45, 20 44, 83 44, 48 44, 13 43, 77 43, 40 26 49, 02 48, 65 48, 28 47, 90 47, 52 47, 12 ♊ 0 52, 92 52, 53 52, 15 51, 75 51, 33 50, 93 4 56, 92 56, 50 56, 08 55, 68 59, 25 54, 83 8 60, 97 60, 53 60, 10 59, 67 99, 25 58, 80 12 65, 07 64, 63 64, 20 63, 75 63, 28 62, 83 16 69, 23 68, 80 68, 35 67, 88 67, 92 66, 95 20 73, 47 73, 00 72, 55 72, 08 71, 62 71, 15 24 77, 73 77, 27 76, 82 76, 35 75, 88 75, 40 28 82, 07 81, 60 81, 13 80, 67 80, 20 79, 72 ♋ 2 86, 42 85, 95 85, 50 85, 02 84, 55 84, 07 6 90, 82 90, 35 89, 90 89, 42 88, 95 88, 47 10 95, 23 94, 77 94, 32 93, 85 9●, 38 92, 92 14 99, 65 99, 20 98, 77 98, 30 97, 83 97, 37 18 104, 08 103, 65 103, 22 102, 77 102, 30 101, 87 22 108, 52 108, 08 107, 67 107, 23 106, 80 106, 35 26 112, 92 112, 52 112, 10 111, 68 111, 27 110, 85 30 117, 32 116, 93 116, 55 116, 15 115, 73 115, 33 A Table of oblique Ascensions. S. D. 13 14 15 16 17 18 ♌ 0 117, 32 116, 93 116, 55 116, 15 115, 73 115, 33 4 121, 70 121, 33 120, 95 120, 58 120, 20 119, 80 8 126, 03 125, 70 125, 33 124, 98 124, 62 124, 25 12 130, 37 130, 03 129, 70 129, 37 129, 03 128, 68 16 134, 67 134, 37 134, 05 133, 73 133, 43 133, 10 20 138, 90 138, 63 138, 35 138, 05 137, 77 137, 47 24 143, 13 142, 88 142, 62 142, 37 142, 10 141, 83 28 147, 32 147, 08 146, 87 146, 63 146, 40 146, 17 ♍ 2 151, 48 151, 28 151, 07 150, 87 150, 67 150, 47 6 155, 62 155, 45 155, 27 155, 10 154, 92 154, 73 10 159, 73 159, 58 159, 43 159, 28 159, 13 158, 98 14 163, 82 163, 70 163, 57 163, 47 163, 33 163, 22 18 167, 88 167, 80 167, 70 167, 62 167, 52 167, 42 22 171, 93 171, 87 171, 82 171, 75 171, 68 171, 62 26 175, 97 175, 93 175, 92 175, 88 175, 85 175, 82 ♎ 0 180, 00 180, 00 180, 00 180, 00 180, 00 180, 00 4 184, 03 184, 07 184, 08 184, 12 184, 15 184, 18 8 188, 07 188, 13 188, 18 188, 25 188, 32 188, 38 12 192, 12 192, 20 192, 30 192, 38 192, 48 192, 58 16 196, 18 196, 30 196, 43 196, 53 196, 67 196, 78 20 200, 27 200, 42 200, 57 200, 72 200, 87 201, 02 24 204, 38 204, 55 204, 73 204, 90 205, 08 205, 27 28 208, 52 208, 72 208, 93 209, 13 209, 33 209, 53 ♏ 2 212, 68 212, 92 213, 13 213, 37 213, 60 213, 83 6 216, 87 217, 12 217, 38 217, 63 217, 90 218, 17 10 221, 10 221, 37 221, 65 221, 95 222, 23 222, 53 14 225, 33 225, 63 225, 95 226, 27 226, 57 226, 90 18 229, 63 229, 97 230, 30 230, 63 230, 97 2●1, 32 22 233, 97 234, 30 234, 67 235, 02 235, 38 235, 75 26 238, 30 238, 67 239, 05 239, 42 239, 80 240, ●0 30 242, 68 243, 07 243, 45 243, 85 244, 27 244, 67 A Table of oblique Ascensions. S. D. 13 14 15 16 17 18 ♐ 0 242, 68 243, 07 243, 45 243, 85 244, 27 244, 67 4 247, 08 247, 48 247, 90 248, 32 248, 73 249, 19 8 251, 48 251, 92 252, 33 252, 77 253, 20 253, 65 12 255, 92 256, 35 256, 78 257, 27 257, 70 258, 13 16 260, 35 260, 80 261, 23 261, 70 262, 17 262, 63 20 264, 77 265, 23 265, 68 266, 15 266, 62 267, 08 24 269, 18 269, 65 270, 10 270, 58 271, 05 271, 53 28 273, 58 274, 05 274, 50 274, 98 275, 45 275, 93 ♑ 2 277, 93 278, 40 278, 87 279, 33 279, 80 280, 28 6 282, 27 282, 73 283, 18 283, 65 284, 12 284, 60 10 286, 53 287, 00 287, 45 287, 92 288, 38 288, 85 14 290, 77 291, 20 291, 65 29●, 12 292, 08 293, 05 18 ●94, 9● 295, 37 295, 80 296, 25 296, 72 297, 17 22 299, 03 299, 47 299, 90 300, 33 300, 75 301, 20 26 303, 08 303, 50 303, 92 304, 32 304, 75 305, 17 ♒ 0 307, 08 307, 47 307, 85 308, 25 308, 67 309, 07 4 310, 98 311, 35 311, 72 312, 10 312, 48 312, 88 8 314, 80 315, 17 315, 52 315, 87 316, 23 316, 60 12 318, 57 318, 90 319, 23 319, 57 319, 92 320, 27 16 322, 38 322, 60 322, 90 323, 22 323, 53 323, 15 20 325, 93 326, 20 326, 48 326, 78 327, 07 327, 37 24 329, 53 329, 78 330, 03 330, 30 330, 55 330, 83 28 333, 05 333, 28 333, 52 33●, 75 333, 97 334, 22 ♓ 2 336, 53 336, 73 336, 93 337, 15 3●7, 35 337, 55 6 339, 07 340, 15 340, 33 340, 50 340, 68 340, 85 10 343, 37 343, 52 343, 67 343, 82 343, 97 344, 12 14 346, 73 346, 85 346, 98 347, 08 34●, 22 347, 33 18 350, 07 350, 17 350, 25 350, 33 350, 43 350, 53 22 353, 40 353, 45 353, 52 353, 57 353, 63 353, 70 26 356, 72 356, 73 356, 77 356, 80 356, 83 356, 87 30 360, 00 360, 00 360, 00 360, 00 360, 00 360, 00 A Table of oblique Ascensions. S. D. 19 20 21 22 23 24 ♈ 0 000, 00 000, 00 000. 00 000, 00 000, 00 000, 00 4 03, 12 03, 08 03. 05 03, 02 02, 98 02, 95 8 06, 25 0●, 18 06. 12 06, 05 05, 98 05, 92 12 09, 38 09, 28 09. 18 09, 10 09, 00 08, 90 16 12, 53 12, 42 12. 28 12, 17 12, 03 11, 90 20 15, 73 15, 58 15. 42 15, 27 15, 10 14, 93 24 18, 97 18, 78 18. 58 18, 40 18, 20 18, 00 28 22, 23 22, 02 21. 80 21, 58 21, 35 21, 13 ♉ 2 25, 38 25, 30 25. 05 24, 80 24, 55 24, 30 6 28, 92 28, 65 28. 35 28, 08 27, 80 27, 52 10 32, 35 32, 05 31. 73 31, 43 31, 12 30, 80 14 35, 83 35, 52 35. 17 34, 83 34, 50 34, 15 18 39, 40 39, 05 38. 68 38, 33 37, 95 37, 60 22 43, 03 42, 67 42. 28 41, 90 41, 50 41, 10 26 46, 73 46, 33 45. 93 45, 53 45, 12 44, 68 ♊ 0 50, 52 50, 10 49. 68 49, 25 48, 82 48, 37 4 54, 40 53, 97 53. 53 53, 07 52, 63 52, 15 8 58, 35 57, 90 57 45 56, 97 56, 50 56, 02 12 62, 38 61, 92 61. 45 60, 97 60, 47 59, 98 16 66, 48 66, 03 65. 53 65, 05 64, 53 64, 02 20 70, 67 70, 18 69. 68 69, 18 68, 67 68, 15 24 74, 92 74, 42 73. 92 73, 42 72, 90 72, 38 28 79, 22 78, 73 78. 22 77, 70 77, 20 76, 67 ♋ 2 83, 58 83, 08 82. 58 82, 07 81, 57 81, 03 6 87, 98 87, 48 86. 98 86, 48 85, 97 85, 45 10 92, 43 91, 95 91. 45 90, 95 90, 33 89, 92 14 96, 90 96, 42 95. 93 95, 48 94, 95 94, 47 18 101, 40 100, 92 100 47 99, 98 99, 48 98, 98 22 105, 92 105, 43 105. 00 104, 52 104, 05 103, 57 26 110, 42 109, 97 109. 53 109, 08 108, 63 108, 17 30 114, 92 114, 50 114. 08 113, 65 113, 50 112, 77 A Table of oblique Ascensions. S. D▪ 19 20 21 22 23 24 ♌ 0 114, 92 114, 50 114. 08 113, 65 113, 50 112, 77 4 119, 42 119, 02 118. 62 118, 20 117, 80 117, 37 8 123, 88 123, 51 123. 13 122, 73 122, ●5 121. 95 12 128, 33 128, 00 127. 63 127, 27 126, 90 126, 53 16 132, 78 132, 47 132. 12 131, 80 131, 45 131. 10 20 137, 18 136, 88 136. 57 136, 27 135, 95 135, 63 24 141, 58 141, 30 141. 01 140, 73 140, 47 140, 17 28 145, 92 145, 85 145. 42 145, 18 144, 9● 144, 67 ♍ 2 150, 25 150, 03 149. 82 149, 58 149, 37 149, 13 6 154, 57 154, 37 154. 18 153, 98 153, 80 153, 60 10 158, 83 158, 68 158. 52 158, 53 158, 20 158, 03 14 163, 10 162, 97 162. 85 162, 72 162, 60 162, 45 18 167, 33 167, 23 167. 15 167, 05 166, 97 166, 85 22 171, 57 171, 50 171. 43 171, 38 171, 32 171, 25 26 175, 80 175, 77 175. 73 175, 70 175, 67 175, 63 ♎ 0 180, 00 180, 00 180. 00 180, 00 180, 00 180, 00 4 184, 20 184, 23 184. 27 184, 30 184, 33 184, 37 8 188, 43 188, 50 188. 57 188, 62 188, 68 188, 75 12 192, 67 192, 77 192. 85 192, 95 193, 03 193, 15 16 196, 90 197, 03 197. 15 197, 28 197, 40 197, 55 20 201, 17 201, 32 201. 48 201, 47 201, 80 201, 97 24 205, 43 205, 63 205. 82 206, 02 206, 20 206, 40 28 209, 75 209, 97 210. 18 210, 42 210, 63 210, 87 ♏ 2 214, 08 214, 15 214. 58 214, 82 215, 07 215, 33 6 218, 42 218. 70 218. 99 219, 27 219, 53 219, 83 10 222, 82 223. 12 223. 43 223, 73 224, 05 224, 37 14 227, 22 227. 53 227. 88 228, 20 228, 55 228, 90 18 231, 67 232, 00 232. 37 232, 73 233, 10 233, 47 22 236, 12 236, 49 236. 87 237, 27 237, 65 238, 05 26 240, 58 240, 98 241. 38 241, 80 242, 20 242, 63 30 245, 08 245, 50 245. 92 246, 35 246, 50 247, 23 A Table of Oblique Ascensions. S. D. 19 20 21 22 23 24 ♐ 0 245, 08 245, 50 245, 92 246. 35 246, 50 247, 23 4 249, 58 250, 03 250, 47 250. 92 251, 37 251, 83 8 254, 08 254, 57 255, ●0 255. 48 255, 95 256, 43 12 258, 60 259, 08 259, 53 260. 02 260, 52 261, 02 16 263, 10 263, 58 264, 07 264. 52 265, 05 265, 53 20 267, 57 268, 05 268, 55 269. 05 269, 67 270, 08 24 272, 02 272, 52 273, 02 273. 52 274, 03 274, 55 28 276, 42 276, 92 277, 42 277. 93 278, 43 278, 97 ♑ 2 280, 78 281, 27 281, 78 282. ●0 282, 80 283, 33 6 285, 08 285, 58 286, 08 286. 58 287, 10 287, 62 10 289, 33 289, 82 290, 32 290. 82 291, 33 291, 85 14 293, 52 293, 97 294, 47 294. 95 295, 47 295, 98 18 297, 62 298▪ 0● 298, 55 299. 03 299, 53 300, 02 22 301, 65 302, 10 302, 55 30●. 03 303, 50 303, 98 26 305, 60 306, 03 306, 47 306. 93 307, 33 307, 85 ♒ 0 309, 48 309, 90 310, 32 310. ●5 311, 18 311, 63 4 313, 27 313, 67 314, 07 314. 47 314, 88 315, 32 8 316, 97 317, 33 317, 72 318. 10 318, 50 318, 90 12 320, 60 320, 95 321, 32 321. 67 322, 05 322, 40 16 324, 17 324, 48 324, 83 325. 17 325, 50 325, 85 20 327, 65 327, 95 328, 27 328. 57 328, 88 329, 20 24 331, 08 331, 35 331, 65 331. 92 332, 20 332, 48 28 334, 62 334, 70 334, 95 335. 20 335, 45 335, 70 ♓ 2 337, 77 337, 98 338, 20 338. 42 338, 65 338, 87 6 341, 03 341, 22 341, 42 341. 60 341, 80 342, 00 10 344, 27 344, 42 344, 58 344. 73 344, 90 345, 07 14 347, 47 347, 58 347, 72 347. 83 347, 97 348, 10 18 350, 62 350, 72 350, 82 350▪ 90 3●1, 00 351, 10 22 353, 75 353, 82 353. 88 353. 95 354, 02 354, 08 26 356, 88 356, 92 356. 95 356. 98 357, 02 357, 05 30 360, 00 360, 00 360. 00 360. 