THe limbe of the Quadrant divi­ded into 90 Degr. represen­teth the Horizon.

That side of the Quadrant where the Sights are, is the Meridian, or XII a Clocke line, unto which is joyned the scale of Moneths with every fift Day, untill they grow so little toward the Solsticeas, that they cannot bee distinguished. This scale▪ hath five Rowes, the midst whereof hath the very same divisions which are on the Meridian line: The two next on both sides are for the parts of the Moneths, which in the two outermost Rowes are noted by their first Letters.

The other side of the Quadrant hath on it the scale of Altitudes above the Horizon.

The short Arching lines within the Quadrant beside the Meridian, are Houre-lines, noted by their Figures, both for the forenoone, and after­noon; [Page 2] and halfe Houre lines: each halfe houre containing 30 min. of an hour, or Deg. 7. 30. Of these Horary lines, those which serve in the morning before the Sunne is full East, or in the evening past the West, (which is onely in Sum­mer halfe yeare) are reversed. And all the Hour lines are noted with two Figures; whereof the upper next the Center and scale of Alti­tudes, serve for the afternoon; and the lower for the forenoon. The two Arches which crosse the Houre lines, and meet at the beginning of the Horizon and scale of Altitudes, are two Quarters of the Ecliptic, and are divided into 90 Degr. a piece, in which are noted the XII Signes by their proper Characters, namely on the upper next the Center are ♈ ♉ ♊ & ♋ ♌ ♍, the Summer or Northerne Signes: and on the lower next the Horizon are ♎ ♏ ♐ & ♑ ♒ ♓, the Winter or Southerne Signes, and contain 30 Degr. a piece. This is the Cir­cle of the Sunnes annuall motion.

The long Arches, which beginning at the Scale of moneths in the Meridian betwixt the two Quarters of the Ecliptic, crosse all the Houre lines, are the parallels of Declination, or the Semidiurnall Arches of the Sunne; the middlemost of which is the Equinoctiall, the outermost above is the Tropick of ♋, and the outermost below is the Tropick of ♑: although [Page 3] between the Equinoctiall and each Tropick Innumerable parallels are understood to be con­tained, yet those which are in the Instrument drawne, at every second Degree of Declinati­on, may be sufficient to direct the eye in tracing out an imaginary parallel from every point gi­ven in the Scale of moneths.

The Equinoctiall and every tenth parallel are for distinction sake made somewhat grosser than the rest, and all the Summer parallels at the East and West line are continued reversedly back unto the Horizon.

Note that upon the right estimation of that imaginary parallel, the manifold use of this Instrument doth especially rely; because the true place of the Sunne all that day is in some part or point of the same Circle.

And note that in this Instrument, the direct Horary lines, and parallels before their reversi­on, shew the houre of the day like a direct South upright Diall: And the Arches of them reversed serve like a direct North upright Diall.

Use I. To finde the Declination of the Sun every day.

Seek the day proposed in the Scale of moneths very exactly, & mark upon what point it falleth in the middle Row of that Scale, or (which is all one) in the Meridian, for there is the Decli­nation [Page 4] of the Sunne from the Equinoctiall, either North or South: which if it fall not di­rectly upon a parallel, but in the space between two, supposing each halfe of that space to containe 60 minutes, estimate with your eye proportionally what minute the point giveth.

Example 1. What is the Sunnes Declina­clition upon Novemb. 13? the day will fall in the space after 20 Degrees, from the Equinoctiall Southward, about 30 minutes: Wherefore the Sunnes Declination is 20°. 30′ South.

Example 2. What is the Sunnes Declinati­on upon August 19? the day wil fal in the space after 8 Degrees, from the Equinoctiall North­ward, one Degree and about 40 minutes: Wherefore the Suns Declination is 9°. 40′. North.

Note that the Declination thus found is to be kept in minde all the day.

Use II. To finde the Semidinunall Arch, or parallel Circle in which the Sunne moveth eve­ry day.

