is 15 deg counted beyond 45 toward the end below or beyond the Horizon Again As S. ♋ is 62 degrees from 45 towards 00 So is the other Point 62 degrees below N taken from 45 viz. at 76 degrees which being laid from N doth over-reach this little page So that to draw the Tropick of ♑ the Point ♋ being his opposite is 28 degrees from Z or 62 deg from S and the other Point of ♑ on the North part of the Meridian is 62 degrees counting from 45 doubly also or 28 degrees from 90 the supposed end of the Tangent which is naturally infinite being the Tangent of 76 degrees or the Semi-tangent of 152 reading the Tangents doubly from the Center which distance from the Center to the Tangent of 76 or as half-tangents 152 laid from Z gives the Point ♑ on the north-North-part of the Meridian below the Horizon the midst between which two Points of ♑ on the South and North part of the Meridian is the Center to draw the Tropick of Capricorn Again to illustrate this difficulty to draw the Tropick of Cancer the Suns Meridian-Altitude in ♑ his opposite sign is 15 degrees above the Horizon on the South part of the Meridian and 15 degrees below the Horizon on the North-part of the Meridian viz. the Extent from the Center to the Tangent of 52 deg 30 min. or the Semi-tangent of 105 reading it doubly being laid from Z gives the Point ♋ below the Horizon the middle between which two Points is the Center to draw the Tropick of Cancer Again for the Equinoctial or Parallel of ♈ the Meridian Altitude in ♈ is 38-28 and the Meridian Altitude likewise in ♎ his opposite Parallel is 38-28 also so that if you count 38-28 doubly beyond 45 which will be at the Tangent of 64 degrees and 14 minuts and take from thence to the Center this distance laid from Z shall give the Point AE below the Horizon and the the middle between the two Points AE is the Center to draw the Aequinoctial Then for the Hour-Lines first set off the Semi-tangent of 38-28 from Z to P and the Secant of 38-28 to the same Radius from Z to L and draw the Line L 45 parallel to EW then make PL a Tangent of 45 degrees and lay off the Tangents of 15-30 and 45 from L both-wayes as you see in the Figure Also As the Sector stands take out the = Tangents of 60 and 75 severally and turn them four times from L both-wayes and note those Points with 6 7 8 9 10 11. Lastly Set one Point of the Compasses in L and open the other to P and draw the Line WPE for the hour of 6. Again Set one Point in 7-15 degrees from L and open the other to P and draw the Hour-line 5 P 5 Set the same Extent also in 7 or 5 on the other side of L and draw the Hour-line 7 P 7 as the Figure sheweth Then Set one Point of the Compasses in 8 30 degrees from L and open the other Point to P and draw the Hour-line 8 P 8 and remove it to the other side of L and draw the Hour-line 4 P 4 And so for all the rest in order Thus having drawn the Figures to draw Lines therein which shall truly represent any Plain whatsoever observe the following Rules 1. The Horizontal-Plain is represented by the Circle E.S.W.N. 2. A direct South or North-Diall is represented by the Line E.Z.W. 4. An East or West Plain is represented by the Meridian-line of 12 viz. S. N. 5. A Polar Plain is represented by the hour of 6 viz. the Line E.P.W. 6. An Equinoctial Plain is represented by the Equinoctial-line E.AE.W. 7. Any Direct Reclining or Inclining-Plain between the two last is called A direct Recliner whose Poles are alwayes in the Meridian and are represented by any Reclining Circle as the two Circles W. ♋ E. and E. ☉ W. do shew 8. An East or West Recliner or Incliner represented by the Circle N.F.S. 9. A Declining and Reclining or Inclining Polar-Plain that is it so Declines and Reclines or Inclines as to lie parallel to the Pole as the Circle 8 P 8 doth represent 10. A Declining Reclining-Plain that so Declines and Reclines as not to fall in the Pole or Equinoctial as generally they will do as the Circle 60 G 60 doth represent which Declines from the South-eastwards and Reclines 62 deg which kind of Plains are various and infinite yet confined to six varieties as afterward Now the way of Drawing these Scheams to represent these varieties is briefly thus by the Sector First to the Radius of the small Tangents draw the Circle N. E. S. W. observing this Method if it be a South Recliner to set the letter N above and E on the right hand and contrarily in North Recliners for we meddle not with Incliners till afterwards and alwayes observe that a South Incliner is the same with a North Recliner and the contrary then cross that Circle with two Diameters precisely in the Center as the Letters shew then according to your Plains Declination from North or South toward either East or West set off the Declination with a Line of Chords or Sines as before is shewed and draw that Line for the Perpendiculer Line of the Plain and laying the same distance as much from E. and W. draw another Line Perpendiculer to the former representing the Plain then on the first Line viz. the Plains Perpendiculer lay off from Z the half Tangent of the Plains Reclination from Z to E and the half Tangent of the complement thereof from Z to Q the contrary way and the whole Tangent of the complement thereof from Z contrary to E on the same Line extended for a Center to draw the Reclining Circle that represents the Plain Lastly You must draw a Circle through Q and P P being alwayes the Semi-tangent of the complement of the Latitude laid alwayes from Z toward N for the North Pole so as to cut the Primitive Circle N.E. S.W. into two equal parts as is shewed in the 10th Proposition of the third Chapter part of which Line doth represent the Stile-Line of the Dial which last work shall be again shewed in the Example Example To draw the Scheam for a Plain Declining from the South to the West 35 degrees and Reclining 20 degrees for the Latitude of 51-30 First to the Radius of your small Line of Tangents being the Latteral distance from the Center to 45 or larger if you please draw the Circle N.E.S.W. representing the Horizon crossing it in the Center with the Lines N.S. W.E. for the North and South and East and West Lines Then Take out the latteral Tangent of half the latitude viz. 19-15 for 38-30 calling the Tangent of 10 the half Tangent of 20 and lay it from Z at the Center to P for the Pole-point Then consider the Declination of your Plain and which way as here 35