00 360, 00 360, 00 A Table of oblique Ascensions. S. D. 25 26 27 28 29 30 ♈ 0 000, 00 000, 00 000, 00 010, 00 000, 00 000, 00 4 02, 88 02, 95 02, 85 02, 80 22, 78 02, 73 8 05, 85 05, 78 05, 70 05, 63 05, 58 05, 50 12 08, 80 08, 70 08, 58 08, 48 08, 38 08, 27 16 11, 77 11, 63 11, 50 11, 35 11, 20 11, 07 20 14, 77 14, 60 14, 43 14, 25 14, 07 13, 90 24 17, 82 17, 60 17, 40 17, 18 16, 98 16, 77 28 20, 90 20, 67 20, 42 20, 18 19, 92 19, 68 ♉ 2 24, 01 23, 77 23, 48 23, 22 22, 92 22, 65 6 27, 22 26, 92 26, 62 26, 30 26, 00 25, 67 10 30, 48 30, 15 29, 82 29, 48 29, 13 28, 78 14 33, 82 33, 45 33, 07 32, 72 32, 32 31, 95 18 37, 22 36, 83 36, 43 36, 03 35, 62 35, 22 22 40, 70 40, 28 39, 88 39, 45 39, 00 38, 57 26 44, 25 43, 83 43, 37 42, 93 42, 47 42, 00 ♊ 0 47, 90 47, 47 47, 00 46, 32 46, 03 45, 53 4 51, 68 51, 20 50, 72 50, 22 49, 72 49, 20 8 55, 53 55, 03 54, 53 54, 00 53, 48 52, 95 12 59, 48 58, 97 58, 43 57, 90 57, 35 56, 82 16 63, 52 62, 98 62, 45 61, 92 61, 33 60, 78 20 67, 63 67, 10 66, 55 66, 00 65, 43 64, 85 24 71, 83 71, 30 70, 75 70, 18 69, 62 69, 03 28 76, 13 75, 58 75, 03 74, 47 73, 88 73, 30 ♋ 2 80, 50 79, 75 79, 40 78, 83 78, 25 77, 67 6 84, 92 84, 38 83, 83 83, 27 82, 68 82, 10 10 89, 40 88, 87 88, 32 87, 77 87, 20 86, 62 14 93, 93 93, 40 92, 85 92, 32 91, 75 91, 18 18 98, 48 97, 98 97, 45 96, 92 96, 35 95, 82 22 103, 08 102, 58 102, 08 101, 55 101, 03 100, 48 26 107, 68 107, 20 106, 73 106, 22 105, 72 105, 20 30 112, 30 111, 87 111, 40 110, 92 110, 43 109, 93 A Table of oblique Ascensions. S. D 25 26 27 28 29 30 ♌ 0 112, 30 111, 87 111. 40 110, 92 110, 43 109, 93 4 116, 93 116, 53 116. 07 115, 62 115, 15 114, 67 8 121, 55 121, 15 120. 71 120, 30 119, 85 119. 40 12 126, 17 125, 78 125. 38 124, 98 124, 57 124, 15 16 130, 77 130, 40 130. 03 129, 67 129, 28 128, 90 20 135, 32 134, 98 134. 65 134, 32 133, 97 133. 62 24 139, 87 139, 75 139, 28 138, 97 138, 65 138, 33 28 144, 40 144, 13 143. 87 143, 65 14●, 30 143, 03 ♍ 2 148, 92 148, 67 148. 43 148, 18 147, 95 147, 68 6 153, ●0 153, 20 153. 00 152, 78 152, 57 152, 35 10 157, 87 157, 70 157. 53 157, 35 157, 17 157, 03 14 162, 33 162, 18 162. 05 161, 90 161, 77 161, 62 18 166, 77 166, 65 166. 55 166, 43 166, 33 166, 22 22 171, 18 171, 12 170. 03 170, 97 170, 90 170, 82 26 175, 60 175, 57 175. 53 175, 40 175, 47 175, 42 ♎ 0 180, 00 180, 00 180. 00 180, 00 180, 00 180, 00 4 184, 40 184, 43 184. 47 184, 52 184, 53 184, 58 8 188, 82 188, 88 188. 97 189, 03 189, 10 189, 18 12 193, 23 193, 35 193. 45 193, 57 193, 67 193, 78 16 197, 67 197, 82 197. 95 198, 10 198, 23 198, 38 20 202, 13 202, 30 202. 47 202, 65 202, 83 202, 97 24 206, 60 206, 80 207. 00 207, 22 207, 43 207, 65 28 211, 08 211, 33 211. 57 211, 82 212, 05 212, 32 ♏ 2 215, 60 215, 87 216. 13 216, 35 216, 70 216, 97 6 220, 13 220. 25 220. 73 221, 03 221, 35 221, 67 10 224, 68 225. 02 225. 35 225, 68 226, 03 226, 38 14 229, 23 229. 60 229. 97 230, 33 230, 72 231, 10 18 233, 83 234, 22 234. 62 235, 02 235, 42 235, 85 22 238, 45 238, 85 239. 28 239, 70 240, 15 240, 60 26 243, 07 243, 47 243. 93 244, 38 244, 85 245, 33 30 247, 70 248, 13 248. 60 249, 08 249, 57 250, 07 A Table of oblique Ascensions. S. D. 25 26 27 28 29 30 ♐ 0 247, 70 248, 13 248, 60 249, 08 249, 57 250, 07 4 252, 32 252, 80 253, 27 253, 78 254, 28 254, 80 8 256, 92 257, 42 257, 92 258, 45 258, 97 259, 52 12 261, 52 262, 02 262, 55 263, 08 263, 65 264, 18 16 266, 07 266, 60 267, 15 267, 68 268, ●5 268, 82 20 270, 60 271, 13 271, 68 272, 2● 27●, 80 273, 38 24 275, 08 275, 62 276, 17 27●, 73 277, 32 277, 90 28 279, 50 280, 05 280, 60 281, ●7 281, 75 282, 33 ♑ 2 283, 87 284▪ 42 284, 97 28, 53 286, 12 2●6, 70 6 288, 17 288, 70 289, 25 289, 82 290, 35 290, 97 10 292, 37 292, 90 293, 45 294, 00 294, 57 295, 15 14 296, 48 297, 02 297▪ 55 298, 08 298, 67 299, 22 18 300, 52 301, 03 301, 57 302, 10 302, 65 303, 18 22 304, 47 304, 97 305, 47 306, 00 306, 52 307, 05 26 308, 32 308, 80 309, 28 309, 78 310, ●8 310, 80 ♒ 0 312, 10 312, 53 313, 00 313, 68 31●, 97 313, 47 4 314, 75 315, 17 316, 63 316, 07 317, 53 317, 00 8 319, 30 319, 72 320, 12 320, 55 321, 00 321, 43 12 322, 78 323, 17 323, 57 323, 97 324, 38 324, 78 16 326, 18 326, 55 326, 93 327, 28 327, 68 328, 05 20 329, 52 329, 85 330, 18 330, 52 330, 87 331, 22 24 332, 78 333, 08 333, 35 33●, 70 334, 00 334, 33 28 335, 99 336, 23 336, 52 336, 78 337, 08 337, 35 ♓ 2 339, 10 339, 33 339, 58 339, 82 340, 08 340, 32 6 342, 18 342, 40 342, 60 342, 82 343, 02 343, 23 10 345, 23 345, 40 345, 57 345, 75 345, 93 346, 10 14 348, 23 348, 37 34●, 50 348, 65 348, 80 348, 93 18 351, 20 351, 30 351, 42 351, 52 351, 62 351, 73 22 354, 15 354, 22 354, 28 354, 37 354, 42 354, 50 26 357, 12 357, 05 357, 15 357, 20 357, 22 357, 27 30 360, 00 360, 00 360, 00 360, 00 360, 00 360, 00 A Table of oblique Ascensions. S. D. 31 32 32. 18 33 34 35 ♈ 0 000, 00 000, 00 000. 00 000, 00 000, 00 000, 00 4 02, 70 02, 67 02. 66 02, 62 02, 58 02, 53 8 05, 43 05, 35 05. 34 05, 27 05, 18 05, 10 12 08, 17 08, 05 08. 03 07, 93 07, 80 07, 68 16 10, 92 10, 78 10. 75 10, 60 10, 45 10, 28 20 13, 70 13, 52 13. 49 13, 32 13, 02 12, 92 24 16, 53 16, 32 16. 28 16, 07 15, 85 15, 58 28 19, 42 19, 17 19 12 18, 87 18, 62 18, 32 ♉ 2 22, 35 22, 07 21. 01 21, 73 21, 43 21, 12 6 25, 33 25, 02 24. 96 24, 67 24, 32 23, 95 10 28, 42 28, 05 27. 98 27, 67 27, 28 26, 88 14 31, 55 31, 15 31. 08 30, 73 30, 32 29, 88 18 34, 78 34, 35 34. 27 33, 90 33, 45 32, 98 22 38, 10 37, 65 37. 57 37, 17 36, 68 36, 17 26 41, 52 41, 03 40. 94 40, 52 40, 00 39, 87 ♊ 0 45, 03 44, 52 44. 42 43, 98 43, 43 42, 87 4 48, 67 48, 12 47. 02 47, 55 47, 00 46, 40 8 52▪ 40 51, 83 51. 73 51, 25 50, 67 50, 05 12 56, 23 55, 63 55. 53 55, 05 54, 43 53, 82 16 60, 20 59, 60 59, 49 58, 98 58, 35 57, 70 20 64, 25 63, 65 63. 54 63, 02 62, 38 61, 72 24 68, 4● 67, 80 67. 69 67, 17 66, 52 65, 85 28 72, 68 72, 07 71. 96 71, 43 70, 78 70, 08 ♋ 2 77, 03 76, 4● 76. 31 75, 80 75, 15 74, 47 6 81, 48 80, 88 80. 77 80, 25 79, 60 78, 93 10 86, 02 85, 42 85. 31 84, 78 84▪ 15 83, 48 14 90, 62 90, 01 89. 90 89, 38 88, 77 88, 12 18 9●, ●7 94, 67 94. 57 94, ●7 93, 47 92, 83 22 99, 95 99, 38 99 28 98, 80 98, 22 97, 60 26 104, ●7 104, 12 104. 02 103, 57 103, 00 102, 40 30 109, 43 108, 92 108. 83 108, 38 107, 83 107, 27 A Table of oblique Ascensions. S. D 31 32 52 18 33 34 35 ♌ 0 1●9, 4● 108, 9● 108, 83 100LS, 38 107, 83 107, 27 4 114, 18 113, 70 113, 61 11●, 18 112, 67 112, 13 8 118, 95 118, 48 118, 40 118, 01 117, 52 117, 03 12 123, 72 123, 28 123, 20 122, 85 122, 38 121, 92 16 128, 52 128, 10 128, 03 127, 70 127, 27 126, 85 20 133, 25 132, 88 132, 81 132, 50 13●, 12 131, 72 24 138, 00 137, 68 137, 62 137, 32 136, 98 136, 62 28 142, 73 142, 43 142, 38 142, 12 141, 82 141, 48 ♍ 2 147, 43 147, 17 147, 12 146, 90 146, 63 146, 35 6 152, 13 151, 90 151, 86 151, 67 151, 43 151, 18 10 156, 80 156, 62 156, 58 156, 42 156, 22 156, 03 14 161, 47 161, 32 161, 29 161, 15 161, 00 160, 83 18 166, 12 166, 00 165, 98 165, 88 165, 77 165, 63 22 170, 80 170, 67 170, 66 170, 60 170, 52 170, 43 26 175, 38 175, 33 175, 32 175, 30 175, 27 175, 22 ♎ 0 180, 00 180, 00 180, 00 180, 00 180, 00 180, 00 4 184, 62 184, 67 184, 68 184, 70 184, 73 184, 78 8 189, 20 189, 33 189, 34 189, 40 189, 48 189, 57 12 193, 88 194, 00 194, 02 194, 12 194, 23 194, 37 16 198, 53 198, 68 198, 71 198, 85 199, 00 199, 17 20 203, 20 203, 38 203, 42 203, 58 203, 78 203, 97 24 207, 87 208, 10 208, 14 208, 33 208, 57 208, 82 28 212, 57 212, 83 212, 88 213, 10 213, 37 203, 65 ♏ 2 217, 27 217, 57 217, 62 217, 88 218, 18 218, 52 6 222, 00 222, 32 222, 38 222, 68 223, 02 223, 38 10 226, 75 227, 12 227, 19 227, 50 227, 88 228, 28 14 231, 48 231, 90 231, 97 232, 30 232, 73 23●, 15 18 236, 28 236, 72 236, 80 237, 15 237, 62 238, 08 22 241, 05 241, 52 241, 60 241, 99 242, 48 242, 97 26 245, 82 246, 30 246, 39 246, 82 247, 33 247, 87 30 250, 57 251, 08 251, 17 251, 62 252, 17 252, 73 A Table of oblique A scensions. S. D. 31 32 52. 18 33 34 35 ♐ 0 250, 57 251, 08 251, 17 251. 62 252, 17 252, 73 4 255, 33 255, 88 255, 98 256. 4● 257, 00 257, 60 8 260, 05 260, 6● 260, 71 261. 20 261, 78 262, 40 12 264, 73 265, ●3 265, 43 265. 93 26●, 53 267, 17 16 269, 38 269, 99 270, 10 270. 62 271, 23 271, 88 20 273, 90 274, 58 274, 69 275. 22 275, 85 276, 52 24 278, 52 279, 12 279, 23 279. 75 280, 40 281, 07 28 282, 97 283, 58 283, 69 284. 20 284, 85 285, 53 ♑ 2 287, 32 287, 93 288, 04 2●8. 57 289, 22 289, 92 6 291, 58 292, 20 292, 31 292. 83 293. 48 294, 15 10 295, 75 296, 15 296, 46 296. 98 297, 62 298, 28 14 299, 80 300, 40 300, 51 301. 02 301, 65 302, 30 18 303, 77 304, 37 304, 47 304. 95 305, 57 306, 18 22 307, 60 308, 17 308, 27 308. 75 309, ●3 309, 95 26 311, 33 311, 88 312, 98 312. 45 313, 00 313, 60 ♒ 0 314, 97 315, 48 315, 58 316. 02 316, 57 317, 13 4 318, 48 318, 97 319, 06 319. 48 320, 00 320, 13 8 321, 90 322, 35 322, 4● 322. 8● 323, 32 323, 83 12 325, 22 325, 65 325, 73 326. 10 326, 55 327, 02 16 328, 45 328, 85 328, 92 329. 27 329, 68 330, 12 20 331, 58 331, 95 332, 02 332. 33 332, 82 333, 12 24 334, 67 334, 98 335, 04 335. 33 335, 68 336, 05 28 337, 65 337, 93 338, 99 338. 27 338, 57 338, 88 ♓ 2 340, 58 340, 83 340, 88 341. 13 341, 38 341, 68 6 343, 47 343, 68 34●, 72 343. 93 344, 15 344, 42 10 346, ●0 346, 48 346, 51 346. 