# An Appendix concerning the Description and Use of a small Portable Quadrant, for the more easie finding of the Hour and Azimuth, and Other Astronomical and Geometrical Conclusions.

## CHAP. I.Of the Description of the Quadrant.

Having described these standing Planes, I will now shew the most of these Conclusions by a small Quadrant. This might be done generally for all Latitudes, by a quarter of the general Astrolabe, described before in the Use of the sector; and particularly for any one latitude, by a quarter of the particular Astrolabe, there also described; which if it be a Foot Semidiameter, may shew the Azimuth unto a Degree, and the time of the Day unto a Minute: But for ordinary use this smaller Quadrant may suffice, which may be made portable in this manner.

1. Upon the Center A, and Semidiameter AB, describe the Ark BC; the same Semidiameter will set of 60 gr. and the half of that will be 30 gr. which being added to the former 60 gr. will make the Ark BC to be 90 gr. the fourth part of the whole Circle, and thence comes the name of a Quadrant.
2. Leaving some little space for the Inscription of the Months and Days, on the same Center A, and Semidiameter AT, describe the Ark TD, which shall serve for either Tropick.
3. Divide the Line AT in the Point E, in such a proportion, as that AT being 10000, AE may be 6556, and there draw another Line EF, which shall serve for the Equator; or AE being 10000, let ET be 5253.
4. Divide AF the Semidiameter of the Equator in the Point G, so as AF being 10000, the Line AG may be 4343: and on the Center G, and Semidiameter GD, describe the Ark ED, which shall serve for a fourth part of the Ecliptick.
5. This part of the Ecliptick may be divided into three Signs, and each Sign into 30 gr. by a Table of Right Ascensions, made as followeth.
 A Table of Right Ascensions. Gra. Aries Taurus Gemini Gr. M. Gr. M. Gr. M. 0 0 0 27 54 57 48 5 4 35 32 42 63 3 10 9 11 37 35 68 21 15 13 48 42 31 73 43 20 18 27 47 33 79 7 25 23 9 52 38 34 32 30 27 54 57 48 90 0

As the Right Ascension of the first Point of ♉ being 27 gr. 54 m. you may lay a Ruler to the Center A and 27 gr. 54 m. in the Quadrant BC, the Point where the Ruler crosseth the Ecliptick shall be the first Point of ♉. In like manner, the Right Ascension of the first Point of ♊ bein 57 gr. 48 m. if you lay a Ruler to the Center A and 57 gr. 48 m. in the Quadrant, the Point where the Ruler crosseth the Ecliptick shall be the first Point of ♊: And so for the rest. But the Lines of distinction between Sign and Sign may be best drawn from the Center G.

6. The Line ET between the Equator and the Tropick, which I call the Line of Declination, may be divided into 23 gr. ½ out of this Table. For let AE the Semidiameter of the Equator be 10000, the distance between the Equator and 10 gr. of Declination may be 1917 more; between the Equator and 20 gr. 4281; the distance of the Tropick from the Equator 5252.
 Gr. Parts 1 176 2 355 3 537 4 723 5 913 6 1106 7 1302 8 1503 9 1708 10 1917 11 2130 12 2348 13 2571 14 2799 15 3032 16 3290 17 3514 18 3763 19 4019 20 4281 21 4550 22 4825 23 5104 Trop. 5258
7. You may put in the most of the principal Stars between the Equator and the Tropick of ♋, by their Declination from the Equator, and the Right Ascension from the next Equinoctial Point. As the Declination of the Wing of Pegasus being 13 gr. 7 m. the Right Ascension 358 gr. 34 m. from the first Point of ♈, or 1 gr. 26 m. short of it. If you draw an occult Parallel through 13 gr. 7 m. of Declination, and then lay a Ruler to the Center A, and 1 gr. 26 m. in the Quadrant BC, the Point where the Ruler cosseth the Parallel shall be the Place for the Wing of Pegasus, to which you may set the name and the time when he cometh to the South at midnight in this manner: W. Peg.* 23 Ho. 54 M. And so for the rest of these five, of any other Stars.
 Ho. M. Ho. M. Ho. M. Pegasus Wing* March 8 23 56 1 06 13 17 Arcturus* October 14 14 00 30 07 21 8 Lions Heart* August 7 9 50 32 28 13 42 Bulls Eye* May 16 4 18 64 18 15 46 Vultures Heart* January 1 19 35 66 26 8 3
8. There being space sufficient between the Equator and the Center, you may there describe the Quadrant, and divide each of the two Sides farthest from the Center A into 100 parts; so shall the Quadrant be prepared generally for any Latitude.

