Selected quad for the lemma: end_n

Word A Word B Word C Word D Occurrence Frequency Band MI MI Band Prominent
end_n day_n hour_n minute_n 1,570 5 11.3251 5 false
View all documents for the selected quad

Text snippets containing the quad

ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A52255 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 ... / by John Newton ... Newton, John, 1622-1678. 1657 (1657) Wing N1053; ESTC R20418 165,070 340

There are 2 snippets containing the selected quad. | View lemmatised text

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 Signes 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 earths middle motion to the beginning of the Aera Alexandri shall be 227. 004686 or 7 sines 17 deg 004686 parts And adding to this Epocha deg 51. 944398 which is the middle motion for 323 years 131 dayes the whole circles being rejected the Radix of the earths middle motion in the beginning of the Christian Aera shall be deg 278. 949084 or 9 signes 8 deg 949084 to which if you add 034223 the equal motion belonging to 034722 the difference between the Meridians 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 Suns true place and distance from the Earth HAving composed tables of the Suns middle motions according to the directions of the last Chapter his true place in the Zodiack 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 moneths and days compleat and to the houres and scruples current every one under his like onely remember that in the Bissextile year after the end of February the dayes must be increased by an Unite then adding them altogether the summe shall be the Suns meane motion for the time given Example Let the time given be May the 12th houre 11 parts 15 before noon at London in the Bissextile yeare 1656 and the Suns 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 Dayes 12 011. 82776   52 Houres 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 Suns mean longitude 421. 67681 Apogaeum substract 96. 46522 Rest mean Anomaly 325. 21459 Whos 's complement to a Circle 34. 78541 is the angle A M E in the Ellipsis And the complement 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 summe 203568 co ar 4. 6912905 Differ 196432 5. 2932122 Tang. ½ summe 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 Suns true place Example The Suns meane longitude 421. 67681 Aequation adde 1 14942 The Suns true place 422. 82623 or 2 Signes 2 degrees 82623 parts of a degree   Lastly to find his distance from the earth I say As the sine of M B H 1. 14942 co ar 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 Suns place by calculation we will now shew how to reduce the Suns mean longitude to his true by the Table of Aequations of the Suns excentrick The Suns 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 ar 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 adde 1. 14940 Suns true place 62. 82621 And in like manner the Logarithme of the Suns distance from the Earth will be found to be 5. 0063633 which being more necessary then the distance it self 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 Dayes SOme there are of late which allow not of any Aequation of Civil Dayes others will have the inequality proceed from two causes First from the unequal motion of the Sun in the Zodiack and the other from the Zodiacks obliquity Tycho whom we shall follow in this particular doth make the difference between the Suns true longitude and his Right Ascension to be the absolute Aequation of naturall dayes the which is also clearly demonstrated according to the Copernican Systeme by Thomas Street in his Ephemeris for the yeare 1655 which being but short is here inserted The Aequation of time demonstrated Let A be the center of the Sun and E of the Earth ♎ E the earths longitude from the Equinoctiall point in the ecliptick ♎ F the like arch projected in the Equator ♎ B the Right Ascension of the Earths or Suns true place G H is a diameter of the Equinoctiall and Meridian of the earths 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 appeare as one right line Then let C D parallel to A F be likewise a diameter of the Equinoctial and Meridian of the meane or equal diurnal revolution Hence C E G the angle of the earths 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 entituled A perpetual Table for the Equation of time composed In which you must enter with the signe and degree of the Suns place either in the uppermost and left hand columnes 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 doe about the Sun and so not onely the earth but the whole Systeme of the Moone is also carryed about the Sun in a yeare And hence according to Hypparchus there ariseth a twofold but according to Tycho a threefold inequality in the Moons motion The first is periodicall and is to be obtained after the same manner as was the
there be a concurrance Example At the visible Conjunction March 27 21. 90999 The true distance of the Moone from the Sun 0●847 The Parallax of Longitude 02775 Their difference 00072 which being so small sheweth that the visible Conjunction is precisely enough found CHAP. 32. To finde the visible Latitude of the Moon at the time of the visible Conjunction IN these Northerne regions which we inhabit the parallax of latitude allwayes makes the Moon to appeare more South then 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 orientall quadrant adde the parallax of longitude to the motion of the Sun agreeing to the difference between the true and visible Conjunction and the summe subtract from the true motion of latitude at the time of the true Conjunction or if the Eclipse happen in the occidentall quadrant adde the said summ● thereto and you have the true motion of latitude at the visible Conjunction by which as formerly taught finde out the true Latitude of the Moone Example Motion of the Sun agreeing to 04943 00202 Parallax of Longitude at visible ☌ 02775 The Summ 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 adde them together the summe is the South visible latitude of the Moone but if North subtract the lesse from the greater there remaines the visible latitude of the Moon which shall be North when the latitude is greater then 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 meane Anomalie● you enter the Table and thence take out the Semidiameter of the Sun and Moone and adde them together and from the summe subduct the visible latitude of the Moone at the visible Conjunction there rests the Scruples of the Suns 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 Summe 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 Suns Eclipse BY the visible latitude of the Moon and the summe of the Semidiameters of the Sun and Moon find the Scruples of incidence as in the Moones 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 finde 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 Moone 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 Suns Eclipse FOr the beginning adde to the minutes of Incidence the motion of the Sun agreeing to the time of Incidence and the summe 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 summe 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 adde to the minutes of incidence the motion of the Sun agreeing to the time of repletion and the sum adde 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 Summe Adde 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 Ecliptique where the Eclipse happens upon which as a Center draw the Peripherie ABCD of the quantity of the summe of the Semidiameters of the Moon and the earths shadow which may be done by helpe of a Scale or Sector of equal divisions also to the quantity of the Semidiameter of the earths shadow draw upon the same center another Peripherie Then because the Moones Eclipse begins on the east part of her body you must upon the west side of your plane note downe 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 marke it with K. Lastly upon the centers F K and H draw three equal circles having for Radius the Semidiameter of the Moone and the worke is done Typus Eclipseos Lunae praedictae Example of the forementioned Eclipse of the Moon March 15. 1652 Summe of the Semidiameters EB 97385 Semidiameter of shadow EM 70954 Initial