68 346, ●8 347, 08 14 349, 08 349, 22 349, 25 349. 40 349, ●5 349, 72 18 351, 83 351, 95 351, 97 352. 07 352, 20 352, 32 22 354, 57 354, 65 354. 66 354. 73 354, 82 354, 90 26 357, 30 357, 33 357. 34 357. 38 357, 42 357, 47 30 360, 00 360, 00 360. 00 360. 00 360, 00 360, 00 A Table of oblique Ascensions. S. D. 36 37 38 39 40 41 ♈ 0 000, 00 000, 00 000, 00 000, 00 000, 00 000, 00 4 02, 50 02, 13 02, 42 02, 37 02, 33 02, 27 8 05, 03 04, 93 04, 85 04, 77 04, 67 04, 57 12 07, 57 07, 43 07, 30 07, 17 07, 02 06, 88 16 10, 12 09, 95 09, 77 09, 58 09, 40 09, 22 20 12, 72 12, 50 12, 28 12, 05 11, 80 11, 58 24 15, 35 15, 10 14, 82 14, 57 14, 27 13, 98 28 18, 03 17, 75 17, 42 17, 12 16, 80 16, 47 ♉ 2 20, 77 20, 45 20, 08 19, 73 19, 37 18, 98 6 23, 58 23, 20 22, 82 22, 42 22, 00 21, 57 10 26, 48 26, 05 25, 63 25, 18 24, 73 24, 25 14 29, 43 28, 97 28, 52 28, 03 27, 53 27, 02 18 32, 50 32, 0● 31, 50 ●0, 97 30, 43 29, ●8 22 35, 67 35, 13 34, 58 34, 03 33, 45 32, 87 26 38, 93 38, 35 37, ●8 37, 18 ●6, 57 35, 93 ♊ 0 42, 30 41, 70 41, 10 40, 47 39, 82 ●9, 15 4 45, 80 45, 18 44, 53 4●, 9● 4●, 20 42, 50 8 49, 42 48, 78 48, 10 47, 43 46, 72 46, 00 12 53, 15 52, 50 51, 82 51, 10 50, 38 49, 63 16 57, 05 56, 37 55, 65 54, 93 54, 18 53, 42 20 61, 05 60, 35 5●, 6● 58, 88 58, 12 57, 33 24 65, 17 64, 47 63, 73 62, 99 62, 20 61, 40 28 69, 40 68, 70 67, 97 67, 22 66, 43 65, 63 ♋ 2 73, 78 73, 07 72, 33 71, 08 70, 78 69, 99 6 78, ●5 77, 55 76, 82 76, 07 75, 28 74, 48 10 82, 82 82, 12 81, 40 80, 65 79, 88 79, 10 14 87, 47 86, 77 86, 07 85, 35 84, ●8 83, 82 18 92, 18 91, 52 90, 83 90, 13 89, 40 88, 65 22 96, 97 96, 32 95, 67 94, 98 94, 28 93, 55 26 101, 82 101, 18 100, 57 99, 90 99, 22 98, 52 30 106, 70 106, 10 105, 50 104, 87 104, 22 103, 55 A Table of Oblique Ascensions. S. D. 36 37 38 39 40 41 ♌ 0 106, 70 106, 10 105, 50 104. 87 104▪ 22 103. 55 4 111, 60 111, 03 110, 45 109. 87 109. 25 108. 62 8 116, 50 115, 9● 115, 43 114. 88 114. 30 113. 70 12 121, 43 120, 95 120, 45 119. 92 119. 37 118. 82 16 126, ●8 125, 93 125, 46 124. 98 124. 47 123. 95 20 131, 32 130, 88 130, 47 130. 02 129. 57 129. 08 24 136, 25 135, 86 135. 47 135. 08 134. 67 134. 23 28 141, 15 140, 82 140, 46 140. 12 139. 73 139. 37 ♍ 2 146, 05 145, 75 145, 45 145. 13 144. 80 144. 48 6 150, 95 150, 68 150, 42 150. 14 149. 87 14●. 58 10 155, 82 155, 60 155, 38 155. 15 154. 90 154. 68 14 160▪ 68 160, 50 160, 32 160. 14 159. 95 159. 77 18 165, 52 165, 38 165, 25 165. 12 164. 98 164. 83 22 170, 35 170, 27 170, 17 170. 08 170. 00 169. 88 26 175, 18 175, 13 175, 10 175. 05 175. 00 174. 95 ♎ 0 180, 00 180, 00 180, 00 180. 00 180. 00 180. 00 4 184, 82 184, 87 184, 90 184. 95 185. 00 185. 05 8 189, 65 189, 73 189, 83 189. 92 190. 00 190. 12 12 194, 48 194, 62 194, 75 194. 88 194. 02 195. 17 16 199, 32 199, 50 199, 68 199. 86 200. 05 200. 23 20 204, 18 204, 40 204, 62 204. 85 205. 10 205. 32 24 209, 05 209, ●2 209, 58 209. 86 210. 13 210. 42 28 213, 95 214, 25 214, 55 214. 87 215▪ 20 215. 52 ♏ 2 218, ●5 219, 18 219, 54 219. 88 220. 27 220. 63 6 223, 75 224, 14 224, 5● 224. 92 225. 33 225. 77 10 228, 68 229, 12 229, 53 229. 98 230. 43 230. 92 14 233, 62 234, 07 234, 54 235. 02 235. 53 236. 05 18 238, 57 239, 05 239, 55 240. 08 240. 63 241. 18 22 243, 50 244, 02 244, 57 245. 12 245. 70 246. 30 26 248, 40 248, 97 249, 55 250. 13 250. 75 251. 38 30 253, 30 253, 90 254, 50 255. 13 255. 78 256. 45 A Table of oblique Ascensions. S. D. 36 37 38 39 40 41 ♐ 0 253, 30 25●, 90 254, 50 255, 13 255, 78 256, 45 4 258, 13 258, 82 259, 4● 260, 10 260, 78 261, 48 8 263, 03 263, 68 264, 33 265, 02 265, 72 266, 45 12 267, 82 268, 48 269, 17 269, 87 270, 60 271, 35 16 272, 53 273, 23 273, 93 274, 65 275, 42 276, 18 20 277, 18 277, 88 27●, 60 279, 35 280, 12 280, 90 24 281, 75 282, 45 283, 18 283, 93 284, 72 285, 52 28 286, 22 286, 93 287, 67 288, 92 289, 22 290, 01 ♑ 2 290, 60 291, ●0 291, 03 292, 78 293, 57 294, ●7 6 294, 83 295, 53 296, ●7 297, 01 279, 80 298, 60 10 298, 95 299, 65 300, 37 301, 12 301, 88 302, 67 14 302, 95 303, 63 304, 35 30●, 07 305, 82 306, 58 18 306, 85 307, 50 308, 18 308, 90 309, 62 310, 37 22 310, 58 311, 22 311, 90 312, 57 313, 28 314, 00 26 314, 20 314, 82 315, 47 316, 10 316, 80 317, 50 ♒ 0 317, 70 318, 30 318, 90 319, 53 320, 18 320, 85 4 321, 07 321, 65 322, 22 322, 82 323, 43 324, 07 8 324, 33 324, 87 325, 42 325, 97 326, 55 327, 13 12 327, 50 328, 00 328, 50 329, 03 329, 57 330, 12 16 330, 57 331, 03 331, 48 331, 97 332, 47 332, 98 20 333, 52 333, 95 334, 37 334, 82 335, 27 335, 75 24 336, 42 336, 80 337, 18 337, 58 338, 00 338, 43 28 339, 23 339, 55 339, 92 340, 27 340, 63 341, 02 ♓ 2 341, 97 342, 25 342, 58 342, 88 343, 20 343, 53 6 344, 65 344, 90 345, 18 345, 43 345▪ 73 346, 02 10 347, 28 347, 50 347, 72 347, 95 348, 20 348, 42 14 349, 88 350, 05 350, 23 350, 42 350, 60 350, 78 18 352, 43 352, 57 352, 70 352, 83 352, 98 353, 12 22 354, 97 355, 07 355, 15 355, 23 355, 33 355, 43 26 357, 50 357, 87 357, 58 357, 63 357, 67 357, 73 30 360, 00 360, 00 360, 00 360, 00 360, 00 360, 00 A Table of oblique Ascensions. S. D. 42 43 44 45 46 47 ♈ 0 000, 00 00, 00 000, 00 000, 00 000, 00 000, 00 4 02, 22 02, 18 02, 13 02, 07 02, 00 01, 92 8 04, 47 04, 37 04, 27 04, 15 04, 03 03, 92 12 06, 73 06, 57 06, 42 06, 25 06, 08 05, 92 16 09, 00 08, 80 08, 60 08, 38 08, 15 07, 92 20 11, 33 11, 07 10, 82 10, 53 10, 25 09, 97 24 13, 70 13, 40 13, 08 12, 73 12, 40 12, 05 28 16, 12 15, 77 15, 40 15, 02 14, 62 24, 20 ♉ 2 18, 60 18, 20 17, 77 17, 33 16, 88 16, 42 6 21, 13 20, 68 20, 20 19, 72 19, 22 18, 68 10 23, 77 23, 27 22, 75 22, 20 21, 65 21, 07 14 26, 48 25, 93 25, 37 24, 78 24, 17 23, 52 18 29, 30 28, 73 28, 10 27, 47 26, 78 26, 08 22 32, 25 31, 62 30, 95 30, 25 29, 55 28, 80 26 35, 27 34, 58 33, 88 33, 17 32, 38 31, 77 ♊ 0 38, 45 ●7, 73 36, 98 36, 23 35, 40 34, 57 4 41, 77 41, 03 40, 23 39, 42 38, 57 37, 68 8 45, 22 44, 45 43, 63 42, 78 41, 87 40, 97 12 48, 85 48, 03 47, 18 46, 30 45, 40 44, 42 16 52, 60 51, 77 50, 88 49, 98 49, 05 48, 05 20 56, 50 55, 65 54, 78 53, 83 52, 88 51, 87 24 60, 57 59, 72 58, 80 57, 87 56, 88 55▪ 87 28 64, 70 63, 92 63, 01 62, 07 61, 07 60, 05 ♋ 2 69, 03 68, 28 67, 35 66, 43 65, 45 64, 42 6 73, 65 72, 78 71, 88 70, 93 69, 97 68, 95 10 78, 27 77, 42 76, 53 75, 60 74, 65 73, 63 14 83, 02 82, 18 81, 30 80, 40 79, 47 78, 47 18 87, 87 87, 07 86, 20 85, 33 84, 4● 83, 43 22 92, 78 92, 01 91, 18 90, 33 89, 45 88, 52 26 97, 78 97, 03 96, 25 95, 43 94, 58 93, 70 30 102, 85 102, 13 101, 38 100, 62 99, 80 98, 97 A Table of oblique Ascensions. S. D. 42 43 44 45 46 47 ♌ 0 102, ●5 102, 13 100LS, 38 100 62 99, 80 98▪ 97 4 107, 95 107, 27 100LS, 57 105. 83 105▪ 07 104. 28 8 11●, 0● 112, 45 111, 78 111. 10 110. 38 109. 63 12 1●8, 25 117, 65 117, 0● 116. ●8 115. 73 115. 03 16 123, 4● 122, 88 122, 32 121. 70 121. 27 120. 47 20 128, 60 128, 10 127, 58 127. ●● 126. 48 125. 90 24 133, 90 133, 35 132, 87 132. 42 131. ●7 131. 33 28 138, 97 138, 57 138, 1● 137. 72 137. 25 136. 78 ♍ 2 144, 13 143, 78 143, 40 143. 03 142. 63 142. 50 6 149, 30 148, 98 14●, 67 148. 33 148. 00 147. 65 10 154, 43 154, 17 153, 92 153. 63 153. 35 153. 07 14 159, 57 159, 37 159, 15 158▪ 93 158. 70 158. 47 18 164▪ 68 164, 52 164, 37 164. 20 164. 03 163. 87 22 169▪ 80 169, 68 169, 58 169. 47 169. ●7 169. 25 26 174, 90 174, 85 174, 80 174. 73 174. 67 174. 63 ♎ 0 180, 00 180, 00 180, 00 180. 00 180. 00 180. 00 4 185, 10 185, 15 185, 20 185. 27 185. 33 185. 37 8 190, 20 190, 32 190, 42 190. 53 190. 63 190. 75 12 195, 32 195, 48 195, 63 195. 80 195. 97 196. 13 16 200, 43 200, 63 200, 85 201. 07 201. 30 201. 53 20 205, 57 2●5, 83 206, 08 206. 37 206. 65 206. 93 24 210, 70 211, 02 211, 33 211. 67 212. 00 212. 35 28 215, 87 216, 22 216, 60 216. 97 217. 37 217. 50 ♏ 2 221, 03 221, 43 221, 87 222. 28 222. 75 223. 22 6 226, 20 226, 65 2●7, 13 227. 58 228. 13 228. 67 10 231, 40 231, 90 232, 42 232. 97 233. 52 234. 10 14 236, 58 ●37, 12 237, 68 238. ●0 238. 73 239. 53 18 241, 75 242, 35 24●, 97 243. 62 244. 27 244. 97 22 246, 92 247, 55 248, 22 248. 90 249. 62 250. 37 26 252, 05 252, 73 253, 43 254. 17 254. 93 255. 72 30 257, 15 257, 87 258, 62 259, 38 260. 20 261. 03 A Table of Oblique Ascensions. S. D. 42 43 44 45 46 47 ♐ 0 257, 15 257, 87 258, 62 259, 38 260, 20 261, 03 4 262, ●2 262, 97 263, 75 264, 57 265, 42 266, 20 8 267, 22 267, 99 268, 82 209, 67 ●70, 55 271, 48 12 272, 13 272, 93 273, 80 274, 67 275, 58 276, 57 16 276, 98 277, 8● 278, ●0 279, 60 280, 53 281, 53 20 281, 73 282, 58 283, 47 284, 40 285, 35 286, 37 24 286, ●5 287, 22 288, 12 289, 07 290, 03 291, 05 28 290, 97 291, 72 292, 65 293, 57 294, ●5 295, 58 ♑ 2 295, 30 296, 08 296, 99 297, 93 298, 93 299, 95 6 299▪ 43 300, 28 301, 20 302, 13 303, 12 304, 13 10 30●, 50 304, 35 305, 32 306, ●7 307, 1● 308, 13 14 307, 40 308, 23 309, 12 310, 02 310, 95 311, 95 18 311, 15 311, 97 312, 82 313, 60 314, 60 315, 58 22 314, 78 315, 55 316, 37 317, 22 318, 13 319, 03 26 318, 23 318, 97 319, 77 320, 58 321, 43 322, 32 ♒ 0 321, 55 322, 27 323, 02 323, 77 324, 60 325, 43 4 324, 73 325, 42 326, 12 326, 83 327, 62 328, ●3 8 327, 75 328, 38 329, 05 329, 75 330, 45 331, 20 12 330, 70 331, 27 331, 90 332, 53 333, 22 333, 92 16 333, 52 334, 07 334, 63 335, 22 335, 83 336, 4● 20 336, 23 336, 73 337, ●5 337, 80 338, 35 338, 93 24 338, 87 339, 32 339, 80 340, 28 340, 78 341, 32 28 341, 40 341, 80 34●, 23 342, 67 343, 12 34●, 58 ♓ 2 343, ●8 344, 23 344, 60 344, 98 345, 38 345, ●0 6 346, 30 346, 60 346, 9● 347, 27 347, 60 347▪ 95 10 348, 63 34●, 9● 349▪ 18 349, 47 349, 75 350, 0● 14 351, 00 351, 20 351, 40 351, 62 351, ●5 352, ●8 18 353, 27 353, 4● 353, 58 35●, 75 35●, 92 354, ●8 22 355, 53 355, 63 355, 73 355, 8● 255, 97 ●56, ●8 26 357, 78 357, 82 357, 87 357, 93 358, 00 35●, 08 30 360, 00 360▪ 00 360, 00 360, 00 360, 00 3●0, 00 A Table of oblique Ascensions. S. D. 47. 