off these kind of Planes To these Hour lines I set their numbers as you may see iâ— the Figure Here you may see that in Declining Dyals the Style doth not stand at the same Elevation above the Plane that it doth in Erect Direct Dyals neither doth it stand over the 12 a clock line but swerves from it towards the Quarter of Declination PROB. X. To make a North Erect Dyal declining Eastwards or Westwards AS in Prob. 5. an Erect Direct North Dyal hath the same Delineation that an Erect Direct South Dyal hath and differs only in the placing the Figures of the Hour lines So a North Erect Dyal that declines Eastwards or Westwards differs from a South Erect Dyal that Declines Eastwards or Westwards the same number of degrees only in placing the Hour lines at the same distance on the contrary side of the Plane and by transposing the Figures of 11 for 1 10 for 2 9 for 3. c. Thus if you draw upon Glass Horn or an Oyled Paper the South Dyal Declining Eastwards as in the foregoing Probleme and place it to its due scituation the back side of it shall be a North Dyal declining towards the West so many degrees as the foreside Declines towards the East and the only difference in it will be the Figures of the Hour lines as was said before PROB. XI To make Direct Reclining or Inclining Dyals DIrect Reclining or Inclining Dyals are the same with Erect Direct Dyals that are made for the Latitude of some other Places The Latitude of which Places are either more then the Latitude of your own Place if the Plane Recline or less if the Plane Incline and that in such a proportion as the arch of Reclination or Inclination of your Plane is Thus a Direct South Dyal Reclining 10. degrees in Londons Latitude viz. 51½ degrees is an Erect Direct Dyal made for the Latitude of 61½ degrees And a Direct South Dyal Inclining 10. degrees in the Latitude 51½ degrees is an Erect Direct Dyal in the Latitude of 41½ degrees and is to be made according to the Directions in Prob. 4. PROB. XII To make Declining Reclining or Declining Inclining Dyals THe distances of the Hour lines either for a Declining Reclining Plane or a Declining Inclining Plane may most easily be found upon the Plane of the Horizon That is as some Authors call it by the Horizontal Dyal by changing the Circles of the Globe one into another So as the Plane of the Horizon may serve to represent the Dyal Plane Yet this way not being natural because you must admit one Circle to be another and that in Young Learners might sometimes breed a little difficulty Gemma Frisius Metius and Blaew hath prescribed a thin Brass plate to be made equal to a Semi-Circle of the Equinoctial and divided from the middle point of it either way into 90 degrees which may not unproperly be called a Gnomonical Semi-Circle This Semi-Circle must be bowed close to the Body of the Globe into a Semi-Circular form and so set to any Reclination or Inclination and then it will represent a Reclining or Inclining Plane And by the motion of the Colure through the several degrees of this Semi-Circle the distances of the Hour lines may be found Thus The Globe Quadrant of Altitude Colure and Hour Index Rectified as by Prob. 4. Bring the lower end of the Quadrant of Altitude to the degree in the Horizon of the Planes Declination if your Plane be a South Declining Recliner and count on the Quadrant of Altitude from the Zenith downwards the number of degrees of Reclination or Inclination and to that number of degrees bring the middle of the Gnomonical Semi-Circle and let the ends of â—t cut the Horizon on either side in the degrees of the Planes Azimuth so shall the Gnomonical Semi-Circle represent a Reclining Plane And so oft as 15. degrees of the Equator passes through the Meridian so oft shall you enquire what degrees of the Gnomonical Semi-Circle the Colure cuts for so many degrees asunder must the several respective Hour lines of a Reclining Declining Plane be in a Semi-Circle divided into 180. degrees But if your Plane be a South Declining Recliner or a North Declining Incliner Bring the Quadrant of Altitude to the degree of the Horizon opposite to the degree of the Planes Declination because the upper side of the Plane lies beyond the Zenith counted from the South point in the South Recliners and from the North point in North Incliners Then find the height of the Style and place of the Substyle thus Keep your Gnomonical Semi-Circle in its position But turn the Quadrant of Altitude about on the Zenith point till the lower end of it comes to the degree of the Horizon opposite to the degree it was placed at before and turn about the Globe till the Colure cut the Quadrant of Altitude above the Horizon in the number of degrees the Plane Reclines from the Zenith so shall the Colure cut the Gnomonical Semi-Circle at Right Angles Then count the degrees contained between the middle of the Gnomonical Semi-Circle and the Colure for that number of degrees is the distance of the Substyle from a Perpendicular line in the middle of your Plane and must be placed Westwards of the said Perpendicular if your Plane decline from the South East-wards or Eastwards if your Plane decline from the South Westwards Then observe how many degrees are contained between the Semi-Circle and the Pole for that number of degrees is the number of degrees that the Style is to be Elevated above the Substyle Example Here at London I would make a Dyal upon a Plane Declining from the South Eastwards 30. degrees and Reclining from the Zenith 20. degrees Londons Latitude is 51½ degrees Therefore Having on the Plane discribed a Semi Circle c. as was directed Prob. 4. I Rectifie the Globe Quadrant of Altitude Colure and Hour Index as by the same Probleme and bring the lower end of the Quadrant of Altitude to 30. degrees from the North point of the Horizon towards the West because that is the degree opposite to the degree of the Planes Declination viz to 30 degrees from the South Eastwards And I bring the middle of the Gnomonical Semi Circle to 20. degrees of the Quadrant of Altitude counted from the Zenith downwards towards the Horizon and the ends of the Gnomonical Semi Circle to the degrees of Azimuth the Plane lies in in the Horizon viz. to 30. degrees from the East point Northwards and to 30. degrees from the West point Southwards so shall 11. degrees 10. minutes of the Gnomonical Semi Circle be comprehended between the Quadrant of Altitude and the Brasen Meridian These 11. degrees 10. minutes shews that the 12 a clock line is distant from the Perpendicular A B 11. degrees 10. minutes and because the Plane Declines to the Eastwards therefore the 12 a clock line must stand on the West side the Plane 11. degrees 10
in the Zenith and bring the first point of ♈ to the Meridian Then count on the Quadrant of Altitude to the Degree of the Suns Declination and bring that degree to the Equinoctial and the degree of the Equinoctial cut by that degree of the Quadrant of Altitude is the degree of the Poles Elevation Example The Suns Amplitude is 33. degrees 20. minutes his Declination is 20 degrees 5 minutes his Complement of Amplitude to 90. is 56 degrees 7 minutes Therefore I Elevate the Pole 56. degrees 7 minutes above the Horizon and screw the Quadrant of Altitude to 56 degrees 7 minutes which is in the Zenith Then I bring the first point of ♈ to the Meridian and number on the Quadrant of Altitude upwards 20. deg 5 min. for the Suns Declination this 20 th degree 5 minutes I bring to the Equinoctial and find it cut there 51 ½ degrees for the Heigth of the Pole PROB. III. The Suns Declination and Hour at East given to find the Heigth of the Pole ELevate the Pole so many degrees as the Suns Declination is and screw the Quadrant of Altitude in the Zenith Then convert the Hours or minutes past 6. given into degrees by allowing 15 degrees for every Hour of Time and for every minute of Time 15 minutes of a Degree and number those degrees or minutes in the Horizon from the East Southwards so shall the Degree of the Quadrant of Altitude cut by the Equator be the Complement of the heigth of the Pole Example The Suns Declination is 20 deg 5 min. Therefore I Elevate the Pole 20 degrees 5 minutes and also screw the Quadrant of Altitude to â—0 degrees 5 minutes which is in the Zenith the Hour the Sun comes to be at East is 8 a clock 53 minutes that is 1 Hour 7 minutes after 6. Therefore I convert 1 Hour 7 minutes into Degrees as before and it gives 16 degrees 50 minutes which number of degrees and minutes I count from the East point Southwards and thither I bring the Quadrant of Altitude Then I look in what degree of the Quadrant of Altitude the Equator cuts and find 38 ½ which is the Complement of the Poles Heigth viz. 51 ½ degrees for the Heigth of the Pole In this Probleme the Declination of the Sun and Elevation of the Pole bears the same Denomination of either North or South for when the Declination and the Elevation are different the Sun cannot come to the East point PROB. IIII. The Declination of the Sun and his Altitude at East given to find the Heigth of the Pole ELevate the Pole to the Complement of the Suns Altitude and screw the Quadrant of Altitude to the Zenith Then bring the Equinoctial point ♈ to the Meridian and number on the Quadrant of Altitude the degrees of the Suns Declination and bring that degree to the Equinoctial and note the degree it cuts for its Complement to 90 is the Heigth of the Pole Example May 10. The Suns Declination is 20 degrees 5 minutes His Altitude at East is 25 degrees 55 minutes here at London I enquire the Heigth of the Pole Therefore I substract 20. 