the moneth and taking 30 degrees from the Scale of Altitudes and putting one point in the line of hours till the other point turned about will but just touch the thâ—ead and I finde it to 23 minutes past 7 but if it had been in the afternoon it would have been 37 minutes past 4. 2. Again on the tenth of August in the Afternoon at 20 degrees high I take 20 degrees from the Scale of Altudes and laying the thread on the day of the moneth viz. the tenth aforesaid counting from the name at the beginning of August toward September and carrying the Compasses in the line of hours till the other point doth but just touch the thread and you shall finde it to be 54 minutes past 4 a clock 3. Again on the 11. of December at 15 degrees high work as before and you shall finde it to be just 12 a clock but to work this you must lay the Rule down on something and extend the thread beyond the Rule for the nighest distance will happen on the out-side of the Rule 4. Again on the 11 of Iune at noon I finde the altitude to be 62 degrees high then laying the thread on the 10 th or 11 th of Iune for then a day is unsensible and working as before you shal finde the point of the Compasses to stay at just 12 a clock the time required for that altitude 4. To finde the Suns rising any day in the year Lay the thread on the day of the month and in the line of hours it sheweth the true hour and minute of the Suns rising or setting for the rising count the morning hours and for the setting count the evening hours 5. To finde if any place lye level or nor Open the rule to his true angle of 60 degrees then set the moveable leg upon the place you would make level and if the thread play just on 60 degrees it is a true level place or else not 6. To try if any thing be upright or not Hang a thread and plummet on the center then aply the head leg of the rule to the wall or post and if it be upright the thread will play just on the innermost line of the scale of altitudes or else not CHAP. III. A further description of the Rule to make it to shew the Suns Azimuth Declination True place right Ascention and the hour of day or night in this or any other Lattitude 1. FIrst in stead of the scale of Altitudes to 62 degrees there is one put to 90 degrees in that place and that of 62 is put by in some other place where it may serve as well 2. The line of hours hath a double margent viz one for hours and the other for Azimuths then every 5 th minute is more properly made 4 or else every 2 minutes and in a large rule to every quarter of a degree of Azimuth or to every single minute of time 3. The degrees ought to be reckoned after 3 maner of wayes first as before is exprest secondly from 60 toward the end with 10 20 30 40 50 60 c. to be so accounted in finding the Azimuch for a particular latitude and and thirdly from the head or 90 toward the end with 10 20 30 40 50 60 70 80 c. for the general finding of Hour and Azimuth in any latitude and many other problems of the Sphere besides to which may be added where room will alow a line of hours beginning at 6 at the head and 12 at the end but reckoning 15 degrees for an hour and 4 minutes for every degree it may do as well without it 4. To the Kalender of moneths and days is added a line of the Suns true place in the Zodiack or where room fails the Characters of the twelve Signs put on that day of the moneth the Sun enters into it and counting every day for a degree may indifferently serve for the use it is chiefly intended for 5. Under that is a line of the Suns right Ascension to hours and quarters at least or rather every fifth minute numbred thus 12 and 24 right under ♈ and ♎ or the tenth of March and so forward to the tenth of Iune or ♋ where stands 6 then backwards to 12 where you began then backwards still to the eleventh of December with 13 14 15 16 17 18 to ♑ then from thence forward to 24 where you first began but when you are streightned for room as on most ordinary Rules you will be then it may very well suffice to have a point or stroke shewing when the Sun shall gradually get an hour of right Ascension and from that for every day count four minutes of time till it hath increased to an hour more and this computation will serve very well and in stead of saying 13 14 15 hours of right Ascension say 1 2 3 c. which will perform the work as well and reduce the time to more proper terms 6. There is fitted two lines one containing 24 houres and the other 29 days and about 13 hours and they serve to finde the time of the Moons coming to the South before or after the Sun and by that the time of high-water at London-bridge or any other place as is ordinary CHAP. IV. The Uses follow in order 1. To finde the Suns Declination LAy the Thread on the day of the moneth then in the line of degrees you have the declination From March the tenth toward the head is the Declination Northward the other way is Southward as by the time of the year is discovered Example On the tenth