47 48 49 50 51 51. 53 ♈ 0 00, 00 00, 00 00, 00 00, 00 00. 00 00, 00 4 01, 90 01, 88 01, 83 01, 77 01. 68 01, 65 8 03, 87 03, 80 03, 6● 03, 53 03. 40 03, 32 12 03, 83 05, 73 05, 53 05, 37 05. 13 05, 02 16 07, 81 07, 67 07, 42 07, 15 06. 87 06, 72 20 09, 82 09, 65 09, 3● 09, 00 08. 67 08, 48 24 11, 88 11, 68 11, 30 10, 92 10. 50 10, 27 28 14, 00 13, 77 13, 33 12, 87 12. 38 12, 12 ♉ 2 16, 19 15, 93 15, 42 14, 88 14. 33 14, 01 6 18, 43 18, 15 17, 57 16, 97 16. 35 16, 00 10 20, 73 20, 35 19, 82 19, 15 18. 47 18, 08 14 23, 18 22, 85 22, 17 21, 43 20. 67 20, 23 18 25, 73 25, 38 24, 47 23, 82 23. 01 22, 55 22 28, 40 28, 03 27, 22 26, 35 25. 47 24, 97 26 31, 22 30, 77 29, 88 28, 98 28. 02 27, 50 ♊ 0 34, 13 33, 68 32, 75 31, 78 30. 77 30, 20 4 37, 23 36, 75 35, 78 34, 77 33. 70 33, 10 8 40, 48 40, 01 38, 98 37, 92 36. 80 36, 13 12 43, 90 43, 40 42, 37 41, 23 40. 08 39, 43 16 47, 53 47, 02 45, 93 44. 78 4●. 58 42, 92 20 51, 38 50, 40 49, 70 4●, 53 47. 32 46, 60 24 55, 35 54, 80 53, 67 52, 48 51. 22 50, 50 28 59, 50 58, 97 57, 83 5●, 63 55. 37 54, 65 ♋ 2 63, 87 63, 3● 6●, 18 61, 00 59 73 59, 01 6 68, 42 67, 87 66, 73 65, 55 64. 30 63, 58 10 73, 12 72, 57 71, 47 70, 30 69. 07 68, 37 14 77, 97 77, 43 76, 33 75, 20 73. 98 73, 32 18 82, 93 82, 43 81, 40 80, 27 79. 13 7●, 47 22 88, 05 87, 57 86, 53 85, 35 84. 35 83, 72 26 93, 27 92, 77 91, 80 90, 78 89. 70 89, 10 30 98, 53 98, 08 97, 15 96, 18 95. 17 94, 60 A Table of oblique Ascensions. S. D 47. 47 48 49 50 51 51. 53 ♌ 0 098, 53 098, 08 097, 15 096, 18 095, 17 094, 60 4 103, 88 103, 45 100LS, 57 101, 67 100, 70 100, 17 8 109, 27 108, 87 103, 05 107, 20 106, 30 105, 80 12 114, 70 114, 32 113. 77 112, 77 111, 95 111, ●8 16 120, 15 119, 80 119. 12 118, 38 117, 62 117, 18 20 125, 62 125, 28 124. 65 123, 98 123, 30 122, 92 24 131, 08 130, 82 130. 2● 129, 62 129, 02 128, 67 28 136, 53 136, 30 135. 80 135, 27 134, 72 134, 40 ♍ 2 142, 02 141, 78 141. 35 140, 88 140, 40 140, 13 6 147, 43 147, 28 146. 90 146, 50 146, 10 145, 87 10 152, 92 152, 75 152. 43 152, 10 151, 77 151, 57 14 158, 33 158, 22 157. 97 157, 70 157, 43 157, 27 18 163, 75 163, 68 163. 48 163, 28 163, 08 162, ●7 22 169, 18 169, 13 169. 00 168, 87 168, 73 168, 65 26 17●, 60 174, 57 174. 51 174, 45 174, 37 174, 33 ♎ 0 180, 00 180, 00 180. 00 180, 00 180, 00 180, 00 4 185, 40 185, 43 185. 49 185, 55 185, 63 185, 67 8 190, 82 190, 87 191. 00 191, 13 191, 27 191, 35 12 196, 25 196, 32 196. 52 196, 72 196, 92 197, 03 16 201, 67 201, 78 202. 03 202, 30 202, 57 202, 73 20 207, 08 207, 25 207. 57 207, 90 208, 23 208, 43 24 212, 57 212, 72 213. 10 213, 50 213, 90 214, 13 28 217, ●8 218, 22 218. 65 219, 12 219, 60 219, 87 ♏ 2 223, 47 223. 70 224. 20 224, 73 225, 28 225, 60 6 228, 92 229. 18 229. 78 230, 38 230, 98 231, ●3 10 234, 38 234, 72 235. 35 236, 02 236, 70 237, 08 14 239, 85 240. 20 240. 20 241, 6● 242, 38 242, 82 18 245, 30 245, 68 246, 62 247, 23 248, 05 248, 52 22 250, 73 251, 13 251. 9● 252, 70 253, 70 254, 20 26 256, 12 256, 55 257. 43 258, 33 259, 30 259, ●3 30 261, 47 261, 92 262. 85 26●, 82 264, 83 265, 40 A Table of oblique Ascensions. S. D. 47 48 49 50 51 51. 53 ♐ 0 261, 47 261, 92 262, 85 263, 12 264, 83 265, 40 4 266, 23 267, 23 268, 20 269, 20 270, 30 270, 90 8 272, 95 272, 43 273, 47 274, 65 275, 65 276, 28 12 277, 07 277, 57 278, 60 279, 72 280, 87 281, 53 16 282, 03 282, 57 283, 67 284, 80 286, 02 286, 68 20 286, 88 287, 43 288, 53 289, 70 290, 93 291, 63 24 291, 58 292, 13 293, 27 294, 45 295, 70 296, 42 28 296, 13 296, 67 297, 82 299, 00 300, 27 300, 99 ♑ 2 300, 50 301, 03 30●, 17 303, 37 304, 63 305, 35 6 304, 65 305, 20 306, 33 307, 52 308, 78 309, 50 10 308, 62 309, 60 310, 30 311, 47 312, 68 313, 40 14 312, 47 312, 98 314, 07 315, 22 316, 42 317, 08 18 316, 10 316, 60 317, 63 318, 77 319, 92 320, 57 22 319, 52 319, 99 321, 02 322, 08 313, 20 343, 17 26 322, 77 323, 25 324, 22 325, 23 326, 30 326, 90 ♒ 0 325, 87 326, 32 327, 25 328, 22 329, 23 329, 80 4 328, 78 329, 23 330, 12 331, 02 331, 98 332, 50 8 331, 60 331, 97 3●2, 78 333, 65 334, 53 335, 03 12 334, 27 334, 62 335, 53 336, 18 336, 99 337, 45 16 336, 82 337, 15 337, 83 338, 57 339, 33 339, 77 20 339, 27 339, 65 340, 18 340, 85 341, 53 341, 92 24 341, 57 341, 85 342, 43 343, 03 343, 65 344, 00 28 343, 81 344, 07 344, 58 345, 12 345, 67 345, 99 ♓ 2 346, 00 346, 23 346, 67 347, 13 347, 62 347, 88 6 34●, 12 348, 32 348, 70 349, 08 349, 50 349, 7● 10 350, 18 350, 35 350, 67 351, 00 351, 33 351, 52 14 352, 19 352, 33 352, 58 352, 85 353, 13 353, 28 18 354, 17 354, 27 354, 47 354, 63 354, 87 354, 98 22 356, 13 356, 20 356, 33 356, 47 356, 60 356, 68 26 358, 10 358, 12 358, 17 358, 32 358, 32 358, 35 30 360, 00 360, 00 360, 00 360, 00 360, 00 360, 00 A Table of oblique Ascensions. S. D. 52 53 54 55 56 57 ♈ 0 00, 00 00, 00 00. 00 00, 00 00, 00 00, 00 4 01, 62 01, 53 01. 47 01, 38 01, 30 01, 20 8 0●, 25 03, 10 02. 95 02, 78 02, 62 02, 43 1● 04, 92 04, 68 04. 45 04, 20 03, 95 03, 67 16 06, 58 06, 28 05. 97 05, 65 05, 28 04, 93 20 08, 30 07, 92 07. 53 07, 12 06, 68 06, 22 24 10, 07 09, 60 09. ●3 08, 63 08, 10 07, 55 28 11, 88 11, 33 10. 78 10, 22 09, 58 08, 93 ♉ 2 13, 75 13, 13 12. 33 11, 83 11, 12 10, 37 6 15, 70 15, 02 14. 30 13, 53 12, 73 11, 87 10 17, 75 16, 98 16. 18 15, 33 14, 43 13, 48 14 19, 87 19, 03 18. 13 17, 50 16, 22 15, 18 18 22, 13 21, 22 20. 25 19, 23 18, 15 17, 00 22 24, 52 23, 52 22. 47 21, 37 20, 20 18, 93 26 27, 03 25, 97 24. 83 23, 65 22, 37 21, 01 ♊ 0 29, 70 28, 37 27. 37 26, 10 24, 73 23, 28 4 32, 57 31, 37 30. 10 28, 73 27, 32 25, 75 8 35, 60 34, 37 33. 01 31, 58 30, 08 28, 45 12 38, 85 37, 53 36. 13 34, 68 33, 05 31, 35 16 42, 32 40, 95 39 52 37, 98 36, 33 34, 55 20 45, 98 44, 60 43. 12 41, 55 39, 85 38, 00 24 49, 88 48, 48 46. 97 45, 38 43, 63 41, 77 28 54, 03 52, 58 51. 08 49, 47 47, 73 45, 85 ♋ 2 58, 40 56, 98 55. 47 53, 82 52, 08 50, 20 6 6●, 97 61, 55 60. 05 58, 45 56, 72 54, 83 10 67, 75 66, 37 64. 88 63, 32 61, 62 59, 77 14 72, 73 71, 37 69. 93 68, 40 66, 73 64, 95 18 77, 87 76, 57 75. 17 73, 68 72, 08 70, 38 22 83, 17 81, 92 80. 58 79, 13 77, 62 75, 98 26 88, 57 87, 37 86. 10 84, 75 83, 32 81, 77 30 94, 10 92, 97 91. 77 90, 63 89, 13 87, 68 A Table of oblique Ascensions. S. D. 52 53 54 55 56 57 ♌ 0 094, 10 092, 97 091, 77 090, 63 089, 13 087, 68 4 099, 70 098, 63 097, 52 096, 33 095, 07 09●, 70 8 105. 37 104, 37 103, 32 102, 23 101, 05 099, 78 12 111, 07 110, 15 109, 18 108, 17 107, 08 105, 93 16 116, 82 115, 98 115, 08 114, 18 113, 17 112, 12 20 122, 58 121, 82 121, 01 120, 19 119, 27 118, 32 24 128, 37 127, 68 126, 95 126, 20 125, 40 124, 52 28 134, 13 133, 53 132, 88 132, 21 131, 50 130, 75 ♍ 2 139, 90 139, 37 138, 80 138, 22 137, 60 136, 95 6 145, 67 145, 20 144, 72 144, 22 143, 70 143, 13 10 151, 40 151, 01 150, 63 150, 21 149, 78 149, 32 14 157, 13 156, 83 156, 52 156, 18 155, 85 155, 48 18 162, 87 162, 63 162, 40 162, 17 161, 90 161, 62 22 168, 58 168, 43 168, 27 168, 12 167, 95 167, 75 26 174, 30 174, 22 174, 13 174, 07 173, 98 173, 88 ♎ 0 180, 00 180, 00 180, 00 180, 00 180, 00 180, 00 4 185, 70 185, 78 185, 87 185, 93 186, 02 186, 12 8 191, 42 191, 57 191, 73 191, 88 192, 05 192, 25 12 197, 13 197, 37 197, 60 197, 83 198, 10 198, 38 16 202, 87 203, 17 203, 48 203, 82 204, 15 204, 52 20 208, 60 208, 99 209, 37 209, 79 210, 22 210, 68 24 214, 32 214, 80 215, 28 215, 78 216, 30 216, 87 28 220, 10 220, 63 221, 20 221, 78 222, 40 223, 05 ♏ 2 225, 87 226, 47 227, 12 227, 79 228, 50 229, 25 6 231, 63 232, 32 233, 05 233, 80 234, 60 235, 48 10 237, 42 238, 18 238, 99 239, 81 240, 73 241, 68 14 243, 18 244, 02 244, 92 245, 82 246, 83 247, 88 18 248, 93 249, 85 250, 82 251, 83 252, 92 254, 07 22 254, 62 295, 63 256, 68 257, 77 258, 95 260, 22 26 260, 30 261, 37 262, 48 263, 67 264, 93 266, 30 30 265, 90 267, 03 268, 23 269, 37 270, 87 272, 32 A Table of oblique Ascensions. S. D. 52 53 54 55 56 57 ♐ 0 265, 90 267, 03 268, 23 269, 37 270, 87 272, 32 4 271, 43 272, 63 273, 90 275, 25 276, 68 278, 23 8 276, 83 278, 08 279, 42 280, 87 282, 38 284, 02 12 282, 13 283, 43 284, 83 286, 3● 287, 92 289, 62 16 287, ●7 288, 63 290, 07 291, 60 293, 27 295, 05 20 292, 25 293, 63 295, 12 296, 68 298, 38 300, 23 24 297, 03 298, 45 299, 95 301, 55 303, 28 305, 17 28 301, 60 303, 02 304, 53 306, 18 307, 92 309, 80 ♑ 2 305, 97 307, 42 308, 92 310, 53 312, 27 314, 15 6 310, 12 311, 52 313, 03 314, 