then to any one whole Hour as suppose the Hour-line of 3 draw two = Lines equally distant on both sides the Line of 3 as IK LM Then Count any way 3 hours and 6 hours from 3 as here 12 and 9 so as the = line may cross the 3 remotest hours as here you see 9 and 12 a clock Hour-lines do cross the = line at I and K then take the distance IK and lay on the Hour-line of 3 from C to N and draw INL = to 9 C Which Work doth constitute the Parallellogram KILM Then lastly Make KI and NI = Tangents of 45 and pâ—ick off every hour half and quarter and minut if you please on the two Lines IK and IL from K and N both wayes as before is already shewed in the Erect Decliners Note also That to supply the defect on the other side when the point M falls out of the Plain the distance from I to the Hour-point from 11 will reach from L to 7 and from I to 10 from L to 8. This is general in all Dials Also note If you like not to lay off the â—irst Hours by the Tangents having made the Table as before you may soon find the Hour-Arks on the Plain for 3 Hours as â—ere 3 12 and 9 Or 4 1 and 8 which â—ould have made the Parallellogram more â—â—uare and consequently more better and â—â—en to draw the rest by the Sector Thus â—ou may see how your Work accords The â—ay by the Table and Contingent-line and 〈◊〉 way by the Sector on the Parallellogram 〈◊〉 by Calculation at last use the Mystery 〈◊〉 Dialling made plain and ready to an â—â—dinary capacity Of North Declining Recliners The other kind viz. North Declining Recliners have also three Varieties as those â— That fall back or recline between the Zenith and Equinoctial 2d Those that recline to the Equinoctial And 3d. Those that recline below the Equinoctial And first of the first Variety reclining less then to the Equinoctial The drawing the Scheam is the same as in the former except in the placing of the Points and Letters For first these Plains behold the North-part of the Horizon and then when you look on the Plain the South is before you and the West on your right-hand and the East on the left then the South and North are alwayes opposite and the point P representing the Elevated Pole of the place which with us being North must be placed towards N downwards as before in South Recliners it was upwards Also It is necessary in the Scheam to draw the Equinoctial-line by laying the half Tangent of 51-32 from Z to AE then the Secant of 38-28 the complement of ZE laid from AE on the Line SN shall be the Center to draw EAEW for the Equinoctial-Circle Thus the Scheam being drawn to find the Requisites thus 1. For the Meridians Elevation or distance from the Perpendiculer AG or GE. By the Secctor As sine 90 Radius ZD 90-0 To Tangent Declination Plain SD 55-0 So sine Reclination Plain ZE 20-0 To Tangent Merid. Perpend GE 26-2 As Tangent of Declin SD 55-0 To = sine of Radius ZD 90-0 So = sine of Reclination ZE 20-0 To Tang. of 12 from Perp. GE 26-02 Whose complement AG 63-58 is the Meridians Elevation above the East-end of the Horizon By the Scheam A Rule laid from Q to G on the Limb gives L then DL and AL are the Arks required 2. To find the Distance on the Meridian from the Pole to the Plain GP By the Sector As sine declin of the Plain GZE 55-0 To sine dist of Mer. Perp. GE 26â—02 So sine of the Radius GEZ 90â—00 To sine of dist on Merid. from Pole to Plain GZ 32-03 As sine of GEZ 90-0 To = sine of GZE 55-0 So = sine of GE 26-2 To sine of GZ 32-03 Which added to 38-28 ZP makes up GP to be 70-31 Or By the Scheam A Rule laid from E to P and G gives on the limb ab the Ark ab is 70-31 3. To find the Stiles height above the Plain PF By the Sector As sine of distance on Mer. from Zenith to the Plain GZ 32-03 To sine of the Plains Reclin ZE 20-00 So sine of dist on Mer. from Pole to the Plain GP 70-31 To sine of the Stiles Elevat above the Plain PF 37-01 As the sine GP 70-31 To the = sine GZ 32-03 So the = sine ZE 20-00 To the sine PF 37-01 By the Scheam A Rule laid from Y to P and F on the limb gives c and d the Stiles height 4. To find the distance of the Substile from the Meridian GF when it is above 90 deg take the comp to 108 deg By the Sector As Tangent of the Reclin ZE 20-00 To sine of dist of 12 from Perp. GE 26-02 So Tang. of the Stiles Elevat PF 37-01 To sine of the Substile from 12 GF 65-24 As sine EG 26-02 To = Tangent ZE 20-0 So = Tangent PF 37-01 To sine GE 65-24 By the Scheam A Rule laid from Q to G and F gives on the limb LF the Ark required 5. To find the Inclination of Meridians FPG By the Sector As sine dist on Merid. from Pole to Plain GP 70-31 To sine Radius opposite Angle GFP 90-00 So sine dist on Plain from 12 to Substile GF 65-24 To sine of the Inclin of Mer. GPF 74-38 As sine GF 65-24 To = sine GP 70-31 So = sine GFP 90-00 To sine GPF 74-38 By the Scheam A Rule