of April it is 11d 48 ' toward the North but on the tenth of October it is 10d 30 ' toward the South 2. As the thread is so laid on the day of the moneth in the line of the Suns place it sheweth that and in the line of the Suns right Ascension his right Ascension also onely you must give it its due order of reckoning as thus it begins at ♈ Aries and so proceeds to ♋ then back again to ♑ at the eleventh of December then forwards again to ♈ Aries where you began 3. To finde the Suns right Ascension in hours and minutes Lay the thread as before on the day of the moneth and in the line of right Ascension you have the hour and minute required computing right according to the time of the year that is begin at the tenth of March or ♈ Aries and so reckon forwards and backwards as the moneths go Example On the tenth of April the Suns place is 1 degree in ♉ Taurus and the Suns right Ascension 1 hour 55 minutes on the tenth of October 27d 1 4 in ♎ Libra and his right Ascension is 13 hours and 42 minutes 4. To finde the Suns Amplitude at rising or setting Take the Suns Declination out of the particular Scale of Altitudes and lay it the same way as the Declination is from 90 in the Azimuth Scale and it shall shew
the Amplitude from the east or west counting from 90. Example May the tenth it is 33. 37. CHAP. V. Having the Suns Declination or day of the moneth to finde the Azimuth at any Altitude required for that day FIrst finde the Suns Declination by the first Proposition of the fourth Chapter then take that out of the particular Scale of Altitudes or scale to 62 degrees then whatsoever the Altitude shall happen to be count the same on the degrees from 60 toward the end of the Rule according to the second maner of counting in the third Proposition of the third Chapter and thereunto lay the thred then the Compasses set to the Declination carry one point along the line of hours on the same side of the thread the Declination is that is to say if the day of the moneth or Declination be on the right side the Aequinoctial then carry the Compasses on the right side but if the Declination be on the South side that is toward the end counting from the tenth of March or Aries or Libra then carry the Compasses along the line of hours and Azimuths on the left side of the thâ—ead as all winâ—er time it will be and having set the Compasses to the least distance to the thread it shâ—ll stay at the Suns true Azimuth from the South required counting as the figures are numbred or from East or West counting from 90. Example 1. On the tenth of Iuly I desire to finde the Suns Azimuth at any Altitude first on that day I finde the Suns Declination to be 20. 45 which number count from the beginning of the particular Scale of Altitudes toward 62 and that distance take between your Compasses then are they set for all that day then supposing the Suns height to be ten degrees lay the thread on 10 counted from 60 toward the left end then carrying the Compasses on the right side of the thread because it is summer or north declination on the line of Azimuths it shall shew 110. 40 the Azimuth from the south required but if you count from 90 it is but 20. 40. from the east or west point northward according to the time of the day either morning or evening Example 2. Again on the 14. of November or the 6. of Ianuary when the Sun hath the same declination south-ward and the same Altitude to work this you must lay the Rule down on something then lay the thread on the Altitude counted from 60 toward the end as before and carrying the Compasses on the south-side of the Aequinoctial along the Azimuth-line till the other point do but just touch the thâ—ead and it shall stay at 36. 45 the Azimuth from south required if it be morning it wants of coming to south if it be after-noon it is past the south Example 3. But if the Sun be in the Aequinoctial and have no declination then it is but laying the thread to the Altitude and in the line of Azimuths the thread shall shew the true Azimuth required As for instance at 00 degrees of altitude the Azimuth is 90 at 10 degrees it is 77. 15 at 20 degrees 62. 45 at 30 degrees high 43. 15 at 35 degrees high 28. 10 at 38 degrees 28 ' high it is just south as by practice may plainly appear But if the Suns altitude be above 45 then the degrees will go beyond the end of the Rule To supply this defect do thus Substract 45 out of the number you would have and double the remainder then lay the Rule down with some piece of the same thickness in a streight line with the moveable leg then take the distance from the tangent of the remainder doubled counted from 60 to the end of the Rule in the line next the edge to the Center lay that distance in the same streight line from the tangent doubled and that shall be the tangent of the Angle above 45 whereunto you must lay the thread for the finding the Azimuth when the Sun is above 45 degrees high CHAP. VI. To finde the hour of the Night by the Moon FIrst by the help of an Almanack get the true time of the New Moon then compute her true place at that time which is always the place of the Sun very nigh at the hour and minute of conjunction then compute how many days old the Moon is then by the line of Numbers say If 29 dayes 13 hours or on the line 29. 