62 316, 37 318, 23 10 314, 02 315, 40 316, 88 318, 45 320, 15 322, 00 14 317, 68 319, 05 320, 48 322, 02 323, 67 325, 45 18 321, 15 322, 47 323, 87 325, 32 326, 95 328, 65 22 324, 40 325, 63 326, 99 328, 42 329, 92 331, 55 26 327, 43 328, 63 329, 90 331, 27 332, 68 334, 25 ♒ 0 330, 30 331, 43 332, 63 333, 90 335, 27 336, 72 4 332, 97 334, 03 335, 17 336, 35 337, 63 338, 99 8 335, 48 336, 48 337, 53 338, 63 339, 80 341, 07 12 337, 87 338, 78 339, 75 340, 77 341, ●5 343, 00 16 340, 13 340, 97 341, 87 342, 50 343, 78 344, 82 20 342, 25 343, 02 343, 82 344, 67 345, 57 346, 52 24 344, 30 344, 98 345, 70 346, 47 347, 27 348, 13 28 346, 25 346, 87 347, 67 348, 17 348, 88 349, 63 ♓ 2 348, 15 348, 67 349, 22 349, 78 350, 42 351, 07 6 349, 12 350, 40 350, 87 351, 37 351, 90 352, 45 10 351, 93 352, 08 352, 47 352, 88 353, 32 353, 78 14 353, 70 353, 72 354, 03 354, 35 354, 72 355, 07 18 355, 42 355, 32 355, 55 355, 80 356, 05 356, 33 22 356, 08 356, 90 357, 05 357, 22 357, 38 357, 57 26 358, 75 358, 43 358, 53 358, 62 358, 70 358, 80 30 360, 00 360, 00 360, 00 360, 00 360, 00 360, 00 A Table of Positions for the Pole of 1 2 3 4 5 6 7 North Declination under the Earth, and South above it. 0 0, 79 1, 58 2, 38 3, 17 3, 98 4, 80 5, 62 1 0, 78 1, 55 2, 33 3, 10 3, 90 4, 70 5, 50 2 0, 75 1, 52 2, 27 3, 03 3, 82 4, 58 5, 37 3 0, 73 1, 48 2, 22 2, 95 3, 73 4, 48 5, 25 4 0, 72 1, 45 2, 17 2, 88 3, 63 4, 38 5, 12 5 0, 70 1, 42 2, 12 2, 82 3, 55 4, 27 5, 00 6 0, 68 1, 38 2, 07 2, 75 3, 45 4, 17 4, 88 7 0, 67 1, 35 2, 01 2, 67 3, 37 4, 07 4, 75 8 0, 65 1, 30 1, 97 2, 60 3, 28 3, 95 4, 63 9 0, 63 1, 27 1, 90 2, 53 3, 18 3, 85 4, 50 10 0, 60 1, 23 1, 85 2, 47 3, 10 3, 73 4, 38 11 0, 58 1, 20 1, 80 2, 38 3, 02 3, 63 4, 25 12 0, 57 1, 17 1, 75 2, 32 2, 92 3, 52 4, 12 13 0, 55 1, 12 1, 68 2, 23 2, 83 3, 42 4, 00 14 0, 53 1, 08 1, 63 2, 17 2, 73 3, 30 3, 87 15 0, 52 1, 05 1, 58 2, 10 2, 63 3, 18 3, 73 16 0, 50 1, 01 1, 52 2, 01 2, 55 3, 07 3, 60 17 0, 48 0, 97 1, 47 1, 93 2, 45 2, 97 3, 47 18 0, 47 0, 93 1, 40 1, 87 2, 35 2, 85 3, 33 19 0, 43 0, 90 1, 35 1, 78 2, 25 2, 73 3, 20 20 0, 42 0, 85 1, 28 1, 72 2, 17 2, 60 3, 05 21 0, 40 0, 82 1, 23 1, 63 2, 07 2, 48 2, 92 22 0, 38 0, 77 1, 17 1, 55 1, 95 2, 37 2, 77 23 0, 37 0, 73 1, 10 1, 47 1, 85 2, 25 2, 63 24 0, 33 0, 70 1, 05 1, 38 1, 75 2, 12 2, 48 25 0, 32 0, 65 0, 98 1, 30 1, 65 1, 98 2, 33 26 0, 30 0, 60 0, 92 1, 22 1, 53 1, 87 2, 18 27 0, 27 0, 57 0, 85 1, 12 1, 43 1, 73 2, 03 28 0, 25 0, 52 0, 78 1, 03 1, 32 1, 60 1, 87 29 0, 23 0, 47 0, 72 0, 95 1, 20 1, 47 1, 72 30 0, 20 0, 43 0, 65 0, 85 1, 08 1, 32 1, 55 31 0, 18 0, 38 0, 58 0, 77 0, 97 1, 18 1, 38 32 0, 17 0, 33 0, 50 0, 76 0, 85 1, 03 1, 22 Latitude of 51 deg. 53 parts. Position. 1 2 3 4 5 6 7 South Declination under the Earth, and North above it. 32 1. 40 2, 83 4, 27 5, 67 7, 12 8, 57 10, 02 31 1. 38 2, 78 4, 18 5, 57 7, 00 8, 42 9, 85 30 1. 37 2, 73 4, 12 5, 48 6, 88 8, 28 9, 68 29 1. 33 2, 70 4, 05 5, 38 6, 77 8, 13 9, 52 28 1. 31 2, 65 3, 98 5, 30 6, 65 8, 00 9, 37 27 1. 30 2, 60 3, 91 5, 22 6, 53 7, 87 9, 20 26 1. 27 2, 57 3, 85 5, 12 6, 43 7, 73 9, 05 25 1. 25 2, 51 3, 78 5, 03 6, 32 7, 62 8, 90 24 1. 23 2, 47 3, 72 4, 95 6, 22 7, 48 8, 75 23 1. 20 2, 43 3, 67 4, 87 6, 12 7, 35 8, 60 22 1. 18 2, 40 3, 60 4, 78 6, 02 7, 23 8, 47 21 1. 17 2, 35 3, 5● 4, 70 5, 90 7, 12 8, 32 20 1. 15 2, 31 3, 48 4, 62 5, 80 7, 00 8, 18 19 1. 13 2, 27 3, 41 4, 55 5, 72 6, 87 8, 03 18 1. 10 2, 23 3, ●7 4, 47 5, 62 6, 75 7, 90 17 1. 08 2, 20 3, 30 4, 40 5, 52 6, 63 7, 73 16 1. 07 2, 15 3, 25 4, 31 5, 42 6, 53 7, 63 15 1. 05 2, 12 3, 18 4, 23 5, 33 6, 42 7, 50 14 1. 03 2, 08 3, 13 4, 17 5, 23 6, 30 7, 37 13 1. 02 2, 05 3, 08 4, 10 5, 13 6, 18 7, 23 12 1. 00 2, 01 3, 02 4, 02 5, 05 6, 08 7, 12 11 0. 98 1, 97 2, 97 3, 95 4, 95 5, 97 6, 98 10 0. 97 1, 93 2, 91 3, 87 4, 87 5, 87 6, 85 9 0. 93 1, 90 2, 85 3, 80 4, 78 5, 75 6, 73 8 0. 91 1, 87 2, 80 3, 73 4, 68 5, 65 6, 60 7 0. 90 1, 83 2, 75 3, 67 4, 60 5, 53 6, 48 6 0. 88 1, 80 2, 70 3, 58 4, 52 5, 43 6, 35 5 0. 87 1, 75 2, 65 3, 52 4, 42 5, 33 6, 23 4 0. 85 1, 71 2, 58 3, 45 4, 3● 5, 22 6, 12 3 0. 83 1, 68 2, 53 3, 38 4, 35 5, 12 5, 98 2 0. 81 1, 65 2, 48 3, 30 4, 15 5, 02 5, 87 1 0. 80 1, 62 2, 4● 3, 23 4, 07 4, 90 5, 73 0 0. 97 1, 58 2, 38 3, 17 3, 98 4, 80 5, 62 A Table of Positions for the Pole of 8 9 10 11 12 13 14 North Declination under the Earth, and South above it. 0 6, 45 7, 22 8, 05 8, 88 9, 73 10, 57 11, 60 1 6, 32 7, 07 7, 87 8, 68 9, 52 10, 33 11, 18 2 6, 17 6, 90 7, 70 8, 50 9, 32 10, 10 10, 9● 3 6, 03 6, 73 7, 52 8, 30 9, 10 9, 87 10, 68 4 5, ●8 6, 58 7, 35 8, 10 8, 88 9, 63 10, 43 5 5, 75 6, 42 7, 17 7, 92 8, 67 9, 42 10, 18 6 5, 60 6, 17 6, 98 7, 72 8, 45 9, 18 9, 93 7 5, 47 6, 10 6, 82 7, 51 8, 23 8, 95 9, 68 8 5, 32 5, 95 6, 63 7, 31 8, 02 8, 70 9, 43 9 5, 18 5, 78 6, 45 7, 11 7, 80 8, 47 9, 17 10 5, 03 5, 62 6, 27 6, 91 7, 58 8, 23 8, 92 11 4, 88 5, 45 6, 08 6, 71 7, 37 8, 00 8, 65 12 4, 73 5, 28 5, 90 6, 51 7, 15 7, 75 8, 40 13 4, 58 5, 12 5, 72 6, 31 6, 92 7, 52 8, 13 14 4, 45 4, 95 5, 53 6, 10 6, 70 7, 27 7, 87 15 4, 28 4, 78 5, 35 5, 90 6, 47 7, 02 7, 60 16 4, 13 4, 62 5, 15 5, 69 6, 23 6, 77 7, 33 17 3, 98 4, 43 4, 97 5, 48 6, 00 6, 52 7, 07 18 ●, 83 4, 27 4, 73 5, 27 5, 77 6, 27 6, 78 19 3, 68 4, 08 4, 57 5, 05 5, 45 6, 00 6, 52 20 3, 52 3, 92 4, 37 4, 83 5, 23 5, 75 6, 23 21 3, 35 3, 73 4, 17 4, 60 5, 05 5, 48 5, 93 22 3, 20 3, 55 3, 97 4, 38 4, 80 5, 22 5, 65 23 ●, 03 3, 37 3, 75 4, 15 4, 55 4, 95 5, 32 24 2, 87 3, 17 3, 55 3, 92 4, 30 4, 67 5, 07 25 2, 70 2, 98 3, 33 3, 68 4, 05 4, 38 4, 75 26 2, 52 2, 78 3, 12 3, 45 3, 78 4, 10 4, 45 27 2, 35 2, 58 2, 90 3, 20 3, 52 3, 82 4, 13 28 2, 17 2, 38 2, 67 2, 95 3, 25 3, 52 3, 82 29 1, 98 2, 18 2, 43 2, 70 2, 97 3, 22 3, 48 30 1, 80 1, 98 2, 20 2, 43 2, 68 2, 90 3, 15 31 1, 60 1, 75 1, 97 2, 18 2, 40 2, 60 2, 82 32 1, 42 1, 53 1, 72 1, 90 2, 10 2, 27 2, 47 Latitude of 51 deg. 53 parts. Position 8 9 10 11 12 13 14 South Declination under the Earth, And North above it. 32 11, 48 12, 90 14. 38 15, 87 17, 37 18, 87 20, 40 31 11, 30 12, 68 14. 13 15, 58 17, 07 18, 53 20, 05 30 11, 10 12, 47 13. 90 15, 33 16, 78 18, 23 19, 72 29 10, 92 12, 25 13. 67 15, 07 16, 50 17, 92 19, 38 28 10, 73 12, 05 13. 43 14, 82 16, 22 17, 61 19, 05 27 10, 55 11, 85 13. 20 14, 57 15, 95 17, 31 18, 73 26 10, 38 11, 65 12. 98 14, 32 15, 68 17, 03 18, 42 25 10, 20 11, 45 12. 77 14, 08 15, 42 16, 75 18, 12 24 10, 03 11, 27 12. 55 13, 85 15, 17 16, 47 17, 80 23 9, 87 11, 07 12. 35 13, 62 14, 9● 16, 18 17, 55 22 9, 70 10, 88 12. 13 13, 38 14, 67 15, 92 17, 22 21 9, 55 10, 70 11. 93 13, 17 14, 42 15, 65 16, 93 20 9, 38 10, 52 11. 73 12, 93 14, 17 15, 38 16, 63 19 9, 22 10, 35 11. 53 12, 72 14, 02 15, 13 16, 35 18 9, 07 10, 17 11. 33 12, 50 13, 70 14, 87 16, 08 17 8, 92 10, 00 11. 13 12, 28 13, 47 14, 62 15, 80 16 8, 77 9, 82 10. 95 12, 08 13, 23 14, 37 15, 53 15 8, 62 9, 65 10. 75 11, 87 13, 00 14, 12 15, 27 14 8, 45 9, 48 10. 57 11, 67 12, 77 13, 87 15, 00 13 8, 32 9, 32 10. 38 11, 45 12, 57 13, 62 14, 73 12 8, 17 9, 15 10. 20 11, 25 12, 32 13, 38 14, 47 11 8, 01 8, 98 10. 01 11, 05 12, 10 13, 13 14, 22 10 7, 87 8, 82 9 83 10, 85 11, 88 12, 90 13, 95 9 7, 72 8, 65 9 65 10, 65 11, 67 12, 67 13, 70 8 7, 58 8, 48 9 47 10, 45 11, 45 12, 43 13, 43 7 7, 43 8, 33 9 28 10, 25 11, 23 12, 18 13, 18 6 7, 30 8, 17 9 12 10, 05 11, 02 11, 95 12, 93 5 7, 15 8, 02 8. 93 9, 85 10, 80 11, 72 12, 68 4 7, 02 7, 85 8. 75 9, 67 10, 58 11, 50 12, 43 3 6, 87 7, 70 8. 58 9, 47 10, 37 11, 27 12, 18 2 6, 73 7, 5● 8. 40 9, 27 10, 15 11, 03 11, 93 1 6, 58 7, 37 8. 23 9, 08 9, 95 10, 80 11, 68 0 6, 45 7, 22 8. 05 8, 88 9, 73 10, 57 11, 43 A Table of Positions for the Pole of 15 16 17 18 19 20 21 North Declination under the Earth, and South above it. 0 12, 30 13. 18 14, 07 14, 95 15. 87 16, 80 17, 77 1 12, 03 12. 90 13, 77 14, 63 15. 52 16, 43 17, 38 2 11, 77 12. 62 13, 45 14, 30 15. 18 16, 07 17, 00 3 11, 50 12. 32 13, 15 13, 97 14. 83 15, 70 16, 62 4 11, 23 12. 07 12, 83 13, 65 14. 48 15, 35 16, 23 5 10, 97 11. 75 12, 53 13, 32 14. 13 14, 98 15, 85 6 10, 68 11. 45 12, 23 13, 00 13. 80 14, 60 15, 45 7 10, 35 11. 17 11, 92 12, 67 13. 45 14, 23 15, 07 8 10, 01 10. 87 11, 60 12, 3 13, 10 13, 87 14, 67 9 9, 97 10. 58 11, 28 12, 00 12, 73 13, 50 14, 28 10 9, 60 10. 28 10, 98 11, 67 12, 38 13, 12 13, 88 11 9, 32 9 98 10, 67 11, 33 12, 03 12, 75 13, 48 12 9, 03 9 6● 10, 33 10, 98 11, 67 12, 37 13, 08 13 8, 75 9 38 10, 02 10, 65 11, 30 11, 98 12, 68 14 8, 47 9 08 9, 70 10, 30 10, 95 11, 60 12, 27 15 8, 18 8, 78 9, 37 9, 95 10, 57 11, 20 11, 87 16 7, 90 8. 47 9, 03 9, 60 10, 20 10, 82 11, 45 17 7, 60 8. 15 8, 70 9, 25 9, 83 10, 42 11, 03 18 7, 30 7. 83 8, 37 8, 88 9, 45 10, 01 10, 60 19 7, 00 7. 52 8, 01 8, 53 9, 05 9, 60 10, 17 20 6, 70 7. 20 7, 68 8, 17 8, 67 9, 18 9, 73 21 6, 40 6. 87 7, 33 7, 78 8, 27 8, 77 9, 30 22 6, 08 6. 58 6, 97 7, 40 7, 87 8, 35 8, 85 23 5, 77 6. 20 6, 62 7, 02 7, 47 7, 92 8, 40 24 5, 45 5. 85 6, 28 6, 63 7, 05 7, 48 7, 93 25 5, 12 5. 50 5, 87 6, 23 6, 63 7, 03 7, 45 26 4, 78 5. 15 5, 48 5, 83 6, 20 6, 57 6, 98 27 4, 45 4. 