But before you draw the particular Lines, you are to fit four Tables under your Latitude.

First, a Table of Meridian Altitudes, for division of the Circle of Days and Months, which may be thus made. Consider the Latitude of the Place, and the Declination of the Sun for each Day of the Year. If the latitude and Declination be alike, both North, or both South, add the Declination to the Complement of the Latitude; if they be unlike, one North, and the other South, subtract the Declination from the Complement of the Latitude, the Remainder will be the Meridian Altitude belonging unto the Day.

Thus in out Latitude of 51 gr. 30 m. Northward, whose Complement is 38 gr. 30 m. the Declination upon the tenth day of June will be 23 gr. 30 m. Northward; wherefore I add 23 gr. 30 m. unto 38 gr. 30 m. the sum of both is 62 gr. for the Meridian Altitude at the tenth of June. The Declination upon the tenth of December will be 23 gr. 30 m. Southward, wherefore I take these 23 gr. 30 m. out of 38 gr. 30 m. there will remain 15 gr. for the Meridian Altitude at the tenth of December; and in this manner you may find the Meridian Altitude for each Day of the Year, and set them down in a Table.

 Dies. 0 5 10 15 20 25 30 Month. Gr. M. Gr. M. Gr. M. Gr. M. Gr. M. Gr. M. Gr. M. January 16 31 17 24 18 26 19 37 20 57 22 24 23 58 February 24 17 25 59 27 45 29 35 31 29 33 25 March 34 35 36 33 38 32 40 30 42 27 44 22 46 15 April 46 37 48 26 50 11 51 50 53 25 54 53 56 15 May 56 15 57 29 58 35 59 33 60 22 61 2 61 32 June 61 36 61 54 62 0 61 58 61 45 61 22 60 49 July 60 40 60 6 59 14 58 13 57 4 55 48 54 25 August 54 7 52 36 50 59 49 17 47 31 45 41 43 26 September 43 26 41 30 39 33 37 36 35 38 33 41 31 46 October 31 46 29 53 28 3 26 16 24 35 22 59 21 29 November 21 12 19 51 18 39 17 36 16 43 16 0 15 28 December 15 28 15 5 15 0 15 2 15 17 15 44 16 22

The Table being made, you may inscribe the Months, and days of each Month into your Quadrant, in the space left below the Tropick. For, lay the Ruler unto the Center A, and 16 gr. 31 m. in the Quadrant BC, there may you draw a Line for the end of December and the beginning of January; then laying your Ruler to the Center A, and 24 gr. 17 m. in the Quadrant, there draw the end of January and beginning of February, and so the rets, which may be noted with J, F, M, A, M, J, &c. the first Letters of each Month, and will here fall between 15 gr. and 62 gr. The second Table which you are to fit, may serve for the drawing and dividing of the Horizon. For drawing of the Horizon,

• As the Co-tangent of the latitude, to the Tangent of the greatest Declination:
• So the Sine of 90 gr. to the Sine of the Intersection where the Horizon shall cross the Tropick.

So in our Latitude of 51 gr. 30 m. we shall find the Horizon to cut the Tropick in 33 gr. 9 m. wherefore if you lay the Ruler to the Center A, and 33 gr. 9 m. in the Quadrant, the Point where the Ruler crosseth the Tropick shall be the Point where the Horizon crosseth the Tropick. And if you find a Point H in the Line AC, whereon setting the Compasses, you may bring the Point at E and this Point in the Tropick both into a Circle, the Point H shall be the Center, and the Ark so drawn shall be the Horizon.

Then for the division of this Horizon,

• As the Sine of 90 gr. to the Sine of the Latitude:
• So the Tangent of the Horizon, to the Tangent of the Ark in the Quadrant, which shall divide the Horizon.