laid from P to Y on the Limb gives g the Ark Eg is 74-38 the Inclination of Meridians Or A Rule laid from P to K gives h Sh is the Inclination of Meridians by which to make the Table as before is shewed and as followeth To draw the Dial. 3 29 38 2 44 38 1 59 38 12 74 38 11 89 38 10 75 22 9 60 22 8 45 22 7 30 22 6 15 22 5 0 22 4 14 38 For drawing the Dial consult with the Scheam laying the Plain AEB and his Perpendiculer CD right before you then note SN is the Meridian-line ZE the Plains perpendiculer with the Meridian G on the left-hand and the Subtile F on the right-hand Also note That the Sun being in the South as S casts â—is beams and consequently the shadow of â—he Stile into the North So that though G be the true Meridian found yet it is the north-North-part that is drawn as an Hour-line â—ut the Substile and other Hours are counâ—ed from the south-South-end thereof as the Tableâ—nd â—nd the Figure of the Dial do plainly make â—anifest being drawn in this manner First draw the Horizontal-line AB then 〈◊〉 C as a Center draw a semi-circle equal 〈◊〉 60 of the Chords and lay off the Meriâ—ian Substile and Stile in their right Sciâ—â—ations as last was declared then draw â—â—ose lines and to the Substile erect a Perâ—endiculer as DE then take
as 12 6 is NR 60-40 both hours and quarters if you have them truly drawn on a large general Scheam as Mr. Lankford hath done Thus much for Direct Plains both Erect and Reclining before I come to speak of Decliners It will not be amiss to shew how to find the declination of a Plain both by the Sun-shine or without by a Magnetical-Needle as followeth As sine of the Substile 41-40 GF to = sine of the Latitude 51-32 NP So is = sine of 90 PFG to sine of GPF 58-7 the Incliner CHAP. III. To find the Declination of any PLAIN FOr finding the Declination of a Plain the most easie way is by a Magnetical-Needle fitted according to Mr. Failes way in the Index of a Declinatory as he calls it being 180 degrees of a Semi-circle divided on an Oblong-Board or Quadrant or a longer Needle in a square Box or fitted with Hinges and a Cover after all which wayes you may have them made at the sign of the Sun-dial in the Minories by Iohn Brown or of any other manner you shall think fit But to our Trianguler Quadrant is a Box and Needle also to be fitted of another form in some things more convenient Whose form is thus First in a piece of Box 5 inches long 2 ½ broad and 6 tenths of one inch thick is a hole made near 4 inches long 1 inch ¾ broad and 4 tenths deep for a Needle to play in about 50 degrees at each end with brass-hinges and a cover and a brace to keep the lid upright an Axis of Thâ—ed and a Plummet playing in the lid and a Horizontal and a South-dial drawn on the Box and Cover also a hasp and glass to keep the Needle close covered and on the bottom a Grove one tenth of an inch deeâ— made just as broad as one leg of the Sector is The use whereof is thus Put your Box and Needle on that leg of the Sector as will be most convenient for your purpose the North or cross-cross-end of the Needle toward the Wall when it is a South decliner and the contrary when it is applyed to a North decliner as the playing of the Needle will tell you better than many words then open or close the Rule till the Needle play right over the Line in the bottom of the Box unless there be variation then you must allow for it Eastwards or Westwards what it is Then I say the quantity of the Angle in degrees and minuts the Sector stands at above or under 90 is the degrees and minuts of Declination being counted from 00 in the little Semi-circle as complements to the Angle of opening as in the 4th Use of the 5th Chapter is largely and plainly shewed Thus you have the quantity of degrees and minuts of Declination but to determine which way consider thus If the Needle will stand still in the middle when the north-North-end is toward the Wall then the first denomination is South if not North. Again When you know where North and South is you may resolve which way the East and West is For observe alwayes if the North be before you then the East is on the right-hand and the West on the left and contrarily If the South be before you the West is on the right-hand and the East on the left Then If the Sun being in the East-point of the Horizon can look on the Plain it is a South-east Plain but if it beholds it when in the West-point it is a South-west Plain Likewise If the Cross-end of the Needle will not stand toward the Wall the Needle playing well and the Sun being due East beholds the Plain then it is so many degrees North-east but if it cannot look on the Plain being due East then it is a North-west Plain declining so many deg as the Sector stands at under or above 90 being alwayes the complement of the Angle the legs of the Sector stand at and found by taking the Angle the legs stand at from 90 when the Angle is less than 90. Or Taking 90 out of the Angle when it stands at an Angle above 90 degrees as a look at the little Semi-circle on the Head sheweth Example Suppose I come to a Wall and putting the Box and Needle on the Leg of the Sector and applying the other Leg to the Wall or on a streight piece of Wood applied to the Wall because of the Walls unevenness and open or close the Legs till the Needle playes right over the Meridian-line drawn on the bottom of the Box then I say the complement of the Angle the Legs of the Sector stands at being alwayes what it wants of or is above 90 degrees is the degrees of Declination and the Coast which way the Needle and Suns being East and West tells you