Using Magical Coordinates

Ptolemaic coordinates integrate more easily with Hermetic theory than any of the other forms of magic given in this book. The integrator is not required to develop a new Virtue or Ability. As soon as a character has completed the tasks required to reconstruct Ptolemy's work, it can be applied immediately to Hermetic magic, and may be taught to others.

There are two stages in integrating Ptolemaic coordinates into Hermetic magic.

First, the character must learn how to measure the array of fixed stars (defined below) by astrological observation. The method for this is included in the corrupt copies of The Geography found in Europe. It takes a season for magi to learn, and is learned automatically by apprentices trained by a master familiar with the technique.

Second, the magus must turn these measurements into coordinates. The character must calibrate the system by observing the array of fixed stars at the system's origin point: the point of zero distance west, zero distance north. This requires a journey

to the Garden of the Hesperides, on Junonia in the Purple Islands.

Characters can learn the coordinates for a place in three ways: astrological observation of the fixed stars, accessing the stellar observations of other magi, or spellcasting. A character does not require starlight to use coordinates; the character can use known coordinates during the day, from inside buildings or, underground.

Observation of the Fixed Stars

Most of the stars do not move relative to each other in the sky, and thus are called the fixed stars. They also form a pattern that makes a set of angles with the horizon and with vertical lines. This pattern, called the array of fixed stars, looks slightly different at every location on Earth. The flawed copies of The Geography available in Europe describe how to quantify these differences.

If an observer knows the array of fixed stars at the system's origin point, he can compare it to the array of fixed stars at his current point. The differences between the two patterns can be reduced to two numbers: the viewer's distance east of origin, and the viewer's distance north of origin. Each place's pair of numbers, expressed as fractions of the surface of the Earth, are a Ptolemaic coordinate.

A character who knows the array of fixed stars at the origin automatically knows the Ptolemaic coordinates for a place after a successful stellar observation. Astronomy is a skill included within the Artes Liberales Ability. A character who makes an Intelligence + Artes Liberales roll against an Ease Factor of 15 makes an accurate observation. This also requires:

• A clear view of the stars for four hours. Although Ptolemy does not note this, a magus with a supernaturally accurate timepiece can shorten the required span of observations to two hours. •
• Simple astronomical tools •
• Four hours of careful calculations, or two hours using tables provided by Ptolemy in his Greatest Compilation. Sound copies of the first part of The Geography contain the Handy Tables, Ptolemy's revision of his earlier reckoners, which are faster and more accurate (+1 to any astrology-related roll, calculations take one hour). •

Without an adequate observation of the array of fixed stars at the origin point, the character cannot derive new points. Ladon has engineered this omission to manipulate those who find his books into recalibrating the system, and visiting his lair.

Learning Coordinates from Other Astronomers

It is also possible to learn coordinates from other astronomers, including Ptolemy himself. Ptolemy lists almost 8,000 coordinates in The Geography, but notes that they are imprecise. Ptolemy's coordinates are extrapolated from descriptions of travel given by earlier authors, or sea captains, rather than stellar observation.

Ptolemy instructs his readers to use his methods to determine coordinates and construct maps with far greater precision than he has. His coordinates for places around Alexandria are perfect, and those within the borders of

the fallen Western Roman Empire are often correct to within a few miles. Coordinates for places outside the Empire's borders are usually far less accurate than this. As an example, all of the coordinates for Scotland are incorrect.

The flawed copies that Ladon has sent to Europe contain a few excellent coordinates. He has selected them carefully to demonstrate the usefulness of the system. He hopes this will encourage magi to reassess the origin point, as described below, so that they can derive their own coordinates.

The ability to cast spells which affect starlight is part of the Celestial Magic Mystery, which is included in Chapter 6: Hermetic Astrology in The Mysteries Revised Edition. The following spell is only available to characters initiated into Celestial Magic.

A Comparison of the Positions of the Fixed Stars

InVi 25

R: Sight, D: Mom, T: Ind

This spell charts the course of the light emanating from the fixed stars. It then compares the angles between these lines, to provide a unique pair of numbers, representing the array. This is the Ptolemaic coordinate for the caster's position, provided that the caster knows the array at origin. A magus is unable to hold coordinates in her mind with sufficient precision to represent a circle less than 500 paces across. Notebooks or devices with coordinates in them allow greater precision.

(Base 10 given in The Mysteries Revised Edition, +3 Sight)

Characters cannot use Ptolemy's system until they know the array of the fixed stars at the point of origin. A complicating factor is that characters cannot go to the origin point. It is so far away that, a semimythical Carthaginian named Hanno

aside, no one has ever gone there. The characters instead need to take measurements that, as a composite, allow them to derive the fixed stellar positions at the origin point.

The characters require three stellar readings. To measure the latitude of the Equator, characters just need to compare stellar observations from any two points that are of the same longitude, but are a known, large distance apart in latitude. The size of the Earth is known, so the difference between these two points can be used to infer how the positions of the stars would continue to change as the astronomer traveled south. To determine the adjustment for the origin's longitude, characters need to go to any point on the Zero Longitude. The only land on that longitude is in the Purple Islands.

Attempts to construct a new system, with a more convenient zero longitude, mysteriously fail. Mystically, the Purple Islands include the westernmost point on Earth. Magi can no more nominate a new west than they could assign a new north.