So in our Latitude of 51 gr. 30 m. we shall find 7 gr. 52 m. belonging to 10 gr. in the Horizon, and 15 gr. 54 m. belonging to 20 gr. And so the rest, as in the Table.

 Ho. Gr. M. Ho. Gr. M Ho. Gr. M Ho. Gr. M Ho. Gr. M Ho. Gr. M 0 0 0 15 11 51 30 24 19 45 38 2 60 53 35 75 71 5 0 47 12 39 25 11 39 1 54 41 71 19 1 34 13 27 26 4 40 0 55 48 73 33 2 21 14 16 26 57 41 0 56 56 74 48 3 8 15 4 27 50 42 0 58 4 76 3 5 3 55 20 15 54 35 28 43 50 43 0 65 59 13 80 77 18 4 42 16 43 29 37 44 1 60 22 78 33 5 29 17 33 30 32 45 3 61 31 79 49 6 17 18 22 31 27 46 5 62 41 81 5 7 4 19 12 32 22 47 8 62 52 82 21 10 7 52 25 20 2 40 33 18 55 48 11 70 65 3 85 83 37 8 38 20 53 34 14 49 14 66 15 84 53 9 27 21 44 35 10 50 19 67 27 86 10 10 14 22 36 36 7 51 24 68 39 87 26 11 2 23 27 37 4 52 29 69 52 88 43 15 11 51 30 24 19 45 38 2 60 53 35 75 71 5 00 90 0

Wherefore you may lay the Ruler to the Center A, and 7 gr. 52 m. in the Quadrant BC, the Point where the Ruler crosseth the Horizon shall be 10 gr. in the Horizon; and so for the rest. But the Lines of distinction between each fifth Degree will be drawn from the Center M.

The third Table for drawing of the Hour-lines must be a Table of the Altitude of the Sun above the Horizon at every Hour, especially when he commeth to the Equator, the Tropick, and some other intermediate Declinations.

If the Sun be in the Equator, and so have no Declination,

• As the Sine of 90 gr. to the Co-sine of the latitude:
• So the Co-sine of the Hour from the Meridian, to the Sine of the Altitude.

Thus in our Latitude of 51 gr. 30 m. at six Hours from the Meridian the Sun will have no altitude, at five the Altitude will be 9 gr. 17 m. at four 18 gr. 8 m. at three 26 gr. 7 m. at two 32 gr. 37 m. at one 36 gr. 58 m. at Noon it will be 38 gr. 30 m. equal to the Complement of the Latitude.

If the Sun have Declination, the Meridian Altitude will be found as before, for the Table of Days and Months,

• If the Hour proposed be six in the Morning or six at Night,
• As the Sine of 90 gr. to the Sine of the latitude:
• So the Sine of the Declination, to the Sine of the Altitude.

Thus in our Latitude the Declination of the Sun being 23 gr. 30 m. the Altitude will be found to be 18 gr. 11 m. the Declination being 11 gr. 30 m. the Altitude will be 9 gr.

• If the Hour proposed be neither twelve nor six,
• As the Co-sine of the Hour from the Meridian, to the Sine of 90 gr.:
• So the Tangent of the Latitude, to the Tangent of a fourth Ark.

So in our Latitude, and one Hour from the Meridian, this fourth Ark will be found to be 52 gr. 28 m. at two 55 gr, 26 m. at three 60 gr. 39 m. at four 68 gr. 22 m. and at five Hours from the Meridian 78 gr. 22 m.

Then consider the Declination of the Sun, and the Hour proposed; if the Latitude and Declination be both alike, as with us in North Latitude, North Declination, and the Hour fall between Noon and six, take the Declination out of the fourth Ark, the remainder shall be our fifth Ark.

But if either the Hour fall between six and midnight, or the Latitude and Declination shall be unlike, add the Declination unto the fourth Ark, and the sum of both shall be your fifth Ark: or if the sum shall exceed 90 gr. you may take the Complement unto 180 gr. This fifth Ark being known,

• As the Sine of the fourth Ark, to the Sine of the Latitude:
• So the Co-sine of the fifth Ark, to the Sine of the Altitude.