For If the North or cross-Cross-end of the Needle be toward the Wall it is a South Plain and if the Sun being in the East can behold it then it is South-east if not a South-west Plain A ready way of counting the Angle found may be thus Take the = distance between Center and Center in the middle of the innermost-lines and lay it latterally from the Center and coâ—nt two degrees more than the Point sheweth after the manner of Chords from 90 at the sine of 45 toward the Compass-point and that shall be the degrees and minuts required Example Suppose the Legs are so opened that the = distance between the two Centers makes the sine of 25 then I say the Lines do stand at an Angle of 50 degrees and the Legs at 48 two degrees less the complement whereof is 42 as if you count thus from 45 you will find 40 from 45 is 10 35 is 20 30 is 30 25 is 40 and 2 degrees more makes 42 the thing desired But If you like not the abating of two degrees then the = distance taken just beâ—ween the two legs right against the Cenâ—ers shall be just the sine of 24 degrees â—r 42 counting after the manner of Chords viz. every 5 degrees on the Sines for 10 on â—he Chords backwards from 45 of the Sines which is 90 in Chords Or If you use the first Rule of the 4th Useâ—f â—f the 5th Chapter viz. by taking the â—ine of 30 and put one Point of the Comâ—asses in the middle Center in the Tangent-â—â—ne and apply the other to the Line of â—ines you shall find it reach to the sine comâ—lement of the Angle the Lines stand at â—iz 40 degrees and 2 degrees more viz. â—2 is the Angle or thing desired as praâ—tice with consideration will make easie Thus by the Needle you may find the â—eclination of a Wall which in cloudy â—eather may stand you in good stead or 〈◊〉 prove a declination taken by the Sun to â—revent mistakes And if nothing draw the â—eedle from its right position but that it â—ay well and you find the Angle truly â—ou may come to less than half a degree And this convenience it hath
help of a Sector with Sines and Tangents to 7-5 such as are usually made But for very far Decliners use that help as directed in Chap. 4. The like work serves to help all sorts of Dials with low Stiles Polar and Meridian Dials also The other 6 sorts yet behind I shall demonstrate only in two of them which do properly enough comprehend them all and the work of one is as easie as the work of the other especially by the help of the Sphear where the hardest is as plain as the Horizontal Therefore 7. Of Declining Reclining-Dials 1. For South Recliners they may recline short of to or beyond the Pole at any Declination as the putting up and down the Plain doth plainly demonstrate Therefore first Of one that Declines South-west 35 and Reclines 20 from the Zenith Set the Notch or Pole of the Plain to the Declination and the Reclining Circle to its Reclination and there make it fast then extend the Axis streight and bring the upper Semi-circle just to touch it and the Hour-circle exactly even with the moving Semi-circle Then First The Axis shews the Stiles height on the Semi-circle to be 12-13 The Thred brought along the Plain while it touches the Meridian and that shews the Meridians Elevation above the Horizon on the North Recliner to be 76-32 or its Depression below the Horizon in South-Recliners and that from the east-East-end as the Sphear sheweth Then 3. The Substile from the Perpendiculer Line of the Plain is 21-6 as the upper Semi-circle sheweth but from the hour 12 or Meridian 7-58 and stands on the East-side of the Meridian The Inclination of the Meridian is 33-29 as the degrees on the Equinoctial between the Meridian and Hour-circle shew All the Hour-Arks are easily found from the Plains Perpendiculer Eastwards and Westwards by applying the Thred to the Hour-circle and Plain being set to the Hours on the Equinoctial The South Pole is elevated in the South-Recliner and the North on the North Incliner If you set Letters to the Sides and Angles according to the former discourse you will see how all the Canons in the Arithmetical Calculation lie as I shewed you before in the Declining Dials And as again thus On the Pole set P. On the Zenith Z. At the west-West-end of the Plain set A. At the east-East-end B. At the South Pole of the Plain C. At the North Pole D. At the east-East-end of the Horizon E. At the West-end W. At the North-end of the Meridian set N. At the South-end S. Where the Hour-circle cuts the Plain F. Where the Meridian cuts the Plain G. Where the fixed Semi-circle cuts the Plain set E. As in the Figure before Then these Canons in short run thus As sine Base ZD 90-00 To Tang. Perpend ND 35-00 So sine of Base ZE 20-00 To Tang. Perpend GE 13-28 Whose complement AG 70-32 is the Meridians elevation As sine of the Side GE 13-28 To sine of the Angle CZE 35-00 So sine of the Angle GFZ 90-00 To sine of the Side GZ 23-57 Which taken from ZP 38-28 leaves 14-33 the distance of the Meridians place from the Pole to the Plain viz. GF As sine of Hypothen GZ 23-57 To sine of Perpend ZE 20-00 So sine of Hypothen PG 14-33 To sine of Perpend PF 12-13 Â the Stile As Tangent of Perpend ZF 20-00 To sine of Base GE 13-28 So Tangent of Perpend PF 12-13 To sine of Base FG 7-58 Â the Substile to 12. As the sine of the Side ZE 20-00 To the sine of the Side GE 13-28 So is the sine of the Angle PFG 90-00 To the sine of the Angle FPG 33-28 Â Inclin Merid. For the Hours in all Dials say thus As sine of 90 To sine of Stiles height So Tangent of the Angle at the Pole To Tangent of the Angle on the Plain 8. For North Declining Reclining-Dials For these Plains