THE Planetary Instrument. OR THE Description and Use of the Theories of the Planets: drawn in true Proportion, either in one, or two Plates, of eight Inches Diameter; by Walter Hayes, at the Cross-Daggers in Moor-Fields.
Being excellent Schemes to help the Conceptions of Young Astronomers; and ready Instruments for finding the Distances, Longitudes, Latitudes, Aspects, Directions, Stations, and Retrogradations of the Planets; either Mechanically, or Arithmetically; with Ease and Speed.
The DESCRIPTION.
THE first Plate (which I call Saturn's Plate) contains the Theories of ♄ ♃ ♂ ♁: also short, but sufficient Tables of their Anomalies; and a Scale for measuring their Distances in Semidiameters of the Earth.
The second Plate (which I call Mars's Plate) contains the Theories of ♂ ♁ ♀ ☿, with like Tables of their Anomalies, and Scale of Distances.
The Sun is in the Center of the Plate. The other Planets have their several Eccentrics & Orbits. These should be Ellipses, but Circles will serve sufficiently, especially for Instruments. Mr. S. Foster disposed these Planets in four Plates, and added thereto other Devices, to be seen in a Book published since his Death. Here they are all contrived in two Plates, or two sides of one Plate: and whereas Mr. F. supposed the Apheliums and Nodes moveable, in these Thories they are fixed, according to Mr. Street's Hypothesis: by which means, though they be framed to the end of 1680, yet not only for this Age, but (with allowance of the Procession of the Aequinoctial) they may serve perpetually.
The Aphelium of a Planet is the point of his Eccentric, which is furthest from the Sun, and from Aphelium is the Anomaly counted.
The Anomaly is the circular Distance of a Planet from his Aphelium. But though the Anomalies be equal, yet their Divisions in every Eccentric are unequal, because they are made to contain the Aggregates of the Anomalies, and Prosthaphoreses of the Orb compounded together.
Where you see two or three pricks on one side the Orbit, and ☊ on the other side, there the Planet goes into North Latitude, and at the opposite Point over the Center, is the Place of ☋, where he goes into South Latitude.
The Use of the THEORIES.
This shall be shewn in three Examples only, which may suffice.
But, Note 1. That I begin the Years and Days 24 hours later than Mr. Street; for I count the last day of December to end in the Noon of the Circumcision; which is the old way: and to that Account these Theories and Tables are fitted: and all Years and Days here are counted Compleat.
Note 2. That in gathering the Anomalies out of the [Page 3] Tables, if the same exceed a Circle, (or 360°) you must by Subtraction, or Division, cast away all whole Circles, take the Remainder for the Anomaly sought. The Numbers in the Tables are Degrees, and Centesimal parts, and for the Diurnal Motion, another Figure is added, to make the Parts Millesimal. In the Tables, A. stands for Anni, that is, Years: D. stands for Days: Incl. stands for Inclination; which is set down in Degrees and Minutes.
EXAMPLE. I.
1675. April 1. I saw Mars above the foremost foot of Apollo, and he seemed to be much diminished in Magnitude.
| First out of the Table for ♁. | For ♂. | ||
| write out for 1672 | 194. 59. | 259. 51. | |
| for two Years more | 359. 75. | 191. 27. | |
| 359. 75. | 191. 27. | ||
| for 90 days the product of 986 by 90 is — | 88. 74. | 524 in 90 — | 47. 16. |
| 1002. 83. | 689. 21. | ||
| for 2 Circles deduct | 720. | deduct | 360. |
| Anomaly of ♁ — | 282. 83. | Anomaly of ♂ | 329. 21. |
Now in the Earths Orbit, at 283, make a prick with Ink for ♁; for there is ♁ for this time: and likewise prick ♂ in his Orbit at 329.
Lay a Ruler from the Place of ♁ over the ☉ (in the Center) and it shall cut in the Limb ♈ 21° 38′, the ☉'s Longitude. Again, lay a Ruler from ♁ to ♂ (I mean, the pricks set for them) and know, that a Line Parallel to your Ruler, passing through the ☉ (or Center) will cut in the Limb the Longitude of ♂.
Take therefore with your Compasses the nearest distance of the Center from the Ruler, and let one foot slide along the Ruler from ♁ to ♂, and beyond him; and let the other [Page 4] foot, keeping even pace with his fellows, pass from the Center to the Limb, and so it shall touch in the Limb ♊ 29½, the Longitude of ♂.
Another way. Mark well the Triangle made by your two Pricks and the Center, that is, by ♁ ♂ & ☉. Measure the sides upon your Scale, and you shall find—
| ☉ ♁ —3500 | Semid. of ♁ |
| ☉ ♂ —5700 | |
| ♁ ♂ —6000 |
Now if you have 2 Thrids from the Center, and lay one upon ♁, and the other upon ♂, the Arch of the Limb between them, is the Measure of the Angle at the ☉, (or of Commutation) and is here 77° 42′. With this Angle and the Sides comprehending it (which are 35 and 57, as before) you may by Pitiscus his third Axiome, Calculate the other Angles, and find Ang. at ♁ (or Elongation) 67°. 41′, and Ang. at ♂ (or Paralloxis Orbis) 34° 37′. The Elongation of ♂ (67° 41′) added to the Long. of ☉ (♈ 21° 38′) makes the Long. of ♂, 89.17. that is ♊ 29.17.