Thus in our Latitude of 51 gr. 30 m. Northward, the Sun having 23 gr. 30 m. of North Declination, if it shall be required to find the Altitude of the Sun for seven in the Morning: here (because the Latitude and declination are both alike to the Northward, and the Hour proposed falleth between Noon and six) you may take 23 gr. 30 m. the Ark of the Declination, out of 78 gr. 22 m. the fourth Ark belonging to the fifth Hour from the Meridian, so there will remain 54 gr. 52 m. for your fifth Ark: Then working according to the Canon, you shall find,

• As the Sine of 78 gr. 22 m. your fourth Ark, to the Sine of 51 gr. 30 m. for the Latitude:
• So the Sine of 35 gr. 8 m. the Complement of your fifth Ark, to the Sine of 27 gr. 17 m. the Altitude required.

If in the same Latitude and Declination it were required to find the Altitude for five in the Morning, here the Hour falling between six and Midnight, if you add 23 gr. 30 m. unto 78 gr. 22 m. the sum will be 101 gr. 52 m. and the Complement to 180 gr. will be 78 gr. 8 m. for the fifth Ark. Wherefore,

• In Rectangulo ODH,
• Ita OD Cosi. Hora, ad DH Tan. DH.
• Cujus aqualis est PR, cujus Compl. DR, novis dr. arcus quarius.

Conferatur Arcus DH cum Arcus Declinationis DS, ita dabitur Arcus HS, cujus Compl. Est SRO prim dr. Arcus quantum. Unde erit,

 Ut Cosi. PR, Hoc est, Ut Sin. DR, Ad Cosi. PZ: ad Sin. EZ: Ita Cosi. SR, Ita Sin. HS, ad Cosi SZ. Ad Sin. AS.

Hins forte prastabit vacare HS Arcum quintus, iat secunda operatio instituetur per solos sinus.

Vel si libet subtractionem sinis quarti Arcus evitare, inveniatur Angulum OHD quod fieri potest variis modis. Nam,

• Ita Cosi. Lat. OD, ad Cosi. An. OHD.
• Ut Sin. DH, ad Sin O:
• Ita Sin. DO, ad Sin. H.
• Ut Sin. DH, ad Tan. DO:
• Ut Sin. DR, ad Sin. EZ,

Invento ut cunque Angulo ad H, erit in Rectangulo HAS,

• Ut Sin. Recti Anguli HAS, ad Sinum Arcus quinti HS:
• Ita Sinus Anguli ad Horiz. SHA, ad Sin. Solaris Altitudinis SA.
• As the Sine of 78 gr. 22 m. to the Sine of 51 gr. 30 m.,
• So the Co-sine of 78 gr. 8 m. to the Sine of 9 gr. 32 m. for the Altitude required.

If in the same Latitude of 51 gr. 30 m. Northward, the Sun having 23 gr. 30 m. of South Declination, it were required the Altitude for nine in the Morning: Here, because the latitude and Declination are unlike, the one North, and the other South, you may add 23 gr. 30 m. the Ark of Declination, unto 60 gr. 39 m. the fourth Ark belonging to the third Hour from the Meridian; so shall you have 84 gr. 9 m. for your fifth Ark. Wherefore,

• As the Sine of 60 gr. 39 m. to the Sine of 51 gr. 30 m.
• So the Co-sine of 84 gr. 9 m. to the Sine of 5 gr. 15 m. for the Altitude required.

And so by one or the other of these means you may find the Altitude of the Sun for any Point of the Ecliptick at all Hours of the Day, and set them down in such a Table as this.

 Hour ♋ ♊ ♌ ♉ ♍ ♈ ♎ ♓ ♏ ♒ ♏ ♑ Gr. M. Gr. M. Gr. M. Gr. M. Gr. M. Gr. M. Gr. M. 12 62 0 58 42 50 0 38 30 27 1 18 18 15 0 11 1 59 43 56 34 48 12 36 58 25 40 17 6 13 52 10 2 53 45 50 55 43 12 32 37 21 51 13 38 10 30 9 3 45 42 43 6 36 0 26 7 15 58 8 12 5 15 8 4 36 41 34 13 27 31 18 8 8 33 1 15 7 5 27 17 24 56 18 18 9 17 0 6 6 6 18 11 15 40 9 0 0 0 5 7 9 32 6 50 11 37 4 8 1 32 21 40

Lastly, You may find what Declination the Sun hath when he riseth or setteth at any Hour.