5 min. from â—0 the remains is 69 deg 55 min. for its Complement wherefore I bring 69 deg 55 min. of the Meridian to the Horizon and to 69 deg 55 min. which is in the Zenith I screw the Quadrant of Altitude then I bring ♈ to the Meridian and count on the Quadran of Altitude upwards 20 deg 5 min and move it about the Equinoctial till those 20 deg 5 min. touch the Equinoctial which I find to be in 38 ½ degrees Therefore I substract those 38 ½ from 90 and the remains is 51 ½ degrees Therefore I say the Pole here at London is Elevated 51 ½ degrees The Declination and the Elevation is alwaies the same either North or South for when they alter their Denomina ions the Sun at East can have no Altitude neither can it indeed reach the East point and therefore in this example because the Declination of the Sun is North it is the North Pole that is Elevated here at London To perform the same otherwise with a pair of Compasses Take off with your Compasses from the Equator or Quadrant of Altitude the number of degrees of Altitude observed and place one foot at the beginning of ♈ on the inner edge of the Horizon and extend the other directly upwards towards the Zenith Then move the Brazen Meridian through the notches of the Horizon till the other point of your Compasses respecting the Zenith reach the Parallel of the Suns Declination So shall the number of degrees on the Meridian be the number of degrees that the Pole is Elevated above the Horizon and is either North or South according as the Suns Declination is as before This may yet otherwise be performed with the Quadrant of Altitude by taking the Nut off the Meridian and laying the edge of its Index specified in Chap. 1. Sect. 6. of the first Book exactly on the East line of the Horizon for when that lies straight between the point of East on the outer Verge of the Horizon and the beginning of ♈ in the inner Verge of the Horizon then shall the upper end of the Quadrant of Altitude point directly to the Zenith and if then you turn the Meridian through the notches of the Horizon till the Suns Altitude on the Quadrant of Altitude cut the Parallel of Declination you will have on the Meridian the heigth of the Pole as before PROB. V. By the Suns Declination and Azimuth at 6. of the Clock given to find the Heigth of the Pole and Almicantar at 6. ELevate the Pole so many degrees as the Suns Azimuth is at 6. and screw the Quadrant of Altitude in the Zenith and bring the first point of ♈ to the Meridian Then number on the Quadrant of Altitude upwards the Complement of the Suns Declination and bring that degree to the Equator So shall the degree of the Horizon cut by the Quadrant of Altitude be the Complement of the Poles Elevation and the degree of the Equator cut by the Quadrant of Altitude shall be the Almicantar of the Sun at 6. of the clock Example The Suns Azimuth at 6 is 12¾ degrees Therefore I Elevate the Pole 12¾ and screw the Quadrant of Altitude to 12¾ degrees which is in the Zenith Then I bring the first point of ♈ to the Meridian The Suns Declination is 20 degrees 5 minutes Therefore I number on the Quadrant of Altitude 69 deg 55 min. which is the Complement of 20 deg 5 min. to 90. this 69 deg 55 min. on the Quadrant of Altitude I bring to cut the Equator and find when 69 deg 55 min cuts the Equator that the Quadrant of Altitude cuts the Horizon in 38½ deg which is the Complement of the Poles Elevation and at the same time the Quadrant of Altitude also cuts the Equator in 15½ degrees which is the
placed at the East or West point of the Horizon Therefore when you would find what Circle of Position any Star or degree of the Ecliptick is in Rectifie the Globe and Quadrant of Altitude and bring the lower end of the Quadrant of Altitude to the East or West point of the Horizon and lift up the Circle of Position till it come to the Star or degree of the Ecliptick proposed and the number of degrees the Circle of Position then cuts in the Quadrant of Altitude is the number of the Circle of Position that the Star or degree of the Ecliptick is in If the Star or degree of the Ecliptick be under the Horizon turn the Globe about till 180 degrees of the Equator pass through the Meridian then will the Star or degree of the Ecliptick be above the Horizon Lift up then the Circle of Position as before to the Star or degree of the Ecliptick and the number of degrees of the Quadrant of Altitude the Circle of Position cuts on the East side is the number of Circles of Position the Star was under the Horizon on the West side Or so many degrees as the Circle of Position cuts on the Quadrant of Altitude in the West side the Horizon is the number of the Circles of Position the Star or degree of the Ecliptick was under the Horizon on the East side PROB. VII To find the Right Ascensions the Oblique Ascensions and the Declinations of the Planets EXamine the Right Ascensions and Declinations of those pricks made to represent each Planet in Prob. 1. of this Book and work by them as you were directed to work by the Sun in Prob. 26 27 28. of the second Book PROB. VIII How to Direct a Figure by the Globe TO Direct a Figure is to examine how many degrees of the Equinoctial are moved Eastwards or Westwards while any Planet or Star in one House comes to the Cusp or any other point of any other House When you would Direct any Promittor to any Hylegiacal point examine the degree of the Equator at the Meridian then turn about the Globe till the Promittor come to the Hylegiacal point and examine again the degree of the Equator at the Meridian and by substracting the lesser from the greater you will have the number of Degrees that passed through the Meridian whiles the place of the Promittor was brought to the Hyâ—â—gâ—â—cal point and that number of degrees shall be the Arch of Dâ—rection Example I would Direct the Body of the Moon in our Figure aforesaid to Medium Câ—â—â— or the tenth House I find by the Globe 20â— degrâ—es 30. minutes of the Equator at the Meridian with the â—eath House and turning the Globe till the prick made to represent the Moon come to the Meridian I find 227 degrees 20 minutes of the Equator come to the Meridian with it Therefore I 〈◊〉 the lesser from the greater viz. 2â—3 degrees 3 minutes from 227. degrees 2â— minutes and have remaining 2â— degrees 50 minutes This 〈◊〉 degrees 50. minutes shews that 23. Years 1â— Moneths must expire ere the Effects promised by the Moons present position shall opperate upon the signification of the 〈◊〉 House If the Body of the Moon had been Directed to any other point the◠〈◊〉 Meridian or Horizon you must have Elevated the Circle of 〈◊〉 〈◊〉 the point proposed and have under-propped it to that 〈◊〉 and 〈◊〉 have turned about the Globe till the prick 〈◊〉 the Moon had come to the Circle of Position and then 〈◊〉 degrees of the Equator that should have passed through the Meridian whiles this motion was making should be the number of degrees of Direction and signifie in Time as foresaid PROB. IX Of Revolutions and how they are found by the Globe BY Revolution is meant the Annual Conversion of the Sun to the same place he was in at the Radix of any Business When you would find a Revolution by the Globe first find the Right Ascension of Mâ—d Heaven at the â—â—adix of the Business as by Prob 26. of the second Book you were directed to find the Right Ascerâ—â—on of the 〈◊〉 and 〈◊〉 add 87 degrees for every Yâ—aâ— since the Radix Then substract 360 so oâ—â— as you can from the whole and the Râ—mâ—â—â—s shall be the Right Ascension oâ— Mid Hâ—aven for the Aâ—â—â—al Revoluâ—â—on Iâ— yâ—u 〈◊〉 the number of degrees of the Equator contained between the Râ—ght Aâ—cension of the Mid Hâ—aven and the Right Ascension of the Sun and convert that number of degrees 〈◊〉 Time by allowing for every 15. degrees 1 Hour of Time it will shew if the Suns place be on the Western side of the Meridian the number of Hours and minutes Afternoon the Revolution shall hâ—ppen on but if on the East side the Meridian the number of Hours and minutes Before-noon the Revolution shall happen on PROB. X. How a Figure of Heaven may be erected by the Revolution thus found SEek the degree of Right Ascension of Mid Heaven and bring it to the Meridian so shall the four Cardinal points of the Globe be the same with the four Cardinal points in Heaven at the time of the Revolution The other Hâ—â—â—ses are 〈◊〉 by the Circle of Position as in the first Probleme of this Book The End of the Fourth Book The Fifth BOOK Shewing the Practical Use of the GLOBES Applying them tâ— the Solution of Gnomonical Problems PRAEFACE DYals are of two sorts Pendent and Fixed Pendeâ— are such as are hung by the hand and turned towards the Sun that by its Beams darting througâ— smal Pin-holes made for that purpose the hour of the Daâ— may be found These are of two sorts Vniversal and Pâ—â—ticular Vniversal Dyals are those commonly called Equiâ—ocâ—â—â— or Ring-Dyals They are used by Sea-men and Trâ—vellers that often shift Latitudes Particular are such as are made and only serve for Particular Latitudes Of these sorts are the several Dyaâ—â— discribed on Quadrants Cilinders c. Fixed Dyaâ—s shall be the matter of this discourse and they are such as are made upon fixed Planes and shew the Hour of the Day by a Stile or Gnomon made Parallel to the Axiâ— of the World Of the several Kinds of Dyal Plains and how you may know them A Plain in Dyalling is that flat whereon a Dyal is discribed There is some disagreement among Older and Later Authors in the naming of Plains for some name them according to the Great Circle in Heaven they ly in and others according to the scituation of the Poles of the Plains Thus they which name them according to the Great Circle in Heaven their Plains ly in call that an Horizontal Plain which others call a Vertical Plain those Vertical which others will call Horizontal and those Polar which others call Equinoctial However they be called it matters not so you can but distinguish their kinds which with a little consideration you may easily learn to do For remembring but upon what grounds either the