also you must rectifie the Sphear to the Latitude and set the Plain to his Declination and Inclination which is given and for which you are to make a North Declining Reclining Dial. As you did in the South-Recliner so work in all respects as you shall bring forth the Quesita's either by the Sphear or Arithmetical-Calculation as is largely shewn And for a Plain that declines 55 degrees from the North towards the East and relines 20 from the Zenith you shall find the Requisites to be as followeth 1. The Meridians Elevation above the Horizon is found to be 63 deg 58 min. But yet observe You must make use of that part of it which is below the Horizon because the Sun being Elevated high on the South-part of the Meridian must needs cast a shadow on the North-part thereof therefore in drawing the Dial-part part is only to be made use of for the Sun to shine on 2. The Stiles Elevation is 37 degrees 00 minuts 3. The Substile from 12 65-24 or from the Plains perpendiculer 39-22 The North Pole is Elevated and in regard the Plain declines to the East the Stile must be set towards the West and it shines on the Plain in Summer-time from the Rising unto 12 But in the Winter-time but a few hours Note also That these Declining Reclining-plains may be referred to a new Latitude and Declination wherein they shall become Upright Decliners as before is hinted The Poor-Mans Dial-Sphear Or another way to demonstrate the Mystery of Dyalling both for Declining and Inclining Plains in a very plain easie way for one 6th part of the cost of the other Brass-Sphear First as to the Description and afterward for the Vse AS to the Description the Figure annexed and a few words shall suffice wherein consider First The plain flat-Board representing the Horizon as ABCD. Secondly The two upright pieces as East and West-points as AE and BF to support the moving Plain Thirdly The Moving-plain moving to any Inclination on the two Points E and F with 180 degrees upon the Plain and noted by ABEF Fourthly Also a Brass-circle as G fastened to the Plain to set it to any degree of Inclination and a skrew as at H that may stay it steady when set to any Reclination Fiftly On the middle of the Horizontal-board is fastened at the Point M a true Horizontal-Dial drawn fit for your Latitude and to turn round on the Point M as IMKL Sixtly A Thred fastened in L the Center of the Horizontal-Dial and in N the Center of the Plain to be both a Stile for the Horizontal-Dial and to represent the Axis of the World also a small Woodden-Quadrant will be useful such a one as half the Plain is to draw Perpendiculers and measure Angles as afterwards in the Uses The Uses follow Use I. To find the Declination of a Plain by the Sun-shining Apply the side AB to the Wall and hold the Instrument level as by help of a Point Plummer fastened at N and the Point playing right on M it is easie to
00 00     15 56 13 25 06 41      13 44 11 11 04 23      11 35 8 59 02 08     5 9 32 6 50 00 06      7 23 4 44       5 26 2 41       3 36 0 41      4 1 32       The Description and some Uses of the Sphear for Dialling and for the better understanding of the general and particular Scheams NExt the Foot and Semi-circle Frame for supporting of it you may consider 1. The fixed Horizon to which the Foot is fastened with 4 skrews numbred and divided into 360 degrees or four 90 deg whose count begins at the Dividees side of the Meridian-Circle 2. The Meridian Circle whose fore-side at the Nadir-point stands in the Center of the Foot this is also divided into 4 90s s and begins to be numbered at the South and North part of the Horizon upwards toward the Zenith and downwards toward the Nadir which Circle is alwayes fixed as the Horizon is 3. The Equinoctial Circle made fast at the East and West Points of the Horizon moving up and down upon the Meridian-Circle according to the Elevation of the Equinoctial in any Latitude this is divided â—â—kewise into four 90s s numbred from the Meridian each wayes to the East and West Points of the Horizon 4. On the Meridian Circle is set 2 moveable Poles to be elevated or depressed fit to the Latitude of any place on the Fiducial-edge of which is fastened the Thred representing the Axis of the World at any Elevation of the Pole 5. On the 2 Pole Points is fastened the Hour Circle which delineates or represents the motion of the Sun or any fixed Star moving in its supposed Diurnal motion about the Poles of the World and may not improperly be called the moveable Meridian Circle or Hour Circle divided as before 6. The Moveable Horizon that moveth about to any Azimuth and slideth or moveth in the fixed Horizon 7. The Plain fixed in 2 opposite Points to the moving Horizon being set either Horizontal when it lies Parallel to the fixed Horizon or Erect when Perpendiculer thereunto or set to any Reclination or Inclination by help of the Semi-circle of Reclination fastened to the backside of the Plain in the 2 Poles thereof 8. You have the upper moving Semi-circle in turning about of which whateveâ— degree the fore-side of the Semi-circle cuts the Perpendiculer-point cuts the compleâ—ment thereof and to be called the upper Semi-circle or Circle alwayes Perpendicuâ—ler to the Plain 9. There ought to be a Thred fastened in the Center of the Plain to be extended to any Altitude or Azimuth required Thus much for Description repeated again in short thus The Horizon The Meridian The Equinoctial Circles The 2 Pole Points and Axis The Hour Circle or Moveable Meridian The Moveable Horizon The Plain The Semi-circle of Reclination The upper Semi-circle and The