Seeke out the true point of the Sunnes De­clination upon the Meridian by Vse I: then from that point by the estimation of your eye, trace out an imaginary parallel: which when it commeth to the East and West line (as in all Northerne parallels it doth) is to bee reversed unto the Horizon or Limbe at the same propor­tionable [Page 5] distance as before. This operation re­quireth exact diligence.

Use III. To finde the time of the Sunes Ri­sing and Setting every day.

Seek out the imaginary parallel, or Semidiur­nal Arch of the Sun for that day by Vse II, and marke where it meeteth with the Horizon; for that is the very point of the Sunnes rising and setting, and the Hour-lines on both sides of it, (by proportioning the distance reasonably, according to 30 minutes for halfe an houre) will shew the time of the Sunnes rising and set­ting.

Thus at London, Novem. 13. the Sun will be found to rise at 9 min. before 8, and to set at 9 min. after 4. Also August 19, the Sunne will be found to rise 12 min. after 5. and to set 12 min. before 7.

Use IV. To finde the Suns Amplitude, Or­tive and Occasive: that is, how many Degrees of the Horizon the Sunne riseth and setteth from the true East and West points every day.

The imaginary parallel of the Sunne, toge­ther with the time of the Sunnes rising, and set­ting, sheweth upon the Horizon the Degree of his Amplitude from East and West, which in all the Northerne parallels is on the North side, and in the Southerne on the South side.

Thus at London, Novem. 13. the Ampl. Ort. [Page 6] will be found 34 Degreees. Also Aug. 19. the Ampl. Ort. will be found 15°. 10′.

Use V. To find the Length of every day and night.

Double the houre of the sunnes-setting, and you shal have the Length of the day: or double the houre of the sunnes-rising, and you shall have the Length of the night.

Use 6. To know the reason and manner of the Increasing and Decreasing of the Dayes and Nights throughout the whole yeare.

When the Sunne is in the Equinoctial, it ri­seth and setteth at 6 a Clocke: But if the Sunne be out of the Equinoctial, declining to­ward the North, the Intersection of the paral­lel of the Sunne with the Horizon is before 6 in the morning, and after 6 in the evening; and the Diurnall Arch greater than 12 houres, and so much more great, the greater the Northerne Declination is. Againe, if the Sunne be decli­ning toward the South, the Intersection of the parallel of the Sunne with the Horizon is after 6 in the morning, and before 6 in the evening; and the Diurnall Arch lesser than 12 hours, and by so much lesser, the greater the Southern De­clination is.

And in those places of the Ecliptic in which the Sunne most speedily changeth his Declination, the Length also of the day is most [Page 7] altered; and where the Ecliptic goeth most parallell to the Equinoctiall, changing the De­clination slowly, the length of the day is but little altered. As for Example; When the Sun is neare unto the Equinoctiall on both sides, the dayes Increase and also Decrease suddenly and apace; because in those places the Ecliptic inclineth to the Equinoctiall in a manner like a straight Line, making sensible Declination. Againe, when the Sunne is neare his greatest Declination, as in the height of Summer, and the depth of Winter, the dayes keep for a good time, as it were, at one stay; because in these places the Ecliptic is in a manner paral­lel to the Equinoctiall, the Length of the day differeth but little, the Declination scarce alte­ring; and because in those two times of the yeare, the Sunne standeth as it were still at one Declination, they are called the Summer Sol­stice, and Winter Solstice. Wherefore wee may hereby plainely see, that the common received opinion, that in every moneth the dayes doe equally increase, is erroneous. Al­so wee may see, that in parallels equally distant from the Equinoctiall, the day on the one side is equall to the night on the other side.

Use VII. To take the height of the Sunne above the Horizon.

Hold the edge of the Quadrant against the [Page 8] Sunne, so that the Sunnes Ray or Beam may at once passe through the hole of both the sights; then shall the thread with the Plummet shew the Sunnes Altitude.