that shadow shall be a Meridian liâ—e Secondly on the backside the Clinatory discribe a Circle and draw a line through the Center to both sides the Circumference cross this line with an other line at Râ—ght Angles in the Center so shall the Circle be divided into four equal parts These four parts you must maâ—k with East West North South and divide each of them into 90. degrees In the Center of this Plain erect a straight wyer prependicularly when you would find a Meridian line examine by the tenth Prob. of the second Book the Amplitude of the Suns Rising or Setting from the East or West points and waiting the just Rising or Setting that Day turn the Instrument about till the shadow of the wyer falls upon the same degree from the East or West the Amplitude is of for then the North and South line in the Instrument will be the same with the North and South line in Heaven Thirdly by the Suns Azimuth Find the Azimuth of the Sun by Prob. 22. of the second Book and at the same instant turn the Instrument till the shadow of the wyer fall upon the degree on the Instrument opposite to the degree of the Suns Azimuth so shall the Meridional line of the Instrument agree with the Meridional line in Heaven You may the same way work by the Azimuth of any Star Only whereas the shadow of the wyer should fall upon the opposite degree aforesaid Now you must place a Sight or Perpendicular upon that opposite degree and turn the Instrument about till the wyer at the Center the Sight in the opposite degree of the Stars Azimuth and the Star in Heaven come into one straight line so shall the Meridian line of the Instrument agree with the Meridional line in Heaven Fourthly It may be found by any Star observed in the Meridian if two Perpendiculars be erected in the Meridian line of your Instrument for then by turning the Instrument till the two Perpendiculars and the Star come into a straight line the Meridian line of your Instrument will be the same with the Meridian line in Heaven See more waies in Mr. Palmer on the Planisphear Book 4. Chap. 9 If your Plain either Recline or Incline apply one of the sides of your Clinatory Parallel to one of the Semi-diameters of the Quadrant to the Plain in such sort that the Plumb-line hanging at liberty may fall upon the Circumference of the Quadrant for then the number of degrees of the Quadrant comprehended between the side of the Quadrant Parallel to the Plain and the Plumb-line shall be the number of degrees of Reclination if thâ— Center of the Quadrant points upwards or Inclination if thâ— Center points downwards If your Reclining or Inclining Plain Decline draw upon it a line Parallel to the Horizon which you may do by applying the back-side of the Clinatory and raising or depressing the Center of the Quadrant till the Plumb-line hang just upon one of the Semi-diameters for then you may by the upper side of the Clinatory draw an Horizontal line if the Plain Incline or by the under side if it Recline If it neither Incline or Recline you may drawâ— an Horizontal line both by the upper and under sides of the Clinatory Having drawn the Horizontal line apply the North 〈◊〉 â— of the Clinatory to it and if the North end of the Needle 〈◊〉 directly towards the Plain it is then a South Plain If the 〈◊〉 point of the Needle points directly from the Plain it is a Norâ—â— plain but if it points towards the East it is an East Plain if towards the West a West Plain If it do not point directly 〈◊〉 East West North or South then so many degrees as the 〈◊〉 declines from any of these four points to any of the other of 〈◊〉 four points so many degrees is the Declination of the Plain 〈◊〉 respect as aforesaid had to the Variation of the Compass Or if you find the Azimuth of the Sun by its Altitude observed just when its beams are coming on or going off youâ— Plain that Azimuth shall be the Azimuth of your Plain Or you may erect a wyer Perpendicularly on your Plain and wait till the shadow of that wyer comes to be Perpendicular with the Horizon which you may examine by applying a Plumb-line to it for then the shadow of the Plumb-line and the shadow of the Perpendicular will be in one then taking the Altitude of the Sun you may by Prob. 22. of the second Book find its Azimuth and thereby know in what Azimuth the Plain of your Dyal lies for the Azimuth your Plain lies in is distant from the Azimuth of the Sun just 90. degrees PROB. I. How by one position of the Globe to find the distances of the Hour-lines on all manner of Plains YOu may have Meridian lines drawn from Pole to Pole through every 15. degrees of the Equinoctial to represent the Horary motion of the Sun both Day and Night and when the Pole of the Globe is Elevated to the height of the Pole in any Place and one of these Meridian lines be brought to the Brazen Meridian all the rest of the Meridian lines shall cut any Circle which you intend shall represent the Plain of a Dyal in the number of degrees on the same Circle that each respective Hour-line is distant from the Noon-line point in the same Circle Thus if you should enquire the distance of the Hour-lines upon an Horizontal Plain in Londons Latitude The Pole of the Globe as aforesaid must be Elevated 51½ degrees and one of the Meridian lines you may chuse the Vernal Colure be brought to the Brazen Meridian which being done you are only to examine in the Horizon Because it is an Horizontal Plain at what distance from the Meridian which in Horizontals is the Noon-line the several Meridians drawn on the Globe intersect the Horizon for that distance in degrees shall be the distance on a Circle divided into 360. degrees that each respective Hour-line must have from the Meridian or a Noon line chosen in the same Circle and lines drawn from the Center of that Circle through those degrees shall be the Hour lines of an Horizontal Plain If your Plain be not Direct but declines East or West 〈◊〉 must number the Declination Eastwards or Westwards reâ—pectively in the degrees of the Horizon and the Quadrant 〈◊〉 Altitude screwed to the Zenith as aforesaid bring the lower end of the Quadrant of Altitude to the said degrees of Declination and the number of degrees cut by the Meridians in the Quadrant of Altitude numbred downwards is the number of degrees that the Hour-lines are distant from the Noon line in a Circle of 360 degrees And lines drawn from the Center of that Circle through those degrees be the Hour lines of half the Day And if you turn about the Quadrant of Altitude upon the Zenith point till the lower end of it come to the degree of the Horizon
Contingence elevated to the Height of the Equinoctial draw line from the Center through every 15 degrees of the Circle of Position and by continuing them intersect the line of Contiâ—gence in the points from whence the Hour lines of an East or West Dyal is to be drawn Example But because in our Latitude the Sun Rises before 4. in the Morning therefore two Hour-lines are yet wanting viz. 5 and 4 which I may find either by applying the thred first to 15 and next to 30 degrees from 0 towards g in the Semi-Circle and so marking where it cuts the Contingent line as before Or else by transfering the distance of the same number of Hour lines from the 6 a clock line already drawn on the side e 〈◊〉 to the side e g as in Prob. 2. of this Book is more fully shewed Having thus marked out on the Contingent line the distances of each Hour I draw a line Parallel to the Contingent line and draw lines from every Hour markt on the Contingent to cross the Contingent line at Right Angles and continue each line to the line Parallel to the Contingent and these lines shall be the Hour lines of an East Plane To these Hour-lines I set Figures as in the Scheam may be seen The Style D K of this Dyal as well as of others must stand Parallel to the Axis of the World it must be also Parallel to all the Hour lines and stand directly over the 6 a clock line and that so high as is the distance between the Center of the Semi-Circle of Position and the point where the 6 a clock line cuts the Contingent line Or which is all one at such a height as when it is laid flat down upon the Plane it may just reach the 3 a clock line PROB. VII To make an Erect Direct West Dyal AN Erect Direct West Dyal is the same in all respects with an Erect Direct East Dyal Only as the East shews the Fore-noon Hours the West shews the After-noon Hours Thus if you should draw the East Dyal on any transparent Plane as on Glass Horn or an Oyled Paper on the one side will appear an East Dyal and on the other a West Only the Figures as was said before must be changed for that which in the East Dyal is 11 in the West must be 1 that which in the East Dyal is 10 in the West must be 2 that which in the East Dyal is 9 in the West must be 3. c. PROB. VIII To make a Polar Dyal POlar Dyals are Horizontal Dyals under the Equinoctial They are of the same kind with East and West Dyals Only whereas East and West Dyals have but the Hour lines of half the longest Day discribed on them these have all the Hour lines of the whole Day and are marked on both sides the Noon line as in the following Figure The Style of this Dyal must stand over the Noon line Parallel to the Plane for then it will also be Parallel to the Axis of the World and its height above the Plane must be the distance between the Center i of the Semi-Circle and the point in the Contingent line cut by the Noon-line But I have inserted the Figure which alone is sufficient Instructions PROB. IX To make Erect South Dyals Declining Eastwards or Westwards DRaw on your Plane an Horizontal line and on it discribe a Semi-Circle as you were taught in Prob 4. Then Rectifie the Globe