Thred Note also Every Circle is divided into 4 times 90 and numbred the most useful way Also on the Plain is set the 12 Months and every single Day on which every respective day if you extend the Thred then in the degrees is the Suns Right Ascention in degrees on the innermost Circle the same in hours and quarters from the next Equinoctial-point on the Line of Declination his mean Declination on the Line of â—he Suns place his mean true place sufficiently true for any illustration in Mathematical practice The Uses whereof in some part follow 1. To rectifie the Sphear to any Latitude count the Elevation of the Pole on the Meridian Circle from the Horizon upwards and downwards from the North and South parts of the Horizon and there make fast with the help of the small skrew the Fiducial-edge of the Poles Points carrying the Hour Circle fixed upon them then the Pole is rightly elevated 2. Count the complement of the Poles Elevation on the Meridian from the South part of the Horizon and to it set the divided side of the Equinoctial Circle then is that rectified also in the Northern Hemisphere or in the Southern if you call the North Pole the South Pole 3. Extend the Thred or Axis passing through the Center to the South Pole and there make it fast and then the Sphear is rectified for many Uses in that Latitude Use I. The Day of the Month being given to find the Suns true Place Lay the Thred in the Center of the Plain on the day of the Month and in the Line of the Suns place you have his place Example On the 5th of November it is 23 degrees in â™ or if the Suns place be given look for that and just against it in the Months is the day required Example The Suns place being 15 degrees ♌ I look for it in the Line of his place and just against it I find Iuly 28 day Use II. To find his Declination any day Look for the day given and right against it in the Line of Declination is his due Declination required Example August the 5th The Declination is 14 degrees 5 minuts from the next Equinoctial-point viz. ♎ Note In the Northern Sines or Summer-time the Sun hath North declination or in Southern Sines or Winter-months the Sun hath South declination Or if you have the Suns declination find that in the Line Declination and right against it in the Months is the day required Example 21 degrees South declination beginning from the Equinoctial towards the Winter Solstice I find Novemb. 15. The like work had been if the Suns place had been given to find his declination Use III. The day given to find the Suns Right-Ascention This is usually reckoned from ♈ to ♈ round in 24 hours but twice 12 is as useful and then it is thus Find the day amongst the Months and Dayes and just against it in the time of Hours is the Suns Right Ascention but note it is not right figured for this use counting onwards from ♈ or the 10th of March to the 13th of Septemb. and from thence to Aries again Likewise the degrees are to be reckoned from ♈ onwards as the Months proceed Example On the 12 of May what is the Suns Right Ascention Lay the Thred on the 12th of May and in the Line of Hours it cuts 9-57′ counting from Aries onwards or in degrees 59-15 counting as before Thus if any one of these 4 general things be given the other may be found Use IV. The Suns Declination and Latitude being given to find the Suns Meridian Altitude The Sphear being rectified count the declination on the Meridian from the Equinoctial that way the declination is either North or South and where the count ends there is the Meridian Altitude required for that day or Declination Example Iune 11. Declination 23-30′ Count 23-30 from 38-30 the place where
do then by the Trianguler-Quadrant having first observed the true hour turn the Horizontal-Dial about on the Point M till the shadow of the Thred or Axis shew the same Hour then the Point on the north-North-end of the Horizontal-Dial shall shew the true Declination of the Plain For any South Decliner the use is obvious But for North-Decliners you must turn the Plain out of the way of the Thred still keeping the same side AB to the Wall and if the Horizontal-Dial hinder put a Parallel-piece between as your Rule or any other thing and you shall have the Point give the Declination on the Southern Semi-circle on the fixed Horizon Use II. The Declination of any Erect Decliner given to find the Substile and Stile Inclination of Meridians and every hour and quarters distance from 12 being the Perpendiculer Line on the Plain First Set the Point at 12 on the Horizontal-Dial to the Declination of the Plain toward the East or West and set the Plain Upright Then first for the Substile Apply the side of the Quadrant to the Plain and cause the shadow of the Thred to play Parallel to the perpendicular Ray of the Quadrant and at the same time it shall shew on the degrees on the Plain the true Substiles distance from 12. Example Suppose the Plain decline 20 degrees South-west you shall find the Substile to be 15 deg and 12′ from 12 and to stand on the East-side of 12 in a South declining West 20 degrees Latitude 51-30 Again for the Stiles Elevation Apply the Quadrant to the flat of the Plain on the Substile Line so as the Thred may cut the Center of the Quadrant and then the Thred shall cut on the Quadrant 35-46 for the Stiles height Again for the Inclination of Meridians The shadow of the Thred when it cuts the Substile 15 deg 12′ on the Plain shall on the Horizontal-Dial cut 1 hour 36 min. which reduced to degrees is 24 deg 50 min. the Inclination of Meridians Again for every Hours distance in degrees and minuts from 12. Turn