Use VIII. To finde the Houre of the day, or what a clock it is.

Having the imaginary parallel or Semidiur­nall Arch of the Sunne, already found and conceived in your minde by Vse II, take the Sunnes height above the Horizon, then stretch­ing the thread over the scale of Altitudes, set the Bead to the Altitude found, move your thread untill the Bead exactly falleth upon the imaginary parallel, for there is the houre fought; and that is the true place of the Sun in the Quadrant at that time; to bee estimated upon the Horary lines, either direct, or rever­sed, according as the parallel is.

Use IX. To finde the Sunnes Azumith or Horizontall distance from the foure Cardi­nall points.

The Bead being set to the houre of the day, as was shewed in the Ʋse next before, the thread shall in the Limbe cut the East or West Azumith; that is, how many Degrees of the Horizon the verticall Circle in which the Sunne is, is distant from the East and West points: The complement of which number giveth the Azumith from the South [Page 9] Meridian, if the Bead fell in the right paral­lels: But if the Bead fall upon the reversed parts, the Azumith is to be accounted from the North Meridian.

Use X. To finde the Meridian Altitude of the Sunne every day.

Stretch the thread over the Meridian, and set the Bead to the true Declination of the Sunne therein; then apply the thread to the scale of Altitudes; and the Bead shall give the Meridian Altitude sought.

Use XI. To finde at what time the Sunne commeth to bee full East or West every day in Summer.

This is shewen by observing at what houre the imaginary parallel meeteth with the East and West line, at which it beginneth to re­verse.

Use XII. To finde how high the Sunne is above the Horizon at any houre, every day.

Set the Bead to the point in which the ima­ginary parallel of that day crosseth the houre given: then applying the thread to the scale of Altitudes, mark upon what Degree the Bead falleth; the same shall bee the Altitude of the Sun required.

Use XIII. To finde how high the Sunne is being in any Azumith assigned every day: and also at what houre.

[Page 10] Set the Bead to the point in which the ima­ginary parallel of that day crosseth the Azu­mith assigned; There also shall bee the houre sought: Then applying the thread to the scale of Altitudes, marke upon what Degree the Bead falleth; The same shall be the Altitude of the Sun required.

These two last Uses serve for the Delinea­tion of the ordinary Quadrants, as that of Gemma Frisius, Munster, Clavius, Master Gunter, &c. and also of Rings, Cylinders, and other Topicall Instruments; and for the find­ing out of the houre by a mans shadow, or by the shadow of any Gnomon, set either per­pendicular, or else parallel to the Horizon.

Use XIV. To finde the Sunnes Longitude, or place in the Ecliptic.

The imaginary parallel of the day being ex­actly traced will cut in the Ecliptick the Signe and Degree wherein the Sunne is: and note, that each semicircle of the Ecliptic is doubly noted with Characters of the Signes; the first and third Quarters goe forward from the E­quinoctial point unto the Meridian, containing ♈ ♉ ♊ & ♎ ♏ ♐: the second and fourth Quarters goe backe from the Meridian unto the Equinoctiall point, containing ♋ ♌ ♍ & ♑ ♒ ♓.

But because neare unto both Tropicks [Page 11] (namely from May 11, to July 10, in the height of Summer, and from November 13, to Januarie 12 in the depth of Winter) the Declination altereth so slowly, that the true place of the Sunne in the Ecliptic cannot be distinguished with any certainty, worke ac­cording to this foure-fold Rule following.

1. Before June 10, out of the number of dayes from May 0, subduct 11: the remains shall be the Degrees of ♊: thus for June 3, (because there is all May and three dayes of June) say 34—11=23 ♊, the place of the Sunne.

2. After June 10, out of the Number of dayes from June 0, subduct 10: the remains shall bee Degrees of ♋: thus for July 3, say 33—10=23 ♋, the place of the Sun.