Quadrant of Altitude Colure and Hour Index as by the same Probleme and bring the lower end of the Quadrant of Altitude to the degree of Declination from the East or West point according is your Declination is Eastwards or Westwards for then the Quadrant of Altitude shall represent a Plane declining from the South Eâ—stwards or Westwards accordingly Then tuâ—n the Globe Eastwards till the Index of the Hour-Circle points to all the Hours before Noon and examine in what number of degrees from the Zenith the Colure cuts the Qâ—â—drant of Altitude when the Index points to each Hour For a line drawn from the Center A through the same number of degrees reckoned from the Perpendicular A B which is the 12 a clock line towards Con the Plane shall be the same Hour-lines the Index points at Example I would make an Erect Dyal declining from the South towards the East 27. degrees The Globe Quadrant of Altitude Vernal Colure and Hour Index Rectified as before I bring the lower end of the Quadrant of Altitude to 27. degrees counted from the East point of the Horizon towards the North Then I turn the Globe East-wards till the Index points to 11 a clock or till 15. deg of the Equator pass through the Meridian and find the Colure cut the Quadrant of Altitude in 9.43 counted from the Zenith 10 19.0 9 25.57 8 35.10 7 45.56 6 60.15 5 79.45 And these are the distances of the Fore-noon Hour-lines which I seek in the West side of the Plane viz. from B towards C and through these distances I draw lines from the Center and these lines shall be the Fore-noon Hour-lines Now herein is a difference between Declining Dyals and Direct Dyals For having found the distances of the Hour lines for one half of the Day be it either for Before Noon or After Noon in a Direct Dyal you have also found the distances for the other half Day because as was said Prob. 3. Equal number of Hours have equal distance from the Noon line But in Declining Dyals it is not so Because the Sun remaining longer upon that side of the Plane which it declines to then it doth upon the contrary side there will be a greater number of Hour lines upon it and by consequence the distance of the Hour lines less then on the contrary side of the Plane Therefore for finding the After Noon Hour lines I turn about the Quadrant of Altitude upon the Zenith point till the lower end of it come to the degree of the Horizon opposite to that degree of Declination that the Quadrant of Altitude was placed at when I sought the Fore Noon Hour lines viz to 27. degrees counted â—om the West towards the South and bring the Verâ—al Colure again to the Meridian and the Index as before to 12. Then turning the Globe Westwards till the Index poinâ—s to 1 a clock or till 15 degr of the Equator pass through the Meridian I find the Colure cut the Quadrant of Altitude in 11.20 counted from the Zenith 2 26.47 3 49.20 4 75.52 And these are the distances of the After Noon Hour lines which distaâ—â—â—â— I seek in the East side of the Plane viz. from B towards D as before and so drawing lines from the Center A through these distances I have all the Afternoon Hour lines also drawn on my Plane You may note that this Plane is capable to receive no more Hour lines After Noon then 4. for when the Colure goes off the Quadrant of Altitude the Sun goes
minutes Then to find all the Fore Noon Hour lines I turn the Globe East-wards till the Index points to 11 a clock or till 15 degr of the Equator pass through the Meridian and find the Colure cut the Gnomonical Semi-Circle in 15. 8 counted from the middle of the Gnomonical Semi Circle 10 18. 56 9 22. 37 8 26. 52 7 32. 37 6 42. 5 5 62. 43 And these are the distances of the Fore Noon Hour lines to which distances you may set Pricks on the West side the Semi Circle of the Plane viz. from B to C. The After Noon Hour lines are found by bringing the Colure again to the Meridian and the Index of the Hour Circle to 12. for then turning the Globe Westwaâ—s till the Index points to 1 a clock or till 15 degr of the Equator pass throug the Meridian I find the Colure cut the Gnomon Semi-Circle in 5. 45 counted from the middle of the Gnomon Semi-Circle 2 2. 54 3 20. 52 4 64. 36 Having drawn the Hour-lines I remove the Quadrant of Altitude to the degree of the Horizon opposite to the degree it was at before viz. to 30. degrees from the South Westwards which is so much as the Plane declines Eastwards But I let the Gnomonical Semi Circle stand as it did And turning about the Globe till the Colure cut the Quadrant of Altitude in 20. degrees counted from the Horizon upwards viz. the degrees of Reclination I find 18. degrees 40. minutes contained between the middle of the Gnomonical Semi Circle and the Brasen Meridian which is the distance of the Substyle from the Perpendicular And I find the Gnomonical Semi Circle cut the Colure in 13. degrees 49. minutes from the Pole which is the Height that the Style must be raised over the Substyle Therefore I prick off in the Semi Circle on the Plane the distance of the Substyle 18. degrees 40. minutes from the Perpendicular Westwards because this Plane declines Eastwards And from the Center A I draw through that prick the line A E which shall be the Substyle and from this Substyle either way I count in the Semi Circle on the Plane 13 degrees 49. minutes and there make a Prick Then from the Center A I draw through that Prick the line A F to represent the Style or Gnomon Then I let fall the Perpendiculer F G upon the Substyle A G So is a Triangle made which if it be erected Perpendicularly upon the Substyle A G the Style A F shall be Parallel to the Axis of the World and cast a shadow upon the Hour of the Day Having made this Dyal you have made four several Dyals whereof this is one And his opposite viz. North Declining Westwards 30. degrees Inclining to the Horizon 70. degrees is another The South Declining Westwards 30. degrees Reclining from the Zenith 20. degrees is another And his opposite viz. North Declining Eastwards 30. degrees Inclining to the Horizon 70. degrees is the other PROB. XIII To make a Dyal upon a Declining Inclining Plane THe Precepts for making these Dyals are delivered in the foregoing Probleme Therefore we shall at first come to an Example I would make a Dyal upon a Plane in Londons Latitude Declining from the South Westwards 25. degrees and Inclining towards the Horizon by the space of an Arch containing 14. degrees Having first discribed on the Plane a Semi Circle as was directed Prob. 4. I rectifie the Globe Quadrant of Altitude Colure and Hour Index as by the same Probleme and bring the lower end of the Quadrant of Altitude to the degree of the Planes Declination viz. to 25. degrees counted from the South Westwards and the ends of the Gnomonical Semi Circle to the degree of Azimuth the Plane lies in viz. to 25. degrees from the West Northwards and the middle of the Gnomonical Semi Circle to the degree of the Planes Inclination viz. 14. degrees counted from the Zenith downwards on the Quadrant of Altitude Then counting the degrees of the Gnomonical Semi Circle contained between the middle of the same and the Brasen Meridian I find 5. degrees 30. minutes These 5. degrees 30. minutes shews the distance of the 12 a clock line from the Perpendicular Therefore I number in the Semi Circle discribed on the Plane from the Perpendicular Westwards Because the middle of the Gnomonical Semi Circle lies Westwards on the Globe from the Meridian And for finding all the Fore-Noon Hour-distances I turn the Globe East-wards till the Index points to 11 a clock or till 15 degr of the Equa pass throug the Meridian and find the Colure cut the Gnomon Semi-Circle in 20. 5 counted from the middle of the Gnomon Semi-Circle 10 36. 57 9 56. 24 8 76. 31 And these are the distances of all the Fore Noon Hour lines to which several distances I make pricks on the West side the Semi Circle on the Plane viz. from B to C. The After Noon Hour lines are found by bringing the Colure again to the Meridian and the Index of the Hour Circle to 12. For then turning the Globe Westwards till the Index points to 1 a clock or till 15. degrees of the Equator pass through the Meridian I find the Colure cut the Gnomonical Semi-Circle in 6. 20 counted from the middle of the Gnomonical Semi Circle 2 18. 2 3 28. 45 4 39. 56 5 52. 30 6 67. 19 7 84. 13 And these are the distances of the After Noon Hour lines which I also prick down at their respective distances from the Perpendicular Eastwards viz. from B towards D on the Plane and by drawing lines from the Center A through all the Pricks I have all the Hour lines that this Plane will admit of Having made this Dyal you have also four Dyals made as well as in the former Probleme For this is one and its opposite viz. North declining Eastwards 25. degrees Reclining 76. degrees is another The South declining Eastwards 25. degrees inclining 14 degrees is another and its opposite viz. North declining Westwards 25. degrees Reclining 76. degrees is another PROB. XIV To find in what Place of the Earth any manner of Plane that in your Habitation is not Horizontal shall be Horizontal IT was said in the Preface that all manner of Planes however scituate are Parallel to some Country or other on the Earth Therefore all manner of Planes are indeed Horizontal Planes and the distances of the Hour lines to be â—â—scribed on them may be found as the distances of the Hour lines of the Horizontal Dyal in Prob. 3. It rests now to learn in what place of the Earth any Plane that is not Horizontal in your Habitation shall become Horizontal And for help of your understanding herein Take these following Rules 1. If your Plane be Erect Direct North or South it shall be an Horizontal in the same Longitude at 90. degrees distance on the Meridian counted from the Zenith of your Place through the Equinoctial See an Example of this