78 5, 10 5, 42 5, 77 6, 12 6, 48 28 4, 12 4. 42 4, 72 5, 00 5, 32 5, 65 5, 98 29 3, 77 4. 0● 4, 32 4, 57 4, 70 5, 17 5, 4● 30 3, 40 3. 65 3, 90 4, 13 4, 40 4, 67 4, 97 31 3, 03 3. 27 3, 48 3, 68 3, 9● 4, 17 4, 43 32 2, 67 2. 87 3, 05 3, 23 3, 45 3, 65 3, 88 Latitude of 51 deg. 53 parts. Position. 15 16 17 18 19 20 21 South Declination under the Earth, and North above it. 32 21, 9● 23, 50 25, ●8 26, 67 28, 28 29, 95 31, 65 31 21, 57 2●, 10 24, 65 26, 22 27, 80 29, 43 31, 10 30 21, 20 22, 72 24, 23 25, 77 27, 33 28, 93 30, 57 29 20, 83 22, 33 23, 82 25, 33 27, 03 28, 4● 30, 05 28 20, 48 21, 95 23, 42 24, 90 26, 4● 27, 92 29, 55 27 20, 15 21, 58 23, 03 24, 4● 25, 97 27, 48 29, 05 26 19, 8● 21, 22 22, 65 24, 07 25, 53 27, 03 28, 55 25 19, 48 20, 87 22, 27 23, 67 25, 10 26, 57 28, 08 24 19, 15 20, 52 21, 88 23, 27 24, 68 26, 12 27, 77 23 18, 83 2●, 17 21, 52 22, 80 24, 27 25, 68 27, 13 22 18, 52 19, 78 21, 17 22, 50 23, 87 25, 25 26, 68 21 18, 20 19, 50 20, 80 22, 12 23, 47 24, 83 26, 23 20 17, 90 19, 17 20, 45 21, 7 23, 07 24, 42 25, 80 19 17, 60 18, 85 20, 12 21, 37 22, 68 24, 00 25, 37 18 17, 30 18, 53 19, 77 21, 02 22, 28 23, 58 24, 93 17 17, 00 18, 22 19, 43 20, 65 21, 90 23, 18 24, 50 16 16, 70 17, 90 19, 10 20, 30 21, 53 22, 78 24, 08 15 16, 42 17, 5● 18, 77 19, 95 21, 17 22, 40 23, 67 14 16, 13 17, 28 18, 43 19, 60 20, 78 22, 00 23, 27 13 15, 85 16, 98 18, 12 19, 25 20, 43 21, 62 22, 85 12 15, 57 16, 68 17, 80 18, 9● 20, 07 21, 23 22, 45 11 15, 28 16, 38 17, 47 1●, 57 19, 70 20, 85 22, 05 10 15, 00 16, 08 17, 15 18, 23 19, 35 20, 48 21, 65 9 14, 73 15, 78 16, 85 17, 90 19, 00 20, 10 21, 25 8 14, 45 15, 50 16, 53 17, 57 18, 63 19, 73 20, 87 7 14, 25 15, 20 16, 22 17, 23 18, 28 19, 37 20, 47 6 13, 92 14, 92 15, 90 16, 90 17, 9● 19, 00 20, 08 5 13, 65 14, 62 15, 60 16, 58 17, 60 18, 62 19, 68 4 1●, 37 14, 33 15, 30 16, 25 17, 25 18, 25 19, 30 3 13, 18 14, 05 14, 98 15, 9● 16, 90 17, 90 18, 92 2 12, 83 13, 75 14, 68 15, 60 16, 55 17, 53 18, 53 1 12, 57 13, 47 14, 37 15, 27 16, 22 17, 17 18, 15 0 12, 30 13, 18 14, 07 14, 95 15, 87 16, 80 17, 77 A Table of Positions for the Pole of 22 23 24 25 26 27 28 North Declination under the Earth, and South above it. 0 18, 73 19, 73 20. 72 21. 75 22. 93 23, 72 25, 00 1 18, 33 19, 32 20. 27 21. 28 22. 45 23, 20 24, 47 2 17, 92 18, 88 19 83 20. 82 21. 95 22, 70 23, 93 3 17, 52 18, 45 19 38 20. 35 21. 47 22, 18 23, 40 4 17, 12 18, 03 18. 93 19 88 20. 98 21, 67 22, 87 5 16, 70 17, 60 18. 48 19 42 20. 48 21, 17 22, 33 6 16, 30 17, 18 18. 03 18. 93 20. 00 20, 65 21, 80 7 15, 88 16, 75 17. 58 18. 47 19 50 20, 13 21, 25 8 15, 48 16, 32 17. 13 18. 00 19 00 19, 62 20, 72 9 15, 07 15, 88 16. 67 17. 52 18. 50 19, 08 20, 17 10 14, 65 15, 43 16. 22 17. 03 18. 00 18, 57 19, 62 11 14, 23 15, 00 15. 75 16. 55 17. 50 18, 03 19, 07 12 13, 80 14, 55 15. 28 16. 07 16. 98 17, 50 18, 52 13 13, 38 14, 10 14. 82 15. 57 16. 47 16, 97 17, 95 14 12, 95 13, 65 14. 35 15. 07 15. 95 16, 42 17, 38 15 12, 52 13, 20 13. 87 14. 57 15. 42 15, 87 16, 82 16 12, 08 12, 75 13. 38 14. 07 14. 88 15, 32 16, 23 17 11, 63 12, 28 12. 90 13. 55 14. 35 14, 75 15, 65 18 11, 18 11, 80 12. 40 13. 03 13. 82 14, 18 15, 05 19 10, 73 11, 33 11. 90 12. 52 13. 27 13, 62 14, 45 20 10, 28 10, 85 11. 40 11. 98 12. 70 13, 03 13, 85 21 9, 82 10, 35 10. 88 11. 43 12. 15 12, 60 13, 23 22 9, 33 9, 85 10. 35 10. 88 11. 55 11, 83 12, 60 23 8, 85 9, 35 9 82 10. 33 10. 98 11, 23 11, 95 24 8, 37 8, 83 9 28 9 77 10. 38 10, 60 11, 30 25 7, 87 8, 32 8. 73 9 18 9 78 9, 97 10, 65 26 7, 37 7, 78 8. 17 8. 60 9 17 9, 33 9, 97 27 6, 85 7, 25 7. 60 8. 00 8. 55 8, 67 9, 28 28 6, 33 6, 68 7. 02 7. 40 7. 90 8, 00 8, 58 29 5, 80 6, 12 6. 43 6. 82 7. 25 7, 32 7, 90 30 5, 25 5, 55 5. 82 6. 13 6. 58 6, 62 7, 12 31 4, 68 4, 95 5. 20 5. 48 5. 90 5, 88 6, 37 32 4, 12 4, 35 4. 57 4. 82 5. 18 5, 15 5, 60 Latitude of 51 deg. 53 parts. Position. 22 23 24 25 26 27 28 South Declination under the Earth, and North above it. 32 33. 35 34, 95 36, 87 38, 68 40, 68 42, 28 44, 40 31 32. 78 34, 52 36, 23 38, 02 39, 97 41, 55 4●, 63 30 32. 22 33, 92 35, 62 37, 37 39, 28 40, 82 42, 88 29 31. 67 33, 35 35, 00 36, 73 38, 62 40, 12 42, 13 28 31. 13 32, 78 34, 42 36, 10 37, 97 39, 43 41, 42 27 30. 62 32, 22 33, 83 35, 50 37, 32 38, 77 40, 72 26 30. 10 31, 68 33, 27 34, 90 36, 70 38, 10 40, 03 25 29. 60 31, 15 32, 70 34, 32 36, 08 37, 47 39, 35 24 29. 10 30, 63 32, 15 33, 73 35, 48 36, 83 38, 70 23 28. 62 30, 12 31, 62 33, 17 34, 88 36, 20 ●8, 05 22 28. 13 29, 62 31, 08 32, 62 34, 30 35, 60 37, 40 21 27. 65 29, 12 30, 55 32, 07 33, 72 35, 00 36, 77 20 27. 18 28, 62 30, 03 31, 52 33, 17 34, 40 36, 15 19 26. 73 28, 13 29, 53 30, 98 32, 60 33, 82 35, 55 18 26. 28 ●7, 67 ●9, 03 30, 27 32, 05 33, 25 34, 95 17 25. 80 27, 18 28, 53 29, 95 31, 52 32, 68 34, 35 ●6 25. 38 26, 7● 28, 05 29, 43 30, 98 32, 12 33, 77 15 24. 95 ●6, 27 27, 57 28, 93 30, 45 31, 57 33, 18 14 24. 52 25, 82 27, 08 28, 43 29, 92 31, 02 32, 62 13 24. 08 25, 37 26, 62 27, 93 29, 40 30, 47 32, 05 12 2●. 67 24, 92 26, 15 27, 43 28, 88 29, 93 31, 48 11 23. 23 24, 47 25, 68 26, 95 28, 37 29, 40 30, 93 10 22. 82 24, 0● 25, 23 26, 47 27, 87 28, 87 30, 38 9 22. 40 2●, 58 24, 77 25, 98 27, 37 28, 35 29, 83 8 21. 98 23, 15 24, 30 25, 50 26, 87 27, 82 29, 28 7 21. 58 22, 72 13, 85 25, 03 26, 37 27, 30 28, 75 6 20. 17 22, 28 23, 40 24, 57 25, 87 26, 78 28, 20 5 20. 77 21, 87 ●2, 95 24, 08 25, 38 26, 27 27, 67 4 20. 35 21, 43 22, 50 23, 62 24, 88 25, 77 27, 13 3 19 95 21, 02 22, ●5 23, 15 24, 40 25, 25 26, 60 2 19 55 20, 58 21, 77 22, 68 23, 92 24, 73 26, 07 1 19 13 20, 15 21, 17 22, 22 23, 42 24, 23 25, 53 0 18. 73 19, 73 20, 72 21, 75 22, 93 2●, 72 25, 00 A Table of Positions for the Pole of 29 30 31 32 33 34 35 North Declination under the Earth, and South above it. 0 26, 13 27, ●0 28. 52 29. 77 31. 07 32, 40 33, 82 1 ●5, 58 26, 72 27. 92 29. 15 30. 42 31, 73 33, 12 2 25, 02 26, 15 27. 32 28. 52 29. 77 31, 05 32, 42 3 24, 47 25, 57 26. 72 27. 88 29. 12 30, 37 31, 72 4 23, 92 24, 98 26. 11 27. 27 28. 47 29, 70 31, 01 5 23, 35 24, 23 25. 50 26. 63 27. 82 29, 02 30, 30 6 22, 80 23, 82 24. 90 26. 00 27. 15 28, 33 29, 60 7 22, ●3 23, 23 24. 28 25. 37 26. 50 27, 65 28, 88 8 21, 67 22, 65 23. 67 24. 73 25. 83 26, 97 28, 17 9 21, 10 22, 05 23. 05 24. 08 25. 17 26, 27 27, 45 10 20, 52 21, 48 22. 43 23. 43 24. 48 25, 57 26, 72 11 19, 95 20, 85 21. 82 22. 78 23. 82 24, 87 26, 00 12 19, 37 20, 25 21. 18 22. 13 23. 13 24, 15 25, 25 13 18, 78 19, 63 20. 55 21. 47 22. 45 23, 43 24, 52 14 18, 20 19, 02 19 90 20. 80 21. 75 22, 72 23, 77 15 17, 60 18, 40 19 25 20. 13 21. 13 21, 98 23, 00 16 17, 00 17, 77 18. 60 19 45 20. 33 21, 25 22, 23 17 16, 38 17, 13 17. 93 18. 75 19 60 20, 50 21, 45 18 15, 75 16, 48 17. 25 18. 05 18. 88 19, 73 20, 67 19 15, 13 15, 83 16. 58 17. 35 18. 15 18, 97 19, 87 20 14, 50 15, 17 15. 88 16. 62 17. 40 18, 18 19, 05 21 13, 85 14, 50 15. 18 15. 88 16. 63 17, 40 18, 17 22 13, 20 13, 82 14. 47 15. 15 15. 85 16, 25 17, 37 23 12, 52 13, 12 13. 73 14. 38 15. 07 15, 77 16, 53 24 11, 85 12, 40 13. 00 13. 62 14. 27 14, 92 15, 65 25 11, 15 11, 68 12. 25 12. 83 13. 43 14, 07 14, 77 26 10, 45 10, 95 11. 48 12. 02 12. 60 13, 20 13, 85 27 9, 57 10, 20 10. 68 11. 20 11. 75 12, 30 12, 92 28 9, 00 9, 25 9 88 10. 37 10. 87 11, 38 11, 97 29 8, 23 8, 63 9 07 9 50 9 97 10, 45 10, 98 30 7, 47 7, 83 8. 22 8. 62 8. 05 9, 48 9, 97 31 6, 68 7, 00 7. 35 7. 55 7. 10 8, 48 8, 93 32 5, 87 6, 15 6. 47 6. 78 6. 13 7, 63 7, 87 Latitude of 51 deg. 53 parts. Position 29 30 31 32 33 34 35 South Declination under the Earth, And North above it. 32 46, 40 48, 45 50. 57 52, 75 55, 00 57, 17 59, 77 31 45, 58 47, 60 49. 68 51, 82 54, 03 56, 32 58, 70 30 44, 80 46, 77 48. 82 50, 92 53, 08 55, 32 57, 67 29 44, 03 45, 97 47. 97 50, 03 52, 17 54, ●8 56, 65 28 43, 27 45, 18 47. 15 49, 17 51, 27 53, 42 55, 67 27 42, 53 44, 40 46. 35 48, 3● 50, 38 52, 50 54, 72 26 41, 82 43, 65 45. 55 47, 52 49, 53 51, 60 53, 78 25 41, 12 42, 92 44. 78 46, 70 48, 70 50, 73 52, 87 24 40, 42 42, 20 44. 03 45, 87 47, 87 49, 88 51, 98 23 39, 75 41, 48 43. 30 45, 07 47, 07 49, 03 51, 10 22 39, 07 40, 78 42. 57 44, 27 46, 27 48, 22 50, 27 21 38, 42 40, 10 41. 85 4●, 50 45, 50 47, 40 49, 47 20 37, 77 39, 43 41. 15 42, 79 44, 73 46, 62 48, 58 19 37, 13 38, 77 40. 45 42, 98 43, 98 45, 83 47, 77 18 36, 52 38, 12 39 78 41, 25 43, 25 45, 07 46, 97 17 35, 88 37, 47 39 10 40, 52 42, 52 44, 30 46, 18 16 35, 27 36, 83 38. 43 40, 80 41, 80 43, 55 45, 40 15 34, 67 36, 20 37. 78 39, 08 41, 08 42, 82 44, 63 14 34, 07 35, 58 37. 13 38, 38 40, 38 42, 08 43, 87 13 33, 48 34, 97 36. 48 38, 68 39, 68 41, 37 43, 12 12 32, 90 34, 35 35. 85 37, 00 39, 00 40, 65 42, 38 11 32, 32 33, 75 35. 22 36, 31 38, 32 39, 93 41, 63 10 31, 75 33, 15 34. 60 ●6, 65 37, 65 39, 23 40, 92 9 31, 17 32, 55 33. 98 35, 97 36, 97 38, 53 40, 18 8 30, 60 31, 95 33. 37 34, 30 36, 30 37, 67 39, 47 7 30, 03 31, 37 32. 92 34, 63 35, 63 37, 15 38, 75 6 29, 47 30, 78 32. 13 33, 98 34, 98 36, 47 38, 03 5 28, 92 30, 20 31. 53 32, 32 34, 32 35, 78 37, 33 4 28, 35 29, 62 30. 92 32, 67 33, 67 35, 10 36, 62 3 27, 80 29, 03 30. 