3. Before December 13, out of the Num­ber of dayes from November 0, subduct 13: the reamines shall be Degrees of ♐: thus for December 3, say 33—13=20 ♐, the place of the Sun.

4. After December 13, out of the Number of dayes from December o, subduct 13: the remaines shall be Degrees of ♑: thus for Ja­nuary 3, say 34—13=21 ♑, the place of the Sunne.

Use XV. To find the Suns Right Ascensi­on every day.

[Page 12] Having by Use XIV. found the place of the Sunne in the Ecliptic, mark diligently upon what houre, and as neare as you can estimate what minute it falleth, counting the houres in the first and third Quarters of the Ecliptic, from the Equinoctiall point; but in the second and fourth Quarters, from the Meridian: and adde thereto in the second Quarter six hours, in the third twelve houres, and in the fourth eighteen houres: so shall you have the Sunnes Right Ascension, not in Degrees, but in time, which is more proper for use.

Example, in ♌ 6. the Sunnes Right As­cension will bee eight houres, one halfe, and about three minutes; that is H: 8: 33. min. reckoning 30′ for halfe an houre.

Use XVI. To find the Houre of the Night by the Starres.

For this, I have set a little Table of five knowne Stars dispersed round about the Hea­vens, with their Declination and Right As­cension for Anno Dom. 1650. Namely the left shoulder of Orion, noted O. The heart of the Lion, noted ♌. Arcturus noted A: the Vul­ture volant, noted V. The end of the wing of Pegasus, noted P.

[Page 13]

THe Operation is thus; first by the height of the Starre taken, and the parallel of its Declination exact­ly traced, seek out the houre of the Starre from the Meridian, as be­fore was taught for the houre of the Day by the Sunne. Se­condly, out of the Right Ascension of the Starre, subduct the Right Ascension of the Sun; the remain [...] sheweth how long time from the Noone before the same starre commeth into the Meridian. Lastly, if the Starre be not yet come to the Meridian, out of the houre of the Starres comming into the Meridian, sub­duct the houre of the Starre: but if the Star be past the Meridian, adde both the houres to­gether; so shall you have the true houre of the Night.

Note, that if the hours out of which you are to subduct bee lesser than the other, you must adde unto them 24.

Use XVII. To finde out the MeridianLine upon any Horizontall plaine.

About the middle of your plaine describe a Circle; and in the Center thereof erect a [Page 14] straight Piece of Wire perpendicularly. When the Sunne shineth, note the point of the Circle which the shadow of the Wire cut­teth, which I therefore call the shadow point; and instantly by Vse IX. seeke the Sunnes A­zumith from the South or North: keepe it in minde. Then from the shadow point, if your observation be in the foore-noon, reckon up­on the circle an Arch equall to the Azumith kept in minde, that way the Sunne moveth, if the Azumith bee South: Or the contrary way if it bee North. But if your observation bee in the afternoone, reckon the North A­zumith that way the Sunne moveth; Or the South Azumith the contrary way.

Lastly, through the end of the Azumith and the center, protract a Diameter for the Meridian line sought: which you may note with S. at the south end, and with N. at the North end.

You may also note the point of the Circle Diametrally opposite to the shadow point with sun;, because it is the Azumith place of the Sun, at the moment of your observation.

Use XVIII. To finde the Declination of a­ny Wall or plaine.

The safest way (because the Magneticall Needle is apt to be drawne awry) will be by an Instrument made in this manner. Provide a [Page 15] rectangular board about ten Inches long, and five broad: in the midst whereof, crosse the breadth, strike a Line perpendicular to the sides; and taking upon it a Center, describe a Circle intersecting the same Line, in two opposite points, to be noted with the Letters T. and A: divide each semicircle into two Quadrants, and every Quadrant into 90 Degrees, begin­ning at the points T and A, both wayes; the first Quad. beginning on the left hand of T. the second Quadrant on the right hand: the third Quadrant above it toward A: And lastly, the fourth Quadrant. And in the Center erect a Wier at right Angles.