Solsticial Colure to the Meridian on the North side the Horizon and screw the Quadrant of altitude to the Zenith which will be in 23½ degrees from the Pole of the World So shall the Ecliptick ly in the Horizon and the Pole of the Ecliptick also ly under the Center of the Quadrant of Altitude as was shewed Prob. 27. Now to find the Longitude of any Star do thus Turn the Quadrant of Altitude about till the graduated edge of it ly on the Star and the degree in the Ecliptick that the Quadrant touches is the Longitude of that Star Example for a Star on the North side the Ecliptick I would know the Longitude of Marchab a bright Star in the wing of Pegasus I find it on the North side the Ecliptick Therefore I elevate the North Pole and placing ♋ on the North side the Meridian I screw the Quadrant of Altitude to the Zenith as aforesaid Then laying the edge of the Quadrant of Altitude upon that Star I find that the end of it reaches in the Ecliptick to ♓ 18. 56. Therefore I say the Longitude of Marchab is ♓ 18. 56. For the Latitude of a Star The Degree of the Quadrant of Altitude that touches the Star is the Latitude of the Star Example The Globe and Quadrant posited as before I find 19. deg 26. min. accounted upwards on the Quadrant to touch Marchab aforesaid Therefore I say the Latitude of Marchab is 19. deg 26. min. And thus by elevating the South Pole and placing the Globe and Quadrant of Altitude as aforesaid I shall find Canicula have 15. degrees 57. min. South Latitude and 21. degr 18. min in ♋ Longitude PROB. XXXIII To find the Distance between any two Places on the Terrestrial Globe THis may be performed either with the Quadrant of Altitude or with a pair of Compasses with the Quadrant of Altitude 〈◊〉 Lay the lower end thereof to one Place and see what degree reaches the other Place for that is the number of degrees between the two Places If you multiply that number of Degrees by 60 the Product shall be the number of English Miles between the two Places Example I would know the distance between London and the most Easterly point of Jamaâ—ca I lay the lower end of the Quadrant of Altitude to Jamaica and extending the other end towards London I find 68½ deg comprehended between them Therefore I say 68½ is the number of degrees comprehended between London and Jamaica If you would find the Distance between them with your Compasses you must pitch one foot of your Compasses in the East point of Jamaica and open your Compasses till the other foot reach London and keeping your Compasses at that Distance apply the feet to the Equinoctial line and you wil find 68½ degree comprehended between them as before If you multiply 68½ by 60 is it gives 4110. English miles If you multiply it by 20 it gives 1370. English Leagues If you multiply it by 17½ it gives 1199. Spanish Leagues If you multiply it by 15 it gives 1054 Dutch Leagues PROB. XXXIV To find by the Terrestrial Globe upon what point of the Compass any two Places are scituate one from another FInd the two Places on the Terrestrial Globe and see what â—umb passes through them for that is the point of the Compass they bear upon Example Bristol and Bermudas are the Places I examine what Rhumb passes through them both and because I find no Rhumb to pass immediately through them both Therefore I take that Rhumb which runs most Parallel to both the Places which in this Example is the tenth Rhumb counted from the North towards the left hand and is called as you may see by this following Figure West South West Therefore I say Bermudos lies scituate from Bristol West South West and by contraries Bristol lies cituate from Bermudas East North East PROB. XXXV To find by the Coelestial Globe the Cosmical Rising and Setting of the Stars WHen any Star Rises with the Sun it is said to Rise Cosmically And when any Star Sets when the Sun Rises it is saâ—d to Set Cosmically To find these Rectifie the Globe to the Latitude of your Place and bring the Place of the Sun to the East side the Horizon and the Stars then cut by the Eastern Semi-Circle of the Horizon Rise Cosmically and those Stars cut by the Western Semi-Circle of the Horizon Set Cosmically Example Novemb. 9. I would know what Stars Rise and Set Cosmically here at London The Suns Place found as by the third Probleme is 〈◊〉 27. Therefore I bring 〈◊〉 27. to the East side the Horizon and in the Eastern Semi-Circle I find Rising with the Sun the right Wing of Cygnus the Star in the end of Aquila's tail Serpentarius and Centaurus Therefore these Constellations are said to the Cosmically In the Western Semi-Circle of the Horizon I find Setting Andromeda the Triangle Taurus Orion anis Major and Argo Navis Therefore I say these Constellations Set Cosmically PROB. XXXVI To find by the Coelestial Globe the Acronical Rising and Setting of the Stars THe Stars that Rise when the Sun Sets are said to Rise Acronically And The Stars that Set with the Sun are said to Set Acronically To find these Rectifie the Globe to the Latitude of your Place and bring the Place of the Sun to the West side the Horizon and the Stars then cut by the Eastern Semi-Circle of the Horizon Rise Acronically And those Stars cut by the Western Semi-Circle of the Horizon Set Acronically Example November 9. I would know what Stars Rise and Set Acronically here at London The Suns Place as before is 〈◊〉 27. Therefore I bring 〈◊〉 27. to the West side the Horizon and in the Eastern Semi-Circle I find Rising the Southern Fiâ—h Fomahant Ceâ—us Taurus Auriga and the Feather in Castor's Cap. Therefore these Constellations are said to Rise Acronically In the Western Semi-Circle of the Horizon I find Setting the Lyons tail Virgo Scorpio and Sagittarius Therefore I say these Constellations Set Acronically PROB. XXXVII To find by the Coelestial Globe the Heliacal Rising and Setting of the Stars WHen a Star formerly in the Suns Beams gets out of the Suns Beams it is said to Rise Heliacally And. When a Star formerly out of the Suns Beams gets into the Suns Beams it is said to set Heliacally A Star is said to be in the Suns Beams when it is made inconspicuous by reason of its neerness to the Suns Light The Bigger Stars are discernable more neer the Suns Light then the Lesser are For Stars of the first Magnitude may according to the received Rules of ancient Authors be seen when the Sun is but 12. degrees below the Horizon but Stars of Second Magnitude cannot be seen unless the Sun be 13. degrees below the Horizon Stars of the third Magnitude require the Sun to be 14. degrees below the Horizon ere they can be seen of the fourth Magniâ—ude 15. degrees of the fifth
the Equinoctial under the Meridian of your Place have a continual Sun-Dyal of it and the hour of the Day given on it at once in two places one by the parting the enlightned Hemisphear from the shadowed on the Eastern side the other by the parting the enlightned Hemisphear from the shadowed on the Western side the Globe Much more might be said on this Probleme But the Ingenuous Artist may of himself find out diversities of Speculations therefore I forbear PROB. XLVI To know by the Terrestrial Globe in the Zenith of what Place of the Earth the Sun is THis may be performed by the former Probleme in the Day time if the Sun shines but not else But to find it at all times do thus Bring the Place of your Habitation to the Meridian and the Index of the Hour-Circle to 12 Then turn the Globe Eastwards if Afternoon or Westwards if Before Noon till the Index of the Hour-Circle pass by so many Hours from 12. as your Time given is either before or After-Noon so shall the Sun be in the Zenith of that Place where the Meridian intersects the Parallel of the Suns Declination for that Day Example May 10 at ¾ of an hour past 4. a clock After Noon I would know in what Place of the Earth the Sun is in the Zenith My Habitation is London Therefore I bring London to the Meridian and the Index of the Hour-Circle to 12. and because it is After Noon I turn the Globe Eastwards till the Index passes through 4 hours and 3 quarters or which is all one till 70 degrees 15 minutes of the Equator pass through the Meridian Then I find by Prob. 5. the Suns Declination is 20. degrees 5. minutes which I find upon the Meridian and in that Place just under that degree and minute on the Globe the Sun is in the Zenith which in this Example is in the North East Cape of Hispaniola Having thus found in what Place of the Earth the Sun is in the Zenith Bring that Place to the Meridian and Elevate its respective Pole according to its respective Elevation so shall all Places cut by the Horizon have the Sun in their Horizon Those to the Eastwards shall have the Sun Setting those to the Westward shall have it Rising in their Horizon those at the Intersection of the Meridian and Horizon under the Elevated Pole have the Sun in their Horizon at lowest but Rising those at the Intersection of the Meridian and Horizon under the Depressed Pole have the Sun in their Horizon at highest but Setting Thus in those Countries that are above the Horizon it is Day-light and in those but 18 degrees below the Horizon it is Twilight But in those Countries further below the Horizon it is at that time dark Night And those Countries within the Parallel of the same number of degrees from the Elevated Pole that the Suns Declination is from the Equinoctial have the Sun alwaies above the Horizon till the Sun have less Respective Declination then the Elevated Pole and those within the same Parallel of the Depressed Pole have the Sun alwayes below their Horizon till the Sun inclines more towards the Depressed Pole As you may see by turning about the Globe for in this position that portion of the Globe intercepted between the Elevated