540 require 860 degrees or 12 signs what shall â—ny less number of days and part of a day require The answer will be The Moons true place at that age Having â—ound her true place then take her alâ—itude and lay the thred on the Moons place found and work as you did for the Sun and note what hour you finde then consider if it be New Moon the hour you finde is theÌ„true hour likewise in the Full but if it be before or after you must substract by the Line of Numbers thus If 29 days 540 parts require 24 hours what shall any number of days and parts require The answer is What you must take away from the Moons hour found to make the true hour of the Night which was required But for more plainness sake I will reduce these Operations to so many Propositions before I come to an Example PROP. 1. To finde the Moons Age. First it is most readily and exactly done by an Ephemerides such a one as you finde in Mr. Lilly's Almanâ—ck or as to her Age onely in any book or Sheet-Almanack but you may do it indifferently by the Epact thus by the Rules of the 152 page in the Appendix to the Carpenters Rule Adde the Epact the moneth and the day of the moneâ—h together and the sum if under 30 is the Moons age but if above consider if the moneth have 30 or 31 days then substract 29 or 30 out and the remainder is the Moons age in days Example August 2. 1660. Epact 28. Month 6. day 2. added makes 36. Now August or sixt moneth hath 31 days therefore 30 being taken away 6 days remains for the moons age required PROP. 2. To finde the Moons place By the Ephemerides aforesaid in Mr. Lilly's Almanack you have it ser down every day in the year but to finde it by the Rule do thus Count six days back from August 2. viz. to Iuly 27. there lay the thread and in the line of the Suns place you have the Moons place required being then near alike then in regard the Moon goes faster than the Sun that is to say in 29 days 13 hours 12 signs or 360 degrees in 3 days 1 sign 6 degr 34 min. 20 sec. in one day o signs 12 degr 11 min. 27 sec. in one hour 30 min. 29 sec. or half a minute adde the signs and degrees and minutes the Moon hath gone in so many days and hours if you know them together and the Sun shall be the Moons true place being added to what she had on
the day of her change but far more readily and as exactly by the line of Numbers or Rule of Three say if 29. 540. require 360. what 6 facit 73 1 4 that is 2 signs 13 degrees 15 minutes to be added to 14 degrees in ♌ and it makes 27 1 4 in ♎ the Moons place for that day Or thus multiply the Moons age by 4 divide the product by 10 the quotient sheweth the signs and the remainder multiplied by 3 sheweth the degrees which you must adde to the Suns place on the day required and it shall be the Moons true place required for that day of her Age. Example Iuly 27. the Sun and Moon is in Leo 14 degr 0. August 2. being 6 days adde the Moons motion 2. 13d 9 ' makes being counted Virgo â™ Libra ♎ 27 deg 9 the place required which on the Rule you may count without all this work or trouble but for plainness sake I am constrained so to do Or thus PROP. 3. To finde the Moons hour To do this you must do the work of the second Chapter and second and third Proposition where note that the Moons place found is to be used as the day of the moneth or Suns declination Example The Moon being 27 degrees in Libra and 20 degrees high I finde the our to be 31 ' past 9 if on the east-side or 29 ' past 2 if on the west-side â—f the Meridian PROP. 4. To finde the true hour of the Night Having found the Moons hour as before consider the Moons age then say by the Line of Numbers or Rule of Three if 29. 540 part require 24 what shall 6 days require facit 4 hours and 52 minutes which taken from 9. 31. rest â— 29. the true time required Example Moons hour 9 31 Time to be subst â— 52 True time remain 3 39. the time required This work is done more readily by the two lines fitted for that purpose for look for 6 the Moons age in one and you shall finde â— hours 52 minutes the time to be substracted in the other CHAP. VII To finde the hour of the Night by the fixed Stars FOr the doing of this I have made choice of twelve principal fixed Stars all within the two Tropicks many more might be added but these will very well serve the turn The names of them and their right Ascension in hours and minutes is set on the Rule and the star is placed in his true Declination on or among the moneths and for to know the stars next to a Tutor a Celestial Globe or a Nocturnal of all the chief stars from the Pole to the Equinoctial and to be had at the Sun-Dial in the Miâ—nories is the best the uses whereof do follow First know the star you observe then observe his Altitude and laying the thread on the star by the second Chapter second and third Proposition get the stars hour then out of the righâ— Ascension of the star take the righâ— Ascension of the Sun found by the fifth Proposition of the third Chapter for that day and note the difference for this difference added to the star hours found shall shew the hour oâ— the night Example On the first of November I observe the Altitude of the Bulls-eye and find it to be 30. then by second and third of the second Chapter I finde the hour to be 7. 