the whole Instrument about as it is then first set till the shadow of the Thred shall fall on every hour and quarter and then the shadow shall cut on the degrees on the Plain the distance of every hour and quarter from 12 for that declination in degrees and minuts which you may draw into a Table for your use and purpose or hereby examine your more exact Calculation and prevent all gross mistakes in your former work Use III. Any Declining North-east or North-west-Dial being given to find the former Requisites for those Dials In the true proper using the Sphear for North-Dials the Stile should look upwards which will appear so to do if you turn the Instrument the bottom upwards for the further help to your fancy but observe that the Hour-Arks and Angles are the same for the North as for the South only the difference is in the Scituation as to the contrary-side and looking upward instead of the South Decliner looking downward as by turning the Instrument appears so that if you draw the Dial as a South-west when you would make a North-west and set right figures and the right way and then your work is effected to your mind to the right intent and purpose Example of a North-East 30 degrees Latitude 51-30 Set the Point at 12 to 30 degrees Westward and apply the Square to the Plain till it just touch the Thred and on the degrees on the Plain it cuts 21-40 for the Substile and at the same time almost half an hour past 2 for Inclination of the Meridians and applying the Quadrant to the Substile-Line on the Plain and to the Thred it cuts 32-35 for the Stiles height being the same and the same way found as for the South Decliner East But observe That for the Hour-Arks you must note That the North-Dial cannot shew 12 at Noon nor any Hours very near Noon which will be seen on the South Decliner East Therefore 4 in the morning is here called 8 and 5 is called 7 and 6 is 6 7 in the morning is called 5 and 8 is to be named 4 And if you turn the Instrument that the shadow of the Thred may fall on those hours it will also cut on the degrees on the Plain the true Hour-Arks required As thus For 8 it sheweth it not at 7 it sheweth 77-00 at 6 it sheweth 58 deg 52 minuts at 5 it cuts on the degrees on the Plain 45-38 at 4 in the morning it cuts on the Plain 35-27 but the shadow falls then on Hour of 8 on the Horizontal-Dial Also note That these numbers are not laid from the Substile but from the Plains Perpendiculer which in all Upright Plains is a Perpendiculer Line and in all other Plains a Perpendiculer to the Horizontal-Line drawn on the Plain And thus proceed with any other the affections are best seen when you turn the Instrument the upper-part downwards Use IV. To find the Requisites and to draw the Hours on a far Declining Erect-Dial S. W. 80. Set the Point to 80 as before S. W. then the Thred and the Quadrant shall shew 38-2 for the Substile and 82-8 on the Horizontal for the Inclination of Meridians and 6-12 for the Stiles Elevation and the shadow of the Thred on the Horizontal-Dial will shew you how close and inconvenient the Hours will be if not helped by the former directions and in like manner will the North-East or West be and likewise helped Use V. To find the Requisites and Hour-Arks from the Perpendiculer of a Declining Inclining Plain with its Affections Set the Point at 12 to the Declination and move the Plain by help of the Arch or Circle of Brass to the Inclination and with the skrew make it fast and steady in that place Then for the Substile Apply the Quadrant to the Plain and also Perpendiculer to the Axis as the edge of the Quadrant being thick will neatly shew then the Thred will shew on the degrees on the Plain the distance of the Substile from the Perpendiculer or the complement thereof from the Horizon which Point note with a spot of Ink for when the shadow of the Thred falls on that spot on the Horizontal Dial it sheweth the Inclination of Meridians that is to say on what hour and minut the Cock of the Dial should stand right over Also The Quadrant applied to the Plain and Thred on the Substile-Line sheweth the true Stiles Elevation above the Plain And lastly making the shadow of the Thred to fall on every Hour on the Horizontal-Dial it shall at the same time shew how many degrees and minuts on the Plain that Hour-line ought to be from the Perpendiculer or from the Horizon and also which way either to the Right or Left East or West or from the Substile or 12 if you will trouble your self to count it from the place found out for the Substile or 12. Example of a Plain Declining
at the Sun or Star and the weighty Plummet will pull the Thred streight and let you know by feeling which way it is playing till it playeth evenly and truly whilst you have the Object precisely in the midst thereof whether it be Sun Moon or any Star or other Object whose Altitude you would observe Then I say when the Plummet playes well and you behold the Object right bend back the Quadrant and see what the Thred cuts on the degrees on the moveable-Leg which shall be the true Altitude required And in my opinion must needs be more exact than any other way of a forward Observation because you are not troubled to mind the Horizon and Sun both at at once An Objection may be The boisterous Winds and the rouling of the Ship will hinder such an Observation Answ. So it will any other way though happily not so much Again I answer One Object is better and more certainly seen than two at any time together and though the Wind blow hard if you can stand to observe at all the heavy Plummet will be sure to draw the Thred