Pole and the Parallel Circle of 20. degrees 5. minutes from the Pole doth not descend below the Horizon neither doth that portion of the Globe intercepted between the Depressed Pole and the Parallel Circle within 20. degrees 5. minutes of that Pole ascend above the Horizon PROB. XLVII To find in what different Places of the Earth the Sun hath the same Altitude at the same time FInd by the former Probleme in what Place of the Earth the Sun is in the Zenith and bring that Place on the Globe to the Zenith and on the Meridian there screw the Quadrant of Altitude and turn it about the Horizon describing degrees of Almicantars thereby as by Prob. 23. and all those Countries in any Almicantar on the Globe shall have the Sun Elevated the same number of degrees above their Horizon Thus those Countries in the tenth Almicantar shall have the Sun Elevated 10. degrees above their Horizon those in the 20 th Almicantar shall have the Sun Elevated 20 degrees above their Horizon those in the 30 th 30. degrees c. So that you may see when the Sun is in the Zenith of any Place All the Countries or Cities in any Almicantar have the Sun in one heighth at the same time above their Horizon But to find in what different Places the Sun hath the same heighth at the same time as well Before or After Noon as at Full Noon and that in Countries that have greater Latitude then the Suns greatest Declination and therefore cannot have the Sun in their Zenith requires another Operation Therefore Elevate its respective Pole according to your respective Latitude and let the Degree of the Brazen Meridian which is in the Zenith represent your Habitation and the degree of the Ecliptick the Sun is in represent the Sun Then bring the Sun to the Meridian and the Index of the Hour-Circle to 12 and turn the Globe Eastwards if Before Noon or Westwards if After Noon till the Index point to the Hour of the Day Then place the lower end of the Quadrant of Altitude to the East point of the Horizon and move the upper end by sliding the Nut over the Meridian till the edge of the Quadrant touch the place of the Sun Then see at what degree of the Meridian the upper end of the Quadrant of Altitude touches the Meridian and substract that number of Degrees from the Latitude of your Place and count the number of remaining degrees on the Meridian on the contrary side the degree of the Meridian where the upper end of the Quadrant of Altitude touches the Meridian and where that number of degrees ends on the Meridian in that Latitude and your Habitations Longitude hath the Sun the same heighth at the same time Example May 10. at 53. minutes past 8. a clock in the Morning I would know in what Place the Sun shall have the same Altitude it shall have at London London's Latitude found by Prob. 1. is 51½ degrees Northwards And because the Elevation of the Pole is equal to the Latitude of the Place as was shewed Prob. 15. Therefore I Elevate the North Pole 51½ degrees so shall 51½ degrees on the Meridian be in the Zenith This 51½ degrees on the Meridian represents London The Suns Place found by Prob. 3. is ♉ 29. Therefore I bring ♉ 29 to the Meridian and the Hour Index to 12. on the Hour Circle Then I turn the Globe Eastwards because it is before Noon till the Index point at 8. hours 53 minutes on the Hour-Circle and place the lower end of the Quadrant of Altitude to the East point in the Horizon and slide the upper end either North or Southwards
the Meridian cut the degree of the Ecliptick on the Cusp of the tenth House The Western Semi-Circle of the Horizon shall cut the degree of the Ecliptick on the Cusp of the Seventh House and the Semi-Circle of the Meridian under the Horizon shall cut the degree of the Ecliptick on the Cusp of the fourth House If you have the day of the Moneth you may by Prob. 3. of the second Book find the Suns Place and if you have the Hour of the Day you may by first rectifying the Globe as by Prob. 2. of the same Book turn about the Globe till the Index of the Hour-Circle point to the same Hour in the Hour-Circle and you will then at the Eastern Semi-Circle of the Horizon have the degree of the Ecliptick that is Rising and by Consequence as aforesaid all the Cardinal points in their respective places Now to find what degree of the Ecliptick occupies the Cusps of the other eight Houses of Heaven Do thus The Globe rectified as aforesaid Move the Semi-Circle of Position upwards till 30 degrees of the Equator shall be contained between it and the Eastern Semi-Circle of the Horizon so shall the Semi-Circle of Position cut in the Ecliptick the degree and minute of the Ecliptick on the Cusp of the twelfth House and its opposite degree and minute in the Ecliptick shall be the Cusp of the sixth House for you must note that if you have but the degree and minute of the Ecliptick upon the Cusps of six of the Houses the opposite degrees and minutes of the Ecliptick shall immediately possess the Cusp of every opposite House Then move the Circle of Position over 30. degrees more of the Equinoctial so shall the degree of the Ecliptick cut by the Circle of Position be the degree of the Ecliptick upon the Cusp of the eleventh House and its opposite degree in the Ecliptick shall be upon the Cusp of the fifth House The degree of the Ecliptick upon the Cusp of the tenth and fourth Houses was found as before Then remove the Circle of Position to the Western side of the Meridian and let it fall towards the Horizon till 30. degrees of the Equator are contained between the Meridian and it so shall the degree of the Ecliptick cut by the Semi-Circle of Position be the degree of the Ecliptick on the Cuâ—p of the Ninth House and the opposite degree of the Ecliptick shall be upon the Cusp of the third House Let the Semi-Circle of Position fall yet lower till it pass over 30. degrees more of the Equator so shall the degree of the Ecliptick cut by the Semi-Circle of Position be the degree of the Ecliptick on the Cusp of the eighth House and the opposite degree of the Ecliptick shall be upon the Cusp of the second House The degrees of the Ecliptick on the Cusp of the seventh House and Ascendent were found as before Example I would erect a Figure of Heaven for July 27. 5. hours oâ— minutes Afternoon 1658. in the Latitude of London viz. 51½ degrees North Latitude I first place the Planets ☊ and ☋ on the Globe as by Prob. 55. of the Second Book was directed yet not exactly as I find them in the Ephemeris for that shews only their place in the Ecliptick at Noon Therefore I consider how many degrees or minutes each Planets motion is in a whole Day or 24. Hours by substracting the Ecliptical degrees and minutes of the Planets place that Day at Noon from the Ecliptical degrees and minutes of the Planets place the next Day at Noon or contrarily if the Planet be Retrograde for the remains of those degrees and minutes is the motion of the Planet that Day Therefore proportionably to that motion I place the Planet forward in the Ecliptick or backward if it be Retrograde As if the Sun should move forward 1 degree that is 60 minutes in a whole Day or 24 Hours then in 12 hours he should move 30 minutes in 6 hours 15 minutes in 4 hours 10 minutes in 1 hour 2½ minutes and so proportionably for any other space of Time which I consider before I place the Planets on the Globe PROB. II. To Erect a Figure of Heaven according to Campanus REgiomontanus as aforesaid makes the beginning of every House to be the Semi Circle drawn by the side of the Semi Circle of Position according to the succession of every 30 th degree of the Equator from the Horizon But Camp 〈◊〉 make it to be the Semi-Circle drawn by the side of the Semi-Circle 〈◊〉 Position according to the succession of every 30 th degree of 〈◊〉 Prime Verticle or East Azimuth which is represented by the Quadrant of Altitude placed at the East point The four Cardinals are the same both according to Regiomontanus and Campanus but the other eight Houses differ Therefore when you would find them according to Campanus Rectifie the Globe and Quadrant of Altitude and bring the lower end 〈◊〉 the Quadrant of Altitude to the East point in the Horizon Then count from the Horizon upwards 30 degrees oâ— the Quadrant 〈◊〉 Altitude and bringing the Circle of Position to those 30 degreeâ— examine where the Circle of Position cuts the Ecliptick which 〈◊〉 the aforesaid time is in 〈◊〉 29. 40 for that degree and minute upon the Cusp of the twelfth House and its opposite degree 〈◊〉 minute in the Ecliptick viz. ♉ 29. 40. is upon the Cusp of 〈◊〉 sixth House Lift up the Circle of Position 30 degrees highâ— upon the Quadrant of Altitude viz. to 60 degrees and 〈◊〉 Circle of Position will cut the Ecliptick in 〈◊〉 15. degrees for the Cusp of the eleventh House and its opposite degree and minute in the Ecliptick viz. ♉ 15. is upon the Cusp of the first House The degree and minute of the Ecliptick on the Cusp 〈◊〉 the Tenth and Fourth Houses is at the Meridian Then transfering the Circle of Position to the West side of the Meridian and the Quadrant of Altitude to the West point in the Horizon Let the Semi-Circle of Position fall 30 degrees from the Meridian on the Quadrant of Altitude and it will cut in the Ecliptick ♎ 16 degrees for the Cusp of the ninth House and its opposite degree and minute in the Ecliptick viz. ♈ 16. is upon the Cusp of the third House Let fall the Circle of Position 30 degrees lower on the Quadrant of Altitude and it will cut the Ecliptick in 〈◊〉 2 degrees for the Cusp of the eight House and its opposite degree viz. ♓ 2. degrees is on the Cusp of the second House The Cusps of the Seventh and Ascendent is the same with Regiomontanus viz. 〈◊〉 27. 47 and â™ 27. 47. The Figure follows PROB. III. To find the length of a Planetary Hour AStrologers divide the Artificial day be it long or short into 12 equal parts and the Night into 12 equal parts These parts they call Planetary Hours The first of these Planetary Hours takes its