• As the Sine of 90 gr. to the Sine of the Hour from 6:
• So the Co-tangent of the Latitude, to the Tangent of the Declination.

And so in the Latitude of 51 gr. 30 m. you shall find that when the Sun riseth, either at 5 in the Summer, or seven in the Winter, his Declination is 11 gr. 37 m. when he riseth at four in the Summer, or eight in the Winter, his Declination is 21 gr. 40 m. which may also be set down in the Table.

That done, you may there see, that in this Latitude the Meridian Altitude of the Sun in the beginning of ♋ is 62 gr, in ♊ 58 gr. 42 m. in ♉ 50 gr. in ♈ 38 gr. 30 m. &c. But the beginning of ♋ and ♑ is represented by the Tropick TD, drawn at 23 gr. 30 m. of Declination, and at the beginning of ♈ and ♎, by the Equator EF. If you draw an occult parallel between the Equator and the Tropick, at 11 gr. 30 m. of Declination, it shall represent the beginning of ♉, ♍, ♏ and ♓, if you draw another occult Parallel through 20 gr. 12 m. of Declination, it shall represent the beginning of ♊, ♌, ♐ and ♒.

Then you may lay a Ruler to the Center A, and 62 gr. in the Quadrant BC, and note the Point where it cosset the Tropick of ♋; then move the Ruler to 58 gr. 52 m. and note where it cosset the Parallel of ♊; then to 50 gr. and note where it crosseth the Parallel of ♉; and again to 38 gr. 30 m. noting where it crosseth the Equator: so the Line drawn through these Points shall shew the Hour of 12 in the Summer, while the Sun is in ♈, ♉, ♊, ♋, ♌, or ♍. In like manner, if you lay the Ruler to the Center A, and 27 gr. in the Quadrant, and note the Point where it crosseth the Parallel of ♓; then move to 18 gr. 18 m. and note where it crosseth the Parallel of ♒; and again to 15 gr. noting where it cosset the Tropick of ♑; the Line drawn through these Points shall shew the Hour of 12 in the Winter, while the Sun is in ♎, ♏, ♐, ♌, ♒, and ♓; so may you draw the rest of these Hour-lines: only that of 7, from the Meridian in the Summer, and 5 in the Winter, will cross the Line of Declination at 11 gr. 37 m. and that of 8 in the Summer, and 4 in the Winter, at 21 gr. 40 m.

The fourth Table for drawing of the Azimuth-lines must likewise be fitted for the Altitude of the Sun above the Horizon at every Azimuth, especially when he cometh to the Equator, the Tropicks, and some other intermediate Declination. If the Sun be in the Equator, and so have no Declination,

• As the Sine of 90 gr. to the Co-sine of the Azimuth from the Meridian:
• So the Co-tangent of the Latitude, to the Tangent of the Altitude at the Equator.

Thus in our Latitude of 51 gr. 30 m. at 90 gr. from the Meridian the Sun will have no Altitude; at 80 gr. the Altitude will be 7 gr. 52 m. at 70 gr. it will be 15 gr. 30 m. at 60 gr. it will be 21 gr. 41 m.

If the Sun have Declination, the Meridian Altitude will be easily found as before, for the Table for Days and Moths. And for all other Azimuths,

• As the Sine of the Latitude, to the Sine of the Declination:
• So the Co-sine of the Altitude at the Equator, to the Sine of a fourth Ark.

When the Latitude and Declination are both alike in all Azimuths from the prime Vertical unto the Meridian, add this fourth Ark unto the Ark of Altitude at the Equator.

When the Latitude and Declination are both alike, and the Azimuth more than 90 gr. distant from the Meridian, take the Altitude at the Equator out of this fourth Ark. When the Latitude and Declination are unlike, take this fourth Ark out of the Ark of the Altitude at the Equator, so shall you have the Altitude of the Sun belonging to the Azimuth.