The use of this Instrument. Apply the long side of the board next T to the Wall when the Sunne shineth upon it, holding it parallel to the Horizon, that it may represent an Horizontall plaine. Marke what Degree the shadow of the Wyer cutteth in the Circle; and instantly seek the Sunnes Azumith, either South or North: Reckon it on the Circle from the shadow to the Meridian, as was taught in the Use next be­fore, noting that end with the Letter contrary to that of the Azumith: as if the Azumith bee South, note it N. and the opposite end S; if the Azumith bee North, note it S, and the opposite end N: whereby also you have the East▪ and West sides: So shall the Arch S A. [Page 16] or N A. give the Declination of the plaine, and the point A, the coast or quarter into which it is.

Example, June 2 in the forenoone, applying the instrument to a wall, I found the shadow in 23 Degr. of Quadr. 2. and the height of the Sunne was 26 Degrees, whereby I found the Azumith to be North 84 Degr. which rec­koned from the shadow against the Sunne, fell upon 61 Degr. in Quad. 1. for one end of the Meridian; and the Opposite end▪ which is N. upon 61 Degr. in Quad. 3. And A was on the East side of N. Wherefore the Declination of that Wall is 61 Deg. from the North Eastward.

Use XIX. To finde the Declination of an up­right wall by knowing the time of the Sunnes comming to it, or leaving it. And contrariwise, the Declination of an upright Wall being known to finde at what time the Sunne will come into it.

Because the Declination of a plain is an arch of the Equinoctiall intercepted between the Horizontall section of the plaine: and the East or West points: Or else (which is all one) be­tween the Meridian, and A, the axis of that Ho­rizontall sexion. Watch till you see the Center of the Sunnejust even with the edge of the Wall: then instantly take the Sunnes Azumith from East or West, by Use IX. the same is the Declination of the wall.

[Page 17] Likewise if the Declination be given, rec­kon it upon the Limbe of your Quadrant from the East and West point; and the thread being applyed to the end of that Arch, shal in the Suns imaginary parallel for that day, cut the houre and time desired.

Use XX. Certaine advertisements necessa­ry for the use of the Quadrant in the night.

In which Questions as concerne the night, or the time before Sunne-rising, and after Sunne­setting, the instrument representeth the lower Hemisphere, wherein the Southern Pole is ele­vated. And therefore the parellels which are above the Equinoctiall toward the Center, shall be for the Southerne or winter parellels: and those beneath the Equinoctiall, for the Nor­therne or Summer parallels: and the East shall be counted for West, and the West for East; altogether contrary to that which was before, when the Instrument represented the upper Hemisphere.

Use XXI. To finde how many Degrees the Sunne is under the Horizon at any time of the night.

Seek the Declination of the Sunne for the day proposed by Use I. and at the same Decli­nation on the contrary side of the Equinoctiall imagine a parallel for the Sunne that night; and marke what point of it is in the very houre and [Page 18] minute proposed: Set the bead to that poynt; then applying the thread to the scale of Alti­tudes, marke upon what Degree the bead fal­leth: for the same shall shew how many De­grees the Sunne is under the Horizon at that time.

Use XXII. To finde out the length of the Crepusculum, or Twi-light.

It is commonly held that Twilight is so long as the Sunne is not more then 18 degrees, un­der the Horizon, the question therefore is, at what time the Sunne cometh to be 18 Degrees under the Horizon any night.

Seek the Sunnes declination for the time pro­posed, and at the same declination, on the con­trary side of the Aequinoctiall, imagine a paral­sel for the Sunne that night: then set the bead at 18 degrees in the scale of Altitudes; and car­ry the thread about till the bead fall upon the imagined parallell: for there shall be the houre or time sought.

And in this very manner you may find the time or houre of the night at any other depressi­on of the Sunne under the Horizon.