Order or Later Authors gave the Plains their Names upon the same grounds you may also learn to know them I confess both waies admit of some just exception against for in the Older Rule a Plain about the Pole is called an Equinoctial Plain when as to a sudden apprehension it would sound more significant to call it a Polar Plain as Later Authors do Again Later Authors call an Horizontall Plain a Vertical Plain when as it sounds more significant to call it an Horizontal Plain as Older Authors do because it lie flat upon the Horizon But I shall give you the names according to both Rules and leave you to your liberty to accept of which you please First therefore you have an Equinoctial Plain otherwise called a Polar Plain This Plain hath two Faces upper and under These two Faces ly in the Plain of the Equinoctial the upper Face beholding the Elevated Pole the under Face the depressed Pole 2. An Horizontal Plain otherwise called a Vertical Plain it lies in the Plain of the Horizon directly beholding the Zenith Erect Plains otherwise called Horizontal Plains are the sides of Walls and these are of seven sorts viz 1. Erect Direct Vertical North or South 2. Erect Direct East or West 3. Erect Vertical Declining 4. Erect Inclining Direct 5. Erect Inclining Declining 6. Erect Reclining Direct 7. Erect Reclining Declining 3. Erect Vertical North or South Direct otherwise called Direct North or South Horizontals behold the North or South Directly and ly in the East or West Azimuth 4. Erect Direct East or West otherwise called Direct East or West Equinoctials behold the East or West Directly and lies in the Plain of the Meridian having its Poles in the Equinoctial 5. Erect Vertical Declining Plains otherwise called Declining Horizontals do not behold the North or South Directly but swerves from them so much as the Azimuth Parallel to their Plains swerves or Declines from them 6. Erect Inclining Direct Plains have the upper side of their Plains Inclining or coming towards you and their Plains do exactly behold either the East West North or South 7. Erect Reclining Direct Plains have the upper side of their Plains Reclining or falling from you and their Plains exactly beholding either the East West North or South 8. Eâ—â—ct Reclining Declining or Erect Inclining Declining Plains are those Plains which are either Inclining or Reclining but 〈◊〉 behold the East West North or South Directly but 〈◊〉 or Decline more or less from them 9. Polar Plains are Parallel to the Axis of the World and to the Mâ—ridians that cuts the East and West or North and South points of the Horizon All these kinds of Plains have two Faces the one beholding the North Pole with the same respect that the other beholds the South Pole except the Equinoctial Plain which because neither Pole is Elevated hath but one Face yet that one contains as many Hour lines as two other Faces These two Faces or Plains will receive just 24. hour lines foâ— the 24 Hour-lines of Day and Night for so much as the one side or Face wanteth or exceedeth 12. the other side shall either exceed or want of 12. Every Dyal Plain is Parallel to the Horizon of some Country or other in the World therefore a Dyal made for any Horizon in the World may be set to such a Position that it will shew you the Hour of the Day in your own Habitation At least for so long as the Sun continues upon that Planâ— All Plains may be aptly demonstrated by the Globe by setting it correspondent to all the Circles in Heaven as by Prob. 2. of the second B ok for if you imagine the Globe in that Position were prest flat into the Plain of any Circle that Flat shall represent a Dyal plain which shall be called after the name of that Circle it is prest into Thus if the Quadrant of Altitude be applyed to any degree of Azimuth and you imagine the Globe were prest flat to the edge of the Quadrant of Altitude so much as that Azimuth Declines from the East West North or South in the Horizon so much shall that flat on the Globe be said to Decline either from the East West North or South Or if you imagine the Globe were prest flat down even with the Plain of the Horizon that flat shall represent an Horizontal Plain because as was said before the Plain lies in that Circle cal'd the Horizon The Style or Gnomon is that straight wyre that casts the shadow upon the Hour of the Day it is alwaies placed Parallel to the Axis of the World There are several waies to find the scituation of all Plains but the readiest and speediest is by a Clinatory The Clinatory is made of a square board as A B C D of a good thickness and the larger the better between two of the sides is discribed on the Center A a Quadrant as E F divided into 90 equal parts or degrees which are figured with 10 20 30 to 90 and then back again with the Complements of the same numbers to 90 between the Limb and the two Semidiameters is made a Round Box into which a Magnetical Needle is fitted and a Card of the Sea Compass divided into 4 Nineties beginning their numbers at the East West North and South points of the Compass from which points the opposite sides of the Clinatory receives their Names of East West North or South Upon the Center A whereon the Quadrant was discribed is fastned a Plumb-line having a Plumbet of Lead or Brass fastned to the end of it which Plumb-line is of such length that the Plumbet may fall just into the Grove G H below the Quadrant which is for that purpose made of such a depth that the Plumbet may ride freely within it without stopping at the sides of it See the Figure annexed But admit there be Variation Having by Prob. 19. of the third Book found the number of degrees of this Variation towards the East or West count the same number of degrees from the North point in the Card either to the Eastwards or Westwards and note the degree in the Card terminating at that number for that degree shall be the North point and its opposite degree the South point 90. degrees from it either way shall be the East and West points Therefore whereas before you were directed to turn the Clinatory till the North point of the Needle point to the Flower-de-luce on the â—aid you mâ—st now turn or move the Clinatory till the North point of the Needle â—arg just over the degree of Variation thus sound and then a line drawn as aforesaid by the side of the Clinatory Paralâ—el to the Needle shall be a North and South line or to speak more properly a Meridional line You may fiâ—d a Mâ—ridian liâ—e several other waies as first If the Sun shine just at Noon hold up a Plumb-line so as the shadow of it may fall upon your Plain and
and prolong it to the farthest extent of the Plane From this Gnomon or Style I let fall a Perpendicular upon the Noon line as F G this Perpendicular is called the Substile and this Perpendicular and its Base which is the Noon line and Hypothenusa which is the Gnomon shall make a Triangle which being erected upon the Base so as the Substile may stand Perpendicular to the Plane the Hypothenusa A F shall be the Gnomon and be Parallel to the Axis of the World and cast a shadow upon the Hour of the Day PROB. IIII. To make an Erect Direct South Dyal DRaw on your Plane an Horizontal line as C A D as was shewed in the Preface in the middle of this line as at A discribe as on a Center the Semi-Circle C B D from the Center A let fall a Perpendicular which shall divide the Semi-Circle into two Quadrants each of which Quadrants you must divide into 90 degrees Then Rectifie the Globe Quadrant of Altitude Colure and Hour Index thus Elevate the Pole of the Globe to the Latitude of your Place and screw the Quadrant of Altitude to the Zenith Then bring the Vernal Colure to the Meridian and the Index of the Hour Circle to the Hour of 12. in the Hour Circle so shall your Globe Quadrant of Altitude Colure and Hour Index be Rectified Aâ—d â—â—us you must alwaies Rectifie them for the making of most sorts of Dyals by the Globe Then to make an Erect Direct South Dyal Bring the lower end of the Quadrant of Altitude to the West point of the Horizon And turn the Globe Westwards till the Index points to all the Hours Afternoon and examine in what numbers of degrees from the Zenith the Colare cuts the Quadrant of Altitude when the Index points to each Hour for a line drawn from the Center A through the same number of degrees reckoned from the Perpendicular A B which is the 12 a clock line towards D on the Plane shall be the same Hour lines the Index points at Thus in our Latitude viz. 51½ degrees the Vernal Coloure being brought to the Meridian and the Index to 12 If you turn the Globe Westwards till the Index points to 1 a clock or till 15 deg of the Equator pass through the Meridian the Colure will cut the Quadrant of Altitude in 9. 18 counted from the Zenith 2 19. 15 3 32. 5 4 48. 0 5 67. 