Thus in our latitude of 51 gr. 30 m. Northward, if it were required to find the Altitude of the Sun in the Azimuth of 60 gr. from the Meridian, when the Declination is 23 gr. 30 m. Northward, you may find the Altitude at the Equator belonging to this Azimuth to be 21 gr. 41 m. by the former Canon; and by this last Canon you may find the fourth Ark to be 28 gr. 15 m. Then because the latitude and Declination are both alike to the Northward, if you add them both together, you shall have 49 gr. 56 m. for the Altitude required.

 OM 90. 60. ME Comp. Lat. OA Com. Azim. AB Alt. Æqua. EZ Lat. ZB Com. AB. DS Declin. SB Arc. 4.
 Lat. 50 Gr. 00 M. Merid. 10 20 30 40 50 60 70 80 90 ♋ 63 30 63 14 62 23 60 54 58 42 55 32 51 25 46 2 31 17 31 22 ♊ 60 12 59 54 59 0 57 23 55 1 51 43 47 18 41 40 34 47 26 48 ♉ 51 31 51 9 0 3 48 10 45 23 41 34 36 38 30 30 23 12 15 5 ♈ 40 0 39 34 38 15 36 0 32 44 28 20 22 45 60 0 8 17 0 0 ♓ 28 30 28 0 26 27 23 50 20 5 15 6 8 52 1 30 6 38 ♒ 19 48 19 14 17 31 14 37 10 27 4 57 1 43 9 40 18 13 ♑ 16 30 14 54 14 7 11 6 6 46 1 5 6 58 14 2 22 43 Lat. 51 Gr. ♋ 62 30 62 14 61 22 59 54 57 40 54 35 50 27 45 8 38 33 30 53 ♊ 59 12 58 54 57 59 56 23 54 0 50 43 46 22 41 51 34 0 26 23 ♈ 39 0 38 34 37 14 35 3 31 49 27 30 22 2 15 29 8 0 0 0 ♓ 27 30 27 1 25 29 22 55 9 13 14 20 8 17 1 10 6 43 ♒ 18 48 18 14 16 33 13 43 9 38 4 17 2 18 9 53 18 0 ♑ 15 30 14 54 13 10 10 12 5 58 0 25 6 23 14 10 22 33 Lat. 52 Gr. ♋ 61 30 61 14 60 22 58 52 56 38 54 33 49 29 44 14 37 58 30 24 ♊ 58 12 58 54 56 28 56 22 53 0 49 43 44 25 40 0 33 28 26 0 ♉ 49 30 49 9 48 3 46 11 43 26 39 44 34 58 29 6 22 15 14 40 ♈ 38 0 37 35 36 17 34 5 30 54 26 40 21 20 14 57 7 44 0 0 ♓ 26 30 26 1 24 31 22 0 18 22 13 26 17 42 0 48 6 46 ♒ 17 48 17 16 15 36 12 48 8 49 3 37 2 45 10 6 18 0 ♑ 14 30 14 56 12 12 9 18 5 10 0 13 6 49 14 19 22 30

If the Declination had been 23 gr. 30 m. to the Southward, you should then have taken this fourth Ark out of the Ark at the Equator; which because it cannot here bee done, it is a sign that the Sun is not then above the Horizon: But if you take the Ark at the Equator out of this fourth Ark, you shall have 6 gr. 34 m. for the Altitude of the Sun when he is in the Azimuth of 60 gr. from the North, and 120 gr from the South part of the Meridian. The like reason holdeth for the rest of these Altitudes, which may be gathered, and set down in a Table.

Lastly, when the Sun riseth or setteth upon any Azimuth, to find his Declination.

• As the Sine of 90 gr. to the Cosine of the Latitude:
• So the Co-sine of the Azimuth from the Meridian, to the Sine of the Declination.
 Azimuths ♋ ♊ ♌ ♉ ♍ ♈ ♎ ♓ ♏ ♒ ♐ ♑ Gr. M. Gr. M. Gr. M. Gr. M. Gr. M. Gr. M. Gr. M. 0 62 0 58 42 50 0 38 30 27 0 18 18 15 0 10 61 43 58 24 49 38 38 4 26 30 17 45 14 25 20 60 51 57 28 48 33 36 46 25 9 16 5 12 41 30 59 52 55 52 46 40 34 34 22 27 13 15 9 45 40 57 20 53 29 43 55 31 21 18 48 9 14 5 34 50 54 3 50 12 40 11 27 5 13 58 3 57 0 6 60 49 56 45 53 35 23 21 41 8 0 70 44 40 40 25 29 27 15 13 1 0 80 38 11 33 46 21 29 7 52 90 30 38 26 10 14 25 0 0 100 22 27 18 2 6 45 6 12 110 14 14 9 58 12 18 120 6 34 2 50 18 8