54 past the Meridian the Suns right Ascension that day finde to be 15 hours 8 minutes the stars right ascension is 4 hours 16 minutes which taken the greatest from the least by adding of 24 hours reâ— 13. 08. then 7. 54. the stars houâ— added makes 21. 02. from which taking 12 hours rest 9. 02. the hour oâ— the night required For more plainness note the work of two or threâ— Examples Stars right Ascension being set on the Rule 4 16 Suns right Asc. Nov. 1. 15 08 Substraction being made by adding 24 remain 13 08 To which you must adde the stars hour found 7 54 Then the remainder taking away 12 hours is 9 02 the true hour Again May 15 by Arcturus at 50 0 ' high westwards The right Asc. of Arcturus is 14hâ— 0 ' Suns right Asc. May 15. is 4 10 The right Asc. of the Sun taken from the R. Asc. of the star rest â— 50 The stars hour at 50 degr high found to be 02 13 Which being added to the difference before makes 1â— 03 or 11 03. Again January 5. by the Great-dog at 15 degrees high east The right Asc. of Great-dog is 06-29 The right Asc. of the Sun is 19 50 Substr made by adding 24 h. is 10-39 Stars hour at 15 degr high is 9 32 Ante M. or P. Septen Which added to the difference found and 12 substracted remains 8. 11 ' for the true Hour of the Night required to be found and so of any other star seâ— down in the Rule as by the trial and prâ—ctice will prove easie and ready to the ingenuous practitioner But by the line of 24 or twice 12 hours and the help of a pair of Compasses you may perform it withouâ— writing it down thus Take the righâ— Ascension of the Sun out of that linâ— of hours between your Compasses being always counted under 12 anâ— set the same from the right Ascensioâ— of the star toward a lesser number oâ— the beginning of the hours and thâ— point shall stay at the remainder that is to be added to the stars hour found then open the Compasses from thence to the beginning of the hours and adde that to the stars hour found and it shall reach to the hour of the night required Example Feb. 6. 1660. by Arcturus 20 degrees high Take 10 hours 1 minute between your Compasses and set it from 14 hours or 2 hours beyond 12 and it shall stay at 3. 59 then take 3. 59 and adde it to 6. 24 the stars hour at 20 degrees high and it shall be 10. 23 the hour of the night required CHAP. VIII To finde the Amplitude or Azimuth of the fixed Stars also their rising setting and southing 1. FIrst for the Amplitude take the stars declination from the particular Scale of Altitudes and lay it from 90 in the Azimuth-line and it shall shew his amplitude from East or West toward South or North according to the declination and time of day morning or evening The same work is for the sun Example The Bulls-eye hath 25. 54 degrees of amplitude so hath the Sun at 15 degrees 48 minutes of declination 2. To finde the Azimuth work as you did for the Sun at the same declination the star hath by Chapter 5. and you shall have your desire Example December 24. at 6 degrees high by the Bulls-eye I finde the Azimuth to be 107. 53. from the south 3 To finde the stars rising and setting lay the thread on the star among the moneths and in the line of hours it shews the stars rising and setting as you counted for the Sun but yet note this is
Declination of 12 principal fixed Stars in the heavens most of which are inserted on the Rule or if room will allow all of them  R. Asc. Declina Stars Names H. M. Deg. M. Pleiades or 7 Stars 03 24 23 20 Bulls-Eye 04 16 15 48 Orions Girdle 05 18 01 195 Little Dog 07 20 06 08 Lyons Heart 09 50 13 40 Lyons Tayl 11 30 16 30 Arcturus 14 00 21 04 Vultures Heart 19 33 08 00 Dolphins Head 20 30 14 52 Pegasus Mouth 21 27 08 19 Fomahant 22 39 31 17s Pegasus lower wing 23 55 13 19  1  3  5 7 4   6  8    Moneths 9  11  2 10 12  1 2 3 4 5 6 7  8 9 10 11 12 13 14 Days 15 16 17 18 19 20 21  22 23 24 25 26 27 28  29 30 31     Week-days S M T W T F Sat Dom. Letter d c b a g f e Leap years 68 80 64 76 60 72 84 Eâ—acts 26 9 12 25 28 11 23 THE Description and Use OF A JOYNT-RULE CHAP. I. The Description of the Lines on the Rule as it is made onely for one Latitude and for the finding the hour of the day onely FIrst open the Joynt of the Rule then upon the head-leg being next to your right hand you have a line beginning at the hole which is the Center of the quadrantal lines and divided from thence