4 6 90. And these are the distances of the Afternoon Hour lines which you must transfer to the East side of your Plane viz from B towards D and draw lines from the Center A through these distances and these lines shall be your Afternoon Hour lines Note once for all when the Colure goes off that Circle you examine the Hour distances in the Sun will shine no longer upon that Plane As in this example the Colure goes off the Quadrant of Altitude at 6 a clock therefore the Sun will not shine longer then till 6 a clock upon this Plane The Hour lines before Noon have the same distance from the Meridian that the Afternoon Hour lines have as was shewed in the last Probleme Only they must be drawn on the West side the Noon line and counted from B towards C. Otherwise You may reduce all Verticals into Horizontals if you Elevate the Pole of the Globe to the Complement of the Latitude of your Place and bring the Vernal Colure to the Meridian under the Horizon and the Index of the Hour Circle to 12 and turn the Globe Westwards for as the Index passes through every Hour on the Hour Circle the Colure shews in the Horizon the distance of the several Afternoon Hour lines from the Meridian or 12 a clock line in the Circle on your Plane numbred from B to D and lines drawn from the Center through these distances on your Plane shall be the Afternoon Hour lines of your Dyal Example Londons Latitude is 51½ degrees Its Complement to 90. is 38½ Therefore I Elevate the Pole 38½ degrees above the Horizon and bring the Vernal Colure to the Meridian under the Horizon and the Index of the Hour Circle to 12 on the Hour Circle Then Turning the Globe Westwards till the Index of the Hour Circle points to 1 a clock or till 15 deg of the Equator pass through the Meridian I find the Colure cut the Horizon in 9 18 from the Intersection of the Meridian and the Horizon as in the former Table 2 19 15 3 32 5 4 48 0 5 67 0 6 90 And these are the distances of the 6 Hour lines from the Merid. By this Example you may see that it is easie to reduce Verticals into Horizonâ—als and Horizontals into Verticals for this Erect Direct South Dyal is an Horizontal Dyal to those People that Inhabite 90 degrees from us viz. in the South Latitude of 38½ degrees Then make a Triangle whereof the Noon line shall be Base from it count the Complement of the Poles Elevation viz. 38½ degrees and through them draw the line A F from the Center A which shall be Hypotenusa Then â—et fall a Perpendicular upon the Noon line A B so is your Triangle made If this Triangle be erected Perpendicularly upon the Base or Noon line The Hypotenusa A F shall stand Parallel to the Axis of the World and cast a shadow upon the Hour of the Day PROB. V. To make an Erect Direct North Dyal IF the Erect Direct South Dyal were turned towards the North and the line C A D were turned downwards and the line marked with 7 be now marked with 5 and the line 8 with 4 the line 5 with 7 and the line 4 with 8 then have you of it a North Erect Direct Dyal All the other Hour lines in this Dyal are useless because the Sun in our Latitude shines on a North Face the longest Day only before 6 in the Morning and after 6 at Night PROB. VI. To make an Erect Direct East Dyal THese sorts of Dyals may better be demonstrated then made by the Globe unless the Axis of your Globe were accessible as in the Wyer-Globe specified in Prob. 1. Therefore when you would make an East or West Dyal or a Polar Dyal Provide a square Board as A B C D draw the straight line e f upon it Parallel to the sides A C and B D. and just in the middle between them Cross this straight line at Right Angles with another straight line as g h quite through the Board Upon this Board with a little Pitch or Wax fasten the Semi-Circle of Position so as both the Poles thereof may ly in the line g h and the middle of the Semi-Circle marked co may ly upon the line e f so shall i be the Center of the Semi-circle of Position In this Center make a smal hole through the Board fit to receive a Wyer or a Nail So may you with this Circle of Position thus fitted and the side C D applyed to a line of
stand the Angle C which A B subtendeth Next follow the 142. degrees 42. minutes of Azimuth which maketh B C of your Triangle to the Horizon and from thence number in the Horizon towards the East point 37 degrees 18. minutes the Complement of the Angle A to 180. degrees and number yet further 52. degrees 42. minutes beyond the East point to make up 90 and there is the Pole of the Arch B C Therefore there shall stand the Angle A which B C subtendeth Then count in the Equator from the first Meridian 90. degrees which will end under the Horizon and there make a prick for there is the Pole of the Arch or side A C. Therefore at that prick shall stand the Angle B which A C subtendeth Here you see your second Triangle made by the Poles of the first adjoyning to the East point of the Globe only the side A B is wanting To get that make a prick upon the Globe against the 52. degres 42. minutes from the East point of the Horizon found before to represent the Angle A Then turn about the Globe and Qudrant of Altitude till that prick and the prick made before for the Angle B are both at once cut by the side of the Quadrant of Altitude and you will find 25. degrees 24. minutes of the Quadrant of Altitude comprehended between the two pricks for the measure of the side A B PROB. XIII How to let fall a Perpendicular that shall divide any Oblique Spherical Triangle into two Right Angled Spherical Triangles THis Probleme is much used when an Oblique Triangle having two sides and an Angle given is to be solved by the Cannon of Sines and Tangents but by the Globe it may be solved without it as was shewed Prob 8 9. Yet because letting fall a Perperdicular is so frequent in all Authors that treat of Trigonometry I have inserted this Probleme also In the Oblique Triangle of the fromer Problemes there is given the sides A B 38½ degrees and B C 25. degrees and the Angle C 25. degrees 24. minutes It is required to let fall a Perpendicular as B a from the Angle B. upon the Base A C and to know both the measure of this Perpendicular and the parts it divides the Base into Therefore Elevate the Pole of the Globe above the Horizon so much as is the measure of the Angle C which in this Example is 25. degrees 24. minutes and bring the intersection of the first Meridian with the Equinoctial to the East point of the Horizon so shall the Angle at the East point of the Horizon comprehended between the Horizon and the first Meridian be equal to the Angle C then count in the first Meridian from the East point of the Horizon the measure of the side B C 25. degrees and having the Quadrant of Altitude screwed to the Zenith bring the graduated edge of it to these 25. degrees so shall the Arch of the Horizon comprehended between the East point and the lower end of the Quadrant of Altitude be the number of degrees that the Perpendicular falls upon the Base counted from the Angle C to a which in this Example is 21¾ degrees and the Arch of the Quadrant of Altitude comprehended between the Horizon and the first Meridian is the measure of the Perpendicular B a 11. degrees And thus by letting fall this Perpendicular you have two Right angled Spherical Triangles made the one B a C wherein is found C a 21¾ degrees B C 25. degrees B a 11. degrees C 25. degrees 24. minutes and a the Right Angle There remains only the angle B unknown which you must find by turning the Triangle as was taught Prob. 1. The other Right angled Spherical Triangle made is B a A wherein is found A a Complement of 21 2 4 degrees to 60 degrees the whole Base before given 38¼ degrees A B 38. degrees 30. minutes B a 11. degrees and a the Right Angle which is more then enough to find the Angl◠A and B as was shewed in the Preface Theorem 1. The End of the Sixth Book Here follows the Ancient STORIES of the several STARS and CONSTELLATIONS Shewing the Poetical Reasons why such Various Figures are placed in HEAVEN Collected from Dr HOOD And First Of the Northern Constellations 1. URSA MINOR This Constellation hath the preheminence because it is neerest of all the rest unto the North Pole And is called of the Greeks 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 whereupon the Pole is called the Pole Arctick for that it is neer unto that Constellation It is also called Helice minor because of the smal revolution which it maketh round about the Pole or rather of Elice a Town in Arcadia wherein Calysto the great Bear and mother to the less was bred It is called Cynosura because this Constellation though it carry the name of a Bear yet it hath the taile of a Dog Last of all it is termed Phoenice because that Thales who first gave the name to this Constellation was a Phoenician And therefore the Phoenicians being taught how to use it in their Navigations did call it by the name of the Country wherein Thales was born It consisteth of 7. stars which the Latines call Septemtriones because by their continual motion those seven stars do as it were wear the Heavens The Spaniards call them all Bosina that is an Horn because they may be very well brought into that form whereof that which is in the end of the tail is called the Pole-star by reason of the neareness thereof unto the Pole of the world for it is distant according to the opinion of most from the true Pole but 23. deg 30. min. The Arabians call it Alrukaba And of the Scythians it is said to be an Iron nail and is worshipped by them as a God The two stars that are in the sholders of the Bear are called Guards of the Spanish word Guardare which is to behold because they are diligently to be looked unto in regard of the singular use which they have in Navigation The reason why this Constellation was brought into the Heavens is diversly set down and first in this manner Saturn having received of the Oracle that one of his Sons should banish him out of his kingdom determined with himselfe to kill all the men children that he should beget whereupon he gave command to Ops his wife being then great that she should shew him the child so soon as ever it was born But she bringing forth Jupiter and being greatly delighted with his hair gave the child unto two Nymphs of Crete dwelling in the mount Dicte whereof this was one and was called Cynosura the other was Helice Jupter after that according to the Oracle he had bereft his Father of the kingdom in recompence of their paines and courtesie translated them both into the Heavens and made of them two Constellations the Lesser Bear and the Greater Bear Othersome say that it was Arcas the son of