32 31, 01 33, 02 34, 43 35, 92 2 27, 25 28, 45 29. 72 30, 37 32, 37 33, 75 35, 22 1 26, 68 27, 88 29. 12 30, 72 31, 71 33, 07 34, 51 0 26, 13 27, 30 28. 52 29, 07 31, 07 32, 40 33, 81 A Table of Positions for the Pole of 36 37 38 39 40 41 42 North Declination under the Earth, and South above it. 0 35, 27 36, 78 38, 38 40, 07 41, 82 43, 70 45, 68 1 34, 53 36, 02 37, 60 39, 25 40, 98 42, 83 44, 78 2 33, 82 35, 10 36, 82 38, 45 40, 13 41, 97 43, 88 3 33, 08 34, 52 36, 03 37, 63 39, 30 41, 08 42, 98 4 32, 35 33, 77 35, 25 36, 82 38, 45 40, 22 42, 05 5 31, 62 33, 00 34, 47 36, 00 37, 60 39, 33 41, 17 6 30, 88 32, 23 33, 67 35, 20 36, 75 38, 45 40, 25 7 30, 15 31, 47 32, 88 34, 37 35, 90 37, 57 39, 33 8 29, 40 30, 70 32, 08 33, 53 35, 05 36, 68 38, 42 9 28, 67 29, 93 31, 28 32, 78 34, 18 35, 78 37, 48 10 27, 90 29, 15 30, 47 31, 85 33, 32 34, 88 36, 55 11 27, 15 28, 37 29, 65 31, 02 32, 43 33, 97 35, 60 12 26, 38 27, 57 28, 82 30, 15 31, 55 33, 05 34, 65 13 25, 67 26, 77 27, 98 29, 30 30, 65 32, 12 33, 68 14 24, 83 25, 95 27, 15 28, 42 29, 78 31, 18 32, 72 15 24, 03 25, 13 26, 30 27, 37 28, 82 30, 23 31, 72 16 23, 07 24, 30 25, 43 26, 63 27, 90 29, 27 30, 71 17 22, 43 23, 47 24, 57 25, 73 26, 95 28, 28 29, 70 18 21, 62 22, 62 23, 68 24, 82 26, 00 27, 30 28, 67 19 20, 78 21, 75 22, 78 2●, 88 25, 01 26, 28 27, 62 20 19, 93 20, 87 21, 87 22, 93 24, 03 25, 25 26, 55 21 19, 07 19, 97 20, 93 21, 95 23, 03 24, 20 25, 47 22 18, 18 19, 05 19, 98 20, 97 22, 00 23, 13 24, 35 23 17, 30 18, 13 19, 01 19, 97 20, 78 22, 05 23, 22 24 16, 40 17, 18 18, 03 18, 93 19, 72 20, 93 22, 05 25 15, 47 16, 22 17, 01 17, 88 18, 78 19, 78 20, 85 26 14, 51 15, 22 15, 98 16, 80 17, 65 18, 62 19, 63 27 13, 58 14, 03 14, 92 15, 70 16, 50 17, 42 18, 38 28 12, 38 13, 10 13, 83 14, 57 15, 32 16, 18 17, 08 29 11, 52 12, 10 12, 72 13, 40 14, 10 14, 95 15, 75 30 10, 47 11, 00 12, 57 11, 20 12, 83 13, 58 14, 37 31 9, 38 9, 87 10, 38 10, 95 11, 53 12, 22 12, 93 32 8, 27 8, 70 9, 17 9, 17 10, 30 10, 80 11, 45 Latitude of 51 deg. 53 parts. Position 36 37 38 39 40 41 42 South Declination under the Earth, And North above it. 32 62, 27 64, 87 67, 60 70. 97 73, 33 76, 60 79, 92 31 61, 15 63, 70 66, 38 69. 18 72, 10 75, 18 78, 43 30 60, 07 62, 57 65, 20 67. 93 70, 80 73, 42 77, 00 39 59, 01 61, 47 64, 05 66. 7● 69, 53 72, 50 75, 63 28 57, 98 60, 40 62, 93 65. 57 68, 32 71, 22 74, 28 27 57, 00 59, 37 61, 85 64. 43 67, 30 69, 98 72, 98 26 56, 02 58, 35 60, 78 63. 3● 65, 98 68, 78 71, 73 25 55, 07 57, 35 59, 73 62. 25 64, 85 67, 62 70, 52 24 54, 13 56, 38 58, 73 61. 20 63, 75 66, 47 69, 32 23 53, 23 55, 43 57, 75 60. 17 62, 68 65, 35 68, 15 22 52, ●5 54, 52 56, 78 59 17 61, 63 64, 27 67, 01 21 51, 47 53, 6● 55, 83 58. 18 60, 60 63, 20 65, 90 20 50, 60 52, 70 54, 90 57 20 59, 60 62, 15 64, 82 19 49, 75 51, 82 5●, 98 56. 25 58, 62 61, 12 63, 75 18 48, 92 50, 95 53, 08 55. 32 57, 63 60, 10 62, 70 17 48, 10 50, 10 5●, 20 54. 40 56, 68 59, 12 61, 67 16 47, 30 49, 27 51, 33 53. 50 55, 90 58, 13 60, 65 15 46, 50 48, 43 50, 47 52. 60 54, 82 57, 17 59, 65 14 45, 70 4●, 62 49, 62 51. 71 53, 90 56, 22 58, 66 13 44, 87 46, 80 48, 78 50. 83 52, 98 55, 28 57, 68 12 44, 15 46, 00 47, 95 49. 98 52, 08 54, 35 56, 72 11 43, 38 45, 20 47, 12 49. 12 51, 20 53, 43 55, 77 10 43, 63 44, 42 46, 30 48. 28 50, 32 52, 52 54, 82 9 41, 87 43, 63 45, 48 47. 43 49, 45 51, 62 53, 88 8 41, 1● 42, 87 44, 68 46. 60 48, 58 50, 72 52, 95 7 40, 38 42, 10 43, 88 45. 77 47, 90 49, 83 52, 03 6 39, 65 41, 33 43, 10 44. 93 46, 88 48, 95 51, 12 5 38, 92 40, 57 42, 30 44. 13 46, 03 48, 07 50, 20 4 38, 18 39, 80 41, 52 43. 32 45, 18 47, 18 49, 30 3 37, 45 39, 05 40, 73 42. 50 44, 33 46, 32 48, 38 2 36, 72 38, 30 39, 95 41. 68 43, 50 45, 43 47, 48 1 36, 00 37, 53 39, 17 41. 88 42, 65 44, 57 46, 58 0 35, 27 36, 78 38, 38 40. 07 41, 82 43, 70 45, 68 A Table of Positions for the Pole of 43 44 45 46 47 48 49 North Declination under the Earth, and South above it. 0 47, 80 50, 12 52, 60 55, 32 58, 40 61, 93 66, 05 1 46, 87 49, 15 51, 60 54, 28 57, 33 60, 82 64, 90 2 45, 93 48, 18 50, 59 53, 25 56, 25 59, 72 63, 75 3 45, 00 47, 22 49, 59 52, 20 55, 18 58, 60 62, 60 4 44, 07 46, 25 48, 58 51, 17 54, 10 57, 48 61, 43 5 43, 12 45, 27 47, 58 50, 12 53, 02 56, 35 60, 27 6 42, 18 44, 28 46, 57 49, 07 51, 93 55, 23 59, 10 7 41, 23 43, 30 45, 55 48, 02 50, 83 54, 10 57, 93 8 40, 27 42, 31 44, 52 46, 95 49, 73 52, 95 56, 42 9 39, 30 41, 32 43, 48 45, 88 48, 62 51, 68 55, 55 10 38, 33 40, 31 42, 45 44, 80 47, 33 50, 6 54, 35 11 37, 35 39, 30 41, 38 43, 70 46, 3● 49, 47 53, 13 12 36, 37 38, 27 40, 33 42, 60 45, 22 48, 28 51, 90 13 35, 37 37, 23 39, 25 41, 48 44, 07 47, 08 50, 65 14 34, 35 36, 18 38, 17 40, 35 42, 90 45, 25 49, 38 15 33, 33 35, 12 37, ●7 39, 20 41, 70 44, 62 48, 10 16 32, 28 34, 03 35, 77 38, 05 40, 50 43, 37 46, 78 17 31, 23 32, 95 34, 80 36, 87 39, 27 42, 08 45, 45 18 30, 17 31, 83 33, 63 35, 65 38, 02 40, 78 44, 10 19 29, 07 30, 70 32, 45 34, 43 36, 73 39, 45 42, 72 20 27, 97 29, 53 31, 25 3●, 18 35, 43 38, 08 41, 30 21 26, 80 28, 18 30, 03 31, 90 34, 18 36, 70 39, 85 22 25, 67 27, 15 28, 77 30, 58 33, 73 35, 27 38, 35 23 24, 48 25, 92 27, 48 29, 23 31, 32 33, 80 36, 82 24 23, 27 24, 65 26, 17 27, 87 29, 88 32, 30 35, 98 25 22, 02 23, 35 24, 80 26, 45 28, 40 30, 73 33, 62 26 20, 75 22, 02 23, 42 24, 98 26, 87 29, 13 31, 92 27 19, 47 20, 63 21, 97 23, 47 25, 28 27, 47 30, 17 28 18, 07 19, 22 20, 48 21, 90 23, 30 25, 73 28, 33 29 16, 67 17, 75 18, 93 20, 28 21, 93 23, 93 26, 43 30 15, 05 16, 23 17, 33 18, 60 20, 15 22, 05 24, 43 31 13, 83 14, 65 15, 67 16, 83 18, 28 20, 07 22, 32 32 12, 17 13, 00 13, 93 15, 00 16, 33 27, 98 20, 43 Latitude of 51 deg. 53 parts. Positi● 43 44 45 46 47 48 49 South Declination under the Earth, and North above it. 32 83, 43 87, 23 91, 27 95, 63 100, 47 106, 88 112, 00 31 82, 77 85, 58 89, 53 93, 80 98, 52 103, 80 109, 78 30 80, 38 84, 00 87, 87 92, 03 96, 65 101, 82 107, 67 29 78, 93 82, 48 86, 27 90, 35 94, 87 99, 93 105, 67 28 77, 53 81, 02 84, 72 88, 73 93, 17 98, 13 103, 77 27 76, 17 80, 60 83, 23 87, 17 91, 52 96, 40 101, 93 26 74, 85 78, 22 81, 78 85, 65 89, 63 94, 73 100, 18 25 73, 58 76, 88 80, 40 84, 18 88, 40 9●, 13 98, 48 24 72, 33 75, 58 79, 03 82, 77 86, 92 91, 57 96, 12 23 71, 12 74, 22 77, 72 81, 40 85, 48 90, 07 95, 28 22 69, 9● 73, 08 76, 43 80, 05 84, 07 88, 60 93, 75 21 68, 78 71, 8● 75, 17 78, 73 82, 70 87, 17 92, 25 20 67, 63 70, 70 73, 95 77, 45 81, 37 85, 78 90, 80 19 66, 53 69, 53 72, 75 76, 20 80, 07 84, 42 89, 37 18 65, 43 68, 40 71, 57 74, 98 78, 78 83, 08 88, 00 17 64, 37 67, 28 70, 40 73, 77 77, 53 81, 78 86, 65 16 63, 32 66, 20 69, 27 72, 58 76, 30 80, 50 85, 32 15 62, 27 65, 12 68, 13 71, 43 75, 10 79, 25 84, 00 14 61, 25 64, 05 67, 03 70, 28 73, 90 78, 02 82, 72 13 60, 23 63, 00 65, 95 69, 15 72, 73 76, 78 81, 45 12 59, 23 61, 97 64, 87 68, 03 71, 58 75, 58 80, 20 11 58, 25 60, 93 63, 87 66, 93 70, 43 74, 40 78, 97 10 57, 27 59, 92 62, 75 65, 83 69, 30 73, 23 77, 75 9 56, 30 58, 91 61, 72 64, 75 68, 18 72, 07 76, 55 8 55, 33 57, 92 60, 68 63, 68 67, 07 70, 92 75, 35 7 54, 37 56, 93 59, 65 62, 62 65, 97 69, 73 74, 17 6 53, 42 55, 95 58, 63 61, 57 64, 87 68, 63 73, 00 5 52, 48 54, 85 57, 62 60, 52 63, 78 67, 50 71, 83 4 51, 53 53, 98 56, 61 59, 47 62, 70 66, 38 70, 67 3 50, 60 53, 01 55, 60 58, 43 61, 62 65, 27 69, 50 2 49, 67 52, 05 54, 60 57, 41 60, 53 64, 15 68, 35 1 48, 73 51, 08 53, 60 56, 35 59, 47 63, 05 67, 20 0 47, 80 50, 12 52, 60 55, 32 58, 40 61, 93 66, 05 A Table of Positions for the Pole of 50 51 51. 53 Position 50 51 51. 53 North Declination under the Earth, and South above it. 0 71, 23 78. 83 90, 00 South Declination under Earth, and North above it. 32 119, 33 129, 33 141, 87 1 70, 03 77. 60 88, 08 31 116, 97 126, 73 139, 13 2 68, 85 76. 37 87, 48 ●0 114, 72 124, 32 136, 62 3 67, 65 75. 12 86, 22 2● 112, 58 122, 00 134, 23 4 66, 45 73. 88 84, 97 28 110, 55 119, 87 132, 00 5 65, 40 72. 63 83, 68 27 108, 62 117, 83 129, 88 6 64, 03 71. 38 82, 40 26 106, 73 115, 87 127, 87 7 6●, 82 70. 12 81, 12 25 105, 00 114, 00 125, 93 8 61, 60 68 83 79, 82 24 103, 28 112, 18 124, 08 9 60, 35 67. 55 78, 50 23 101, 62 110, 45 122, 28 10 59, 10 66. 25 77, 18 22 100, 02 108, 77 12●, 57 11 57, 83 64. 95 75, 85 21 98, 47 107, 13 118, 88 12 56, 57 63. 53 74, 48 20 96, 93 105, 55 117, 27 13 55, 27 62. 27 73, 12 19 95, 47 104, 00 11●, 68 14 53, 95 60. 90 71, 72 18 94, 02 102, 48 114, 13 15 52, 58 59, 52 70, 30 17 92, 60 101, 02 11●, 63 16 51, 25 58. 10 68, 85 16 91, 22 99, 57 111, 15 17 49, 87 56. 65 67, 37 15 89, 88 98, 15 109, 70 18 48, 45 54. 18 65, 87 14 88, 52 96, 77 108, 28 19 47, 00 53. 67 64, 32 13 87, 20 95, 40 106, 88 20 45, 53 52. 12 62, 73 12 85, 90 94, 05 105, 52 21 44, 00 50. 53 61, 1● 11 84, 63 92, 72 104, 15 22 4●, 45 48. 90 59, 4● 10 83, ●2 91, 42 102, 82 23 40, 85 47. 22 57, 72 9 82, 12 90, 12 101, 50 24 39, 18 4●. 48 55, 92 8 80, 92 88, 83 100, 18 25 ●7, 47 4●. 67 54, 07 7 79, 65 87, 55 98, 88 26 35, 70 41. 80 52, 13 6 78, 43 86, 28 97, 60 27 ●3, 85 39 83 50, 12 5 77, 07 85, 03 96, 32 28 31, 92 37. 