Another way. Transfer your Triangle upon Paper, and there, by help of a Scale of Chords, or a small Quadrant, and Compasses, you may easily find all the Angles very near the truth; Viz. Ang. ad ☉ 77° 42′. Ang. ad ♁ 67° 54′. Ang. ad ♂ 34° 24′.
Note, That the reason of ♂ his Diminution is the Increase of his Distance from the Earth; for you may measure it upon the Plate 6000: but in his ☍ he may be distant but 1320, and never above 2350.
For the Latitude of ♂, lay one Thrid from the Center to ☊, and another Thrid to ♂, the Arch of the Limb intercepted by the Thrids (76.10.) is Argumentum Latitudinis.
Now as the Radius to the Tang. of 1.52′, the Inclination of ♂ : So is the Sine of 76.10′ to the Tang. of 1.49′; the North Latitude of ♂ seen at the Sun.
And as ♁ ♂ to ☉ ♂; so is the Tang. of the Lat. at the Sun, to 1. 44′; the Tang. of Lat. seen at the Earth.
EXAMPLE II.
1677. Octob. 28. (being St. Simon and Jude's.) at Noon, I seek ☿ Place.
| ♁ | ☿ | ||
| 1672. — | 194.59 | 155.83 | |
| A. 4. (or 4 Years) | 359.98 | 218.90 | |
| Days 300 — | 295.80 | 147.60 | |
| 850.37 | 522.33 | ||
| Substract the Circles— | 720. | 360. | |
| Anom. of ♁ | 130.37 | 162.33. | Anom. of ☿ |
Prick the ♁ and ☿ in their Orbits, at the end of these Anomalies, and you shall see the Prick for ☿ fall in the very Node at ☊; and laying a Thrid, or Ruler from the Center to ☿ or ♁, it shall cut them both, and shew that ☿ is in a Corporal Conjunction with ☉. This ♂ ☉ ☿ would be observed: for by the help of fit Glasses, ☿ may be seen in the ☉ for several hours; and according to the best Tables, he shall pass within 4 or 5 minutes of the ☉'s Center in North Lat.
EXAMPLE III.
1673. May 25. In the day time I saw ♀ with a Telescope, horned like the ☽ at 3 or 4 days old; and though she was so much waned, she appeared bigger and brighter than at any time since she came last out of the Sun-beams.
| ♁ | ♀ | ||
| 1672. | 194. 59 | 62. 54 | |
| 144 days. | 141. 98 | 230. 69 | |
| Anom. ♁ | 336. 57 | 293. 23 | Anom. ♀. |
Prick these Planets in their Anomalies, as before was taught, Lay a Ruler from ♁ over the Center, and it shall cut in the Limb the Long. of the ☉, II 14.11′. The Ruler thus lying, draw a Thrid from the Center over ♀. Now between the Ruler and the Thrid is the Angle of Commutation (163°) and there adjoyneth to it the Supplement thereof (17°) which in your Triangle is Angulus ad ☉, and is measured by the Limb.
Lay your Ruler from ♁ to ♀, and the Parallel Line made, [Page 6] or imagined to be made, with your Compasses through the Center, will cut ♋ 17°; the Long. of ♀, and the Arch between this and the ☉'s Place before found, is the Elongation of ♀ from ☉ Eastwards, 32.49′. And the Summe of the Commutation and Elongation taken out of 180, leaves the Angle at ♀ 130.11.
Another way. In the Triangle ♁ ♀ ☉, you may take all the sides in your Compasses, and measure them upon the Scale, that is, ☉ ♁ 3520. ☉ ♀ 2450, and ♁ ♀ 1370. Then either by Protraction find the Angles: or, the Angle of Commutation being known (17°) and the sides including by Ax. 3. Pitisci, you may compute the Angle at the ♁ 32.49 and the Angle at ♀ 130.11.
This Angle at ♀ measureth her Waxing and Waning.
Let the Radius be 100, the Diameter of ♀ 200, the Angle being 130.11′, the versed Sine thereof (165) measureth the dark part of the Diameter; the residue (35) is light: So ♀ is Waned 165/200 of her Diameter; that is almost 10 Digits; and yet she seems much bigger than when she was Full: because 2 Digits of light in her present Distance (of 1370) contain more Seconds of light than her full Disk could contain; when coming from the ☉, she was distant about 6000, as you may measure upon the Plate.
How these Plates may be also useful for Observing Altitudes, Azimuths, Declinations, and Inclinations of Plains, &c. They who have any Skill in the Mathematicks, may easily discern without further Admonition.