Perpendiculer and for ought I know you may come as near this way as any other however this at most times may confirm and prove the other and may be useful in Rivers and Harbours and misty-Dayes when you may see the Sun well enough but not the Horizon at all Use III. To find the Suns Altitude by a backward Observation as with a Back-staff or Davis-Quadrant Skrew the turning-sight to the Leg-Center or Center to the degrees on the moveable-Leg and set the object-sight to the long stroke by 00-60 on the out-side of the Loose-piece and put the sliding Horizon-sight on the out-side of the moveable-Leg then hold the Object-sight upwards and the small-hole in the piece turning on the â—dge or to the small-hole in the middle of the Horizon-sight which you please close to your eye and looking through that hole and the middle-hole of the turning-sight to the true Horizon turning your self about and lifting up or pressing down the Horizon-sight close to the moveable-Leg till the shadow of the upper-edge of the shadow-sight being next to the Sun fall at the same time just on the middle of the turning-sight Then I say the edge or middle of the Horizon-sight that you looked through shall cut the true Altitude of the Sun required Being the same way as you do observe with a Davis-Quadrant or Back-staff Use IV. To find the Suns Distance from the Zenith by the Trianguler-Quadrant Skrew the turning-sight to the Leg-Center and put the Object-sight whose oval-hole is remotest from the Quadrant in the hole in the end of the Head-Leg or rather in a hole on the general Scale between the turning-sight and the Sun and put the Horizon-sight on the out-side of the moveable-Leg then hold the turning-sight toward the Sun and the small-hole in the edge of the Horizon-sight to your eye then look through that hole and the turning-sight till you see the shadow the Object-sight to fall just on the turning-sight or the shadow of the turning-sight to fall just on the object-sight which is all one though the first be more easie because you shall see the Horizon through the turning-sight and that both at once Then I say the degrees cut by the Horizon-sight shall be the Suns distance from the Zenith required Being the very same work and done in the same manner and producing the same Answer viz. the Suns distance from the Zenith that the Davis-Quadrant doth Note That this way you may observe very conveniently till the Sun be 20 degrees distance from the Zenith and by the adding of a 60 Arch as in Davis Quadrant or to 45 will be enough it will do as well as any Davis Quadrant being then the same thing But I conceive the complement of the Altitude being the same will do as well which Altitude is better found by this Instrument than the distance from the Zenith by a Davis Quadrant is as in the next Use will be seen Use V. To find the Suns Altitude when near the Zenith or above 90 degrees above some part of the Horizon In small Latitudes or in places near the Equinoctial or under it the Sun will be found to be in or near the Zenith and if you count from some part of the Horizon above 90 degrees distant from it then instead of setting the sliding Object-sight to the long stroke at 00 on the Loose-piece you must set it 30 degrees more towards the Head-leg then observe as you did before and whatsoever the Horizon-sight cuts you must add 30 degrees more to it and the sum shall be the true Altitude required Example Suppose that in the Latitude of 10 deg North on the 10th of Iune when the Suns Declination is 23 degrees and 31 min. Northward Suppose that at noon I observe the Suns Meridian Altitude skrewing the Turning-sight to the Leg-Center and setting the Object-sight to the 30 degrees on the Loose-piece near the end of the Head-leg and the Horizon-sight on the movable-Leg then hold up the Quadrant with the shadow-sight toward the Sun and the small-hole in the Horizon-sight toward your eye and look to the Horizon through that and the turning-sight the shadow of the right-edge of the shadow-sight that cuts the degree of 30 at the same time falling on the middle of the turning-sight you shall find the Horizon-sight to cut on 46-29 minuts to which if you add 30 the degrees the shadow-sight is set forwards it makes up 76-29 the Suns true Altitude on that day in that Latitude 76-29 the Meridian Altitude and 23-31 the Declination added together make 100 deg 00 from which taking 90 there remains 10 the Latitude of the place 1. In this Observation first you may note this That if you had stood with your back toward the South you would have had 103 degrees and 31 minuts for the sliding Horizon-sight would have stayed at 73 degrees 30 to which if you add 30 it makes 103-31 which a Davis Quadrant will not do 2. In the holding it you may lean the head of the Rule to your breast and command it the better as to steady holding 3. You may turn the Turning-sight about to any convenient Angle to make it fit to look through to the Horizon and also to receive the shadow of the shadow-sight If the brightness of the Sun offend the eyes you may easily apply a red or a blue Glass to darken the Sun beams and the Sights may be painted white to make a shadow be seen better Use VI. To find the Latitude at Sea by a forward Meridian Observation of the Altitude according to Mr Gunter's Bow Skrew the Turning-sight to the Leg-Center and set the shadow-sight to the Suns-Declination and the Horizon-sight to the moving Leg or Loose-piece and the Turning-sight to your eye then let the shadow-sight cut the Horizon and the Horizon-sight the Sun moving it higher or lower