80 48, 0● 4 76, 02 83, 78 95, 03 29 29, 88 35. 63 45, 77 3 74, 82 82, ●5 93, 78 30 27, 75 33. 35 43, 38 2 7●, 6● 81, 30 92, 52 31 25, 30 30. 93 40, 87 1 72, 43 80, 00 91, 92 32 23, 10 28. 33 38, 1● 0 71, 23 78, 83 90, 00 A Table showing the Elevation of the Pole upon the several circles of Position of the 11, 12. 2, and 3. Houses for 6● degrees of Latitude. Latitude 11 & 3 12 & 2 Poles Elevat. Poles Elevat. 1 0, 48 0, 85 2 0, 98 1, 72 3 1, 48 2, 58 4 1, 98 3, 45 5 2, 48 4, 32 6 3, 00 5, 18 7 3, 52 6, 07 8 4, 03 6, 95 9 4, 53 7, 82 10 5, 05 8, 68 11 5, 57 9, 55 12 6, 08 10, 43 13 6, 60 11, 30 14 7, 12 12, 18 15 7, 63 13, 07 16 8, 15 13, 95 17 8, 68 14, 83 18 9, 22 15, 72 19 9, 75 16, 60 20 10, 30 17, 50 21 10, 85 18, 38 22 11, 42 19, 28 23 11, 63 20, 18 24 12, 53 21, 08 25 13, 12 21, 99 26 13, 70 22, 89 27 14, 30 23, 80 28 14, 90 24, 71 29 15, 50 25, 63 30 16, 12 26, 55 31 16, 73 27, 48 31 16, 73 27. 48 32 17, 35 28. 42 33 17, 98 29. 35 34 18, 63 30. 28 35 19, 30 31. 23 36 19, 97 32. 18 37 20, 65 33. 13 38 21, 33 34. 08 39 22, 03 35. 03 40 22, 75 36. 00 41 23, 48 36. 97 42 24, 23 37. 95 43 25, 00 38. 93 44 25, 78 39 92 45 26, 57 40. 90 46 27, 37 41. 89 47 28, 18 42. 88 48 29, 03 43. 89 49 29, 90 44. 90 50 30, 78 45. 92 51 31, 68 46. 93 51. 53 32, 18 47. 47 52 32, 62 47. 95 53 33, 57 48. 98 54 34, 53 50. 01 55 35, 53 51. 05 56 36, 55 52. 08 57 37, 58 53. 13 58 38, ●5 54. 18 59 39, 75 55. 23 60 40, 88 56. 30 A general Table of Positions. 55 54 53 52 51. 53 5● 50 The Poles Elevation upon every circle of Position. 1 0, 70 0, 73 0, 75 0, 78 0, 79 0, 02 0, 83 2 1, 40 1, 45 1, 50 1, 57 1, 58 1, 62 1, 68 3 2, 00 2, 18 2, 27 2, 35 2, 38 2, 43 2, 52 4 2, 80 2, 92 3, 03 3, 13 3, 17 3, 25 3, 37 5 3, 51 3, 65 3, 78 3, 92 3, 98 4, 07 4, 22 6 4, 22 4, 38 4, 55 4, 71 4, 80 4, 88 5, 07 7 4, 83 5, 12 5, 32 5, 50 5, 62 5, 70 5, 92 8 5, 65 5, 87 6, 08 6, 30 6, 45 6, 53 6, 77 9 6, 37 6, 60 6, 85 7, 10 7, 22 7, 37 7, 63 10 7, 10 7, 37 7, 63 7, 9● 8, 05 8, 22 8, 50 11 7, 82 8, 12 8, 42 8, 73 8, 88 9, 05 9, 38 12 8, 57 8, 88 9, 22 9, 57 9, 73 9, 92 10, 27 13 9, 30 9, 65 10, 02 10, 40 10, 57 10, 77 11, 17 14 10, 05 10, 43 10, 83 11, 23 11, 43 11, 65 12, 08 15 10, 82 11, 23 11, 65 12, 08 12, 30 12, 53 13, 00 16 11, 58 12, 02 12, 48 12, 95 13, 18 13, 43 13, 92 17 12, 37 12, 83 13, 32 13, 82 14, 07 14, 30 14, 87 18 13, 15 13, 65 14, 17 14, 70 14, 95 15, 25 15, 82 19 13, 95 14, 48 15, 03 15, 60 15, 87 16, 18 16, 80 20 14, 77 15, 33 15, 92 16, 52 16, 80 17, 13 17, 78 21 15, 60 16, 20 16, 82 17, 45 17, 77 18, 12 18, 78 22 16, 43 17, 07 17, 73 18, 40 18, 73 19, 10 19, 82 23 17, 28 17, 97 18, 65 19, 37 19, 73 20, 10 20, 87 24 18, 32 18, 87 19, 60 20, 35 20, 72 21, 13 21, 93 25 19, 05 19, 80 20, 57 21, 37 21, 75 22, 18 23, 03 26 19, 97 20, 75 21, 57 22, 40 21, 93 23, 27 24, 15 27 20, 90 21, 72 22, 58 23, 47 23, 72 24, 37 25, 32 28 21, 85 22, 72 23, 62 24, 55 25, 00 25, 50 26, 50 29 22, 65 23, 75 24, 68 25, 67 26, 13 26, 67 27, 72 30 23, 85 24, 80 25, 78 26, 82 27, 30 27, 87 28, 98 31 24, 88 25, 88 26, 92 28, 00 28, 52 29, 12 30, 28 32 25, 95 27, 00 28, 08 29, 22 29, 77 30, 40 31, 62 33 27. 05 28, 15 29, 30 30, 48 31, 08 31, 73 33, 02 34 28. 18 29, 35 30, 55 31, 80 32, 40 33, 10 34, 47 35 29. 37 30, 58 31, 85 33, 17 33, 48 34, 55 35, 98 36 30. 58 31, 87 33, 20 34, 58 35, 27 36, 03 37, 57 37 31. 85 33, 20 34, 60 36, 07 36, 78 37, 60 39, 22 38 33. 17 34, 58 36, 07 37, 62 38, 38 39, 25 40, 97 39 34. 55 36, 03 37, 60 39, 25 40, 07 40, 98 42, 80 40 35. 98 37, 57 39, 22 40, 97 41, 48 42, 80 44, 75 41 37. 50 39, 17 40, 75 42, 78 43, 70 44, 75 46, 83 42 39 08 40, 85 42, 73 44, 70 45, 68 46, 82 49, 07 43 40. 77 42, 65 44, 65 46, 77 47, 80 49, 03 51, 48 44 42. 55 44, 55 46, 70 48, 98 50, 12 51, 45 54, 13 45 44. 45 46, 60 48, 90 51, 38 52, 60 54, 07 57, 05 46 46. 48 48, 80 51, 28 54, 00 55, 32 56, 98 60, 33 47 48. 67 51, 18 53, 92 56, 92 58, 40 59, 27 64▪ 13 48 51. 05 53, 80 56, 82 60, 20 61, 60 64, 07 68, 73 49 53. 67 56, 70 60, 10 64, 00 66, 05 68, 68 74, 85 50 56. 57 59, 98 63, 90 68, 62 71, 23 74, 82 90, 00 51 59 85 63, 80 68, 53 74, 75 78, 83 90, 00 51. 53 61. 88 65, 20 71, 53 79, 53 90, 0 52 63. 67 68, 42 74, 70 90, 00 53 68 32 74, 62 90, 00 54 74. 53 90, 00 55 90 〈…〉 A Catalogue of the more notable Fixed Stars, with their Longitude, Latitude, and Magnitude, for the year 1650 Complete. About the North Pole. Names of the Stairss. Longit. D. Parts Latit. D. Parts. Mag. The Polar Star ♊ 23, 74916 66, 04167 N 2 The higher of the 2 in □ of them that precede of the lesser Bear ♌ 7, 98250 72, 85000 N 2 The lower of the same ♌ 15, 39183 75, 38333 N 3 That nearest the Pole ♊ 27, 20750 63, 91667 N 6 The higher preceding in □ of the greater Bear ♌ 10, 27417 49, 66667 N 2 The lower of the same ♌ 14, 43250 45, ●5000 N 2 The higher of those following of the Quadrat ♌ 26, 13250 51, 61667 N 2 The lower of the same ♌ 25, 45750 47, 10000 N 2 The last but two in the tail ♍ 3, 87417 54, 30000 N 2 The last but one in the tail ♍ 10, 64917 56, 36667 N 2 The last in the tail ♍ 21, 90750 54, 41667 N 2 The tongue of the Dragon ♏ 18, 64917 76, 28333 N 4 The bright Star in the head ♑ 17, 77417 81, 88333 N 5 The Girdle of Ceph●us ♉ 0, 9241● 71, 11667 N 3 Arcturus ♎ 19, 35●●● ●1, 04167 N 1 The bright Star of the Crown ♍ 7, 34917 44, 38333 N 2 The head of Hercules ♐ 11, 22417 37, 38333 N 3 The bright Star of the Harp ♑ 10, 41417 61, 78333 N 1 The bright Star of the Swan, in the breast of ♓ 0, 59917 59, 93333 N 2 Cassiopeia ♉ 2, 99917 46, 58333 N 3 The head of Medusa ♉ 21, 32417 22, 37500 N 3 In the the right side of Perse●s ♉ 26, 99083 30, 08333 N 2 The little Goat Capella ♊ 16, 96417 22, 84167 N 1 In the head of Ophiuchus ♐ 17, 54083 35, 95000 N 3 Names of the Stars. Longit. D. Parts Latit. D. Parts. Mag. In the middle of the Serpent's neck ♍ 17, 20750 25, 58333 N 2 The bright Star in the shoulder of the Eagle ♑ 26, 85750 29, 35833 N 2 The bright Star of the tail of the Dolphin ♒ 9, 24083 29, 13333 N 3 The Mouth of Pegasus ♒ 27, 07417 22, 12500 N 3 The first Star of the wing Pegasus ♓ 18, 64917 19, 43333 N 2 In the putting forth of the thigh of Pegasus ♓ 24, 52417 ●1, 11667 N 2 The head of Anromeda ♈ 9, 49083 25, 70000 N 2 The more Southern in the Girdle ♈ 25, 52417 25, 98333 N 2 In the South foot Androm●da ♉ 9, 35750 27, 77500 N 2 In the top of the Triangle ♉ 2, 02417 16, 82500 N 4 About the Zodiac. Names of the Stars. Longit. D. Parts Latit. D. Parts. Mag. The first Star of Aries ♈ 28, 32417 7. 13333 N 4 The bright Star in the top of the head of Aries ♉ 2, 80750 9 95000 N 3 The south Eye of Taurus ♊ 4, 91583 5. 51667 S 1 The north Eye of Taurus ♊ 3, 69083 2. 60833 S 3 The bright Star of the Pleiades ♉ 25, 10750 4. 00000 N 5 The higher head of Gemini ♋ 15, 39083 10. 03333 N 2 In the lower head of Gemini ♋ 18. 42417 6. 63333 N 2 Bright foot of Gemini ♋ 18, 55750 6. 80●33 S 2 In the South arm of Cancer ♌ 8, 76583 5. 13333 S 2 The bright Star in the neck of Leo ♌ 24, 19083 8. 78333 N 3 The Heart of Leo ♌ 24, 99083 0. 43333 N 2 In the extreme of the tail of Leo ♍ 16, 75750 12. ●0000 N 1 In Virgo's wing. Vindemia●rix ♎ 5, 08083 16. 25833 N 1 Virgins Spike ♎ 18, 97417 1. 98333 N 3 South Ballance ♏ 10, 22417 0. 43333 N 1 North Ballance ♏ 14, 50750 8. 58333 N 2 The highest in the forehead of Scorpio ♏ 28, 30750 1. 08333 N 2 Scorpions heart ♐ 4, 92417 4. 45000 N 1 Names of the Stars. Longit. D. Parts Latit. D. Parts. Mag. Former of the 3. in the head of Sagit. ♑ 8, 64917 1, 40833 N 4 Northern in the former horn ♑ ♑ 29, 00750 7, 04167 N 3 The succeeding bright Star in the tail of Capricorn ♒ 18, 70750 2, 48333 S 3 The left shoulder of Aquarius ♒ 17, 52417 8, 70000 N 3 The shank of Aquarius ♓ 4, 07417 8, 16667 S 3 In the effusion ♒ Fomahant ♒ 28, 89917 21, 00000 S 1 In the mouth of the south Fish ♓ 13, 74083 9, 06667 N 5 The bright ✴ in the joining of both nets of Pisces ♈ 24, 49083 9, 06667 S 3 Towards the South Pole. Names of the Stars. Longit. D. Parts Latit. D. Parts. Mag. In the snout of the Whale ♉ 10, 22417 7. 83333 S 4 Bright ✴ of the tail of the Whale ♓ 27, 64083 20. 78333 S 2 Bright shoulder of Orion ♊ 13, 90750 16. 10000 S 2 Middlemost of the Belt of Orion ♊ 18, 60750 24. 55833 S 2 Bright ✴ in the left Foot Orion ♊ 11, 99083 31. 18333 S 1 Orion's foot in the River ♊ 10, 40750 27. 90833 S 3 The last in the tail of the Hare ♊ 27, 07417 38. 43333 S 4 Great Dogs mouth. Sirius ♋ 9 29917 39 50000 S 1 Lesser Dog. protion ♋ 21, 01583 15. 95000 S 2 In the top of the Ships stern ♌ 6, 59917 43. 30000 S 3 Brightest in Hydra ♍ 22, 46583 22. 40000 S 1 In the Southern Hemisphere. Names of the Stars. Longit. D. Parts Latit. D. Parts. Mag. Bright ✴ of the Crane's head ♒ 12, 56667 12. 83333 S 2 Going out of the Crane's tail ♒ ●7, 5833● ●4. 60000 S 2 Bright ✴ of the Phaenix's neck ♓ 9, 8833● 40. 16667 S 2 Head of Indus ♑ 28, 30000 ●2. 50000 S 4 The Peacock's head ♑ 17, 45000 ●6. 00000 ● 2 The Sparrows head ♎ 19, 01667 72. 43333 S 5 In the bill of the Goose ♒ 4. 60000 45. 91667 S 3 The head of Hydrus ♓ 4, 68333 64. 08333 S 3 FINIS.