And thus in our Latitude of 51 gr, 30 m,. when the Azimuth is 80 gr. from the meridian, the Declination will be found to be 6 gr. 12 m. if the Azimuth be 70 gr. the Declination will be found 12 gr. 18 m. if 60 gr. then 18 gr. 8 m. And so the rest, which may be also set down in the Table.

That done, if you would draw the Line of East or West, which is 90 gr. from the Meridian, lay the Ruler to the center A, and 30 gr. 38 m. numbred in the Quadrant from C to ward B, and note the Point where it crosseth the Tropick of ♋; then move the Ruler to 26 gr. 10 m. and note where it crosseth the Parallel of ♓; then to 14 gr. 45 m. and note where it crosseth the Parallel of ♉; then to 0 gr. 0 m. and you shall find it crosseth the Equator in the Point F: so a Line drawn through these Points shall shew the Azimuth belonging to East and West. The like reason holdeth for all the rest.

These Lines being thus drawn, if you set two Sights upon the Line AC, and hang a Thread and Plummet on the Center A, with a Bead upon the Thread, the Fore-side of the Quadrant shall be finished.

On the Back-side of the Quadrant you may place the Nocturnal described before in the Use of the Sector, which consisteth of two parts.

The one is an Hour-Plane, divided equally according to the 24 Hours of the Day, and each Hour into Quarters, or Minutes, as the Plane will bear. The Center represents the North Pole; the Line drawn through the Center from XII to XII stands for the Meridian, and the lower XII stands for the Hour of XII at midnight.

The other part is a Rundle for such Stars as are near the North Pole, together with the twelve Months, and the Days of each Month, fitted to the Right Ascension of the Sun and Stars, in this manner.

First consider where the Sun will be at the beginning of the 5, 10, 15, 20, 25, 30, and if you will, every day of each Month, and find the Right Ascension belonging to the place of the Sun, as I shewed before.

For example: The Sun at midnight, the las of December, or beginning of January, will be communibus annis about 20 gr. 40 m. of ♑, whose Right Ascension is 292 gr. 20 m. At midnight, the last of January, or beginning of February, he will be about 22 gr. 12 m. of ♒, whose Right Ascension is 314 gr. 35 m. and so the rest, which may be set down in a Table.

That done, consider the Longitude and Latitude of the Stars, and thereby find their Right Ascension and Declination as I shewed before, and set them down in a Table. These Tables thus made, let the uppermost part of the Rundle be made even with the innermost Circle of the Hour-Plane, and a convenient space allowed to contain the divisions for the Days, and names of the Months. Then lay the Center of this Rundle upon the Center of some other Circle divided into 360 gr. and by the Center and 292 gr. 20 m. in that Circle, draw a Line for the beginning of January: In like manner, by the Center and 324 gr. 35 m. draw a Line for the end of January and beginning of February; and so the rest of the days of each Month.

For the Inscription of the Stars, let one of the Lines from the Center, as that at the beginning of July, or rather let a movable Index be divided from the Center toward the inward Circle of the Months into 40 gr. more or less, which may be done for speed equally, but for exactness in such manner as the Semidiameter of the General Astrolabe was divided before in the Use of the Sector. So laying the Index to the Right Ascension in the outward Circle, you may prick down the Stars by their Declination in the Index.

For example: If the Right Ascension of the Pole-star be 6 gr. 18 m. and his Declination 87 gr. 10 m. having set the Center of the Index both to the Center of the Rundle and of the other Circle, turn the Index to 6 gr. 28 m. in that outward Circle, and prick down the Star by 87 gr. 20 m. in the edge of the Index, that is, at the distance of 2 gr. 40 m. from the Pole. The like reason holdeth for the rest of the Stars, which may be distinguished according to their Magnitudes, and then be reduced into their Forms, as in the Example. So the Quadrant will be fitted both for Day and Night.