downward toward the head into as many degrees as the Suns greatest altitude in that latitude will be which with us at London is to 62 degrees which line I call the Scale of Altitudes divided to whole halfs and sometime quarters of degrees 2. Secondly On the other leg and next to the inside is the line of hours usually divided into hours quarters and every fifth minute beginning at the head with 4 and so proceeding to 5 6 7 8 9 10 11 and 12 at the end and then back again with 1 2 3 4 5 6 7 8 for the morning and afternoon hours 3. Next to this is a Kalendar of Moneths and Days in two lines the uppermost contains that half year the days lengthen in and the lowermost the shortning days as by the names of the moneths may appear the name of every moneth standing in the moneth and at the beginning of the moneth and all but the two moneths that have the longest and the shortest days viz. Iune and December are divided into single days the tenth day having a figure 10 or a point or prick on the head of the stroke and the fifth onely a longer stroke without a prick and the beginning of every moneth a long stroke and every single day all alike of one shortness according to the usual manner of distinguishing on lines 4. And lastly you have a line of degrees for so they be most properly called and they are the same with the equal limb on quadrants and serve for the same use viz. for taking of Altitudes or Horizontal Angles and are divided usually to whole and half degrees of the quadrant and figured with 30 40 50 600 7010 8020 and 90 just on the head cutting the center or point where the Scale of Altitudes and the Line of Hours meet which point for distinction sake I call The rectifying point And the reckoning on this line as to taking of Altitudes is thus At the number 600 is the beginning then towards the head count 10 20 30 where the 90 is then begin at the end again count as the figures shew you to 90 at the head as before CHAP II. The Uses of the Rule follow 1. To Rectifie or set the Rule to his true Angle OPen the Rule to 60 degrees which is done thus indifferently make the lines on the head and the lines on the other leg meet in a streight line then is the Scale of Altitudes and the line of Hours set to an Angle of 60 degrees the rectifying point being the center of that Angle Or to do it more exactly do thus put one point of a pair of Compasses into the rectifying point then open the other to 10 20 30 or 40 on the Scale of Altitudes the Compasses so opened and the point yet remaining in the rectifying point turn the other to that margenal line in the line of hours that cuts the rectifying point and there stay it then remove the point that was fixed in the rectifying point and open or shut the Rule till the point of the Compasses will touch 10 20 30 or 40 being the point you set the Compasses too in the Scale of Altitudes in the innermost line that cuts the center and the rectifying point then is it set exactly to 60 degrees and fitted for observation 2. To finde the Suns Altitude at any time Put a pin in the center hole at the upper end of the Scale of Altitudes and on the pin hang a thread and plummet then if the Sun be low that is to say under 25 degrees high as in the winter it will always be then lift up the moveable leg where the moneths and the degrees be till the shadow of the end fall just on the meeting of that leg with the head then the thread shall shew the Suns altitude counting from 600 towards the head either 10 20 25 or any degree between But if the Sun be above 25 or 30 degrees high lift up the head leg till the shadow of that play as before or make the shadow of the pin in the center hole play on the innermost line of the Scale of Altitudes where the pin standeth then the thread will fall on the degree and part of a degree that his true altitude shall be But if the Sun be in a cloud and can not be seen so as to give a shadow then look up along by the head-leg or moveable leg just against the middle of the round body of the Sun and the thread playing evenly by the degrees shall show the true altitude required The like must you do for a Star or any other object whose altitude you would find 3. Having found the Suns altitude and the day of the moneth to finde the hour of the day Whatsoever you finde the altitude to be take the same off from the Line of Altitudes from the center downwards with a pair of Compasses then lay the thread being put over the pin on the day of the moneth then put one foot of the Compasses in the line of hours in that line that cuts the rectifying point and carry it further off or nigher till the other foot of the Compass being turned about will just touch the thred at the nearest distance then the point of the Compasses on the line of hours shall shew the true hour and minute of the day required Example on the 2. of July 1. I observe the altitude in the morning and I finde it to be 30 degrees high then laying the thread on the day of