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**
Attention: the edition of Astrological Chart Calculations described below is now out of print. A new expanded edition,
as a 6 x9 paperback of about 200 pages, is near the end of production and should be available in a few months. Watch for an announcement.
**

*From the Introduction:*

The material contained in this document has been assembled for the purpose of maintaining the tradition of casting horoscopes by hand in a meaningful way. With the advent of the computer, the mathematical skills and astronomical insights involved in chart casting have become endangered. Today these skills are being kept alive primarily by Kepler College and the requirements of certification exams such as those of the National Council of Geocosmic Research, the American Federation of Astrologers, and a number of small regional schools. While the computerized experience of astrology is certainly labor-saving, it bypasses information that explains how the astrological chart, now calculated in split seconds, came to be what it is.

Prior to the 20^{th} century, astrological chart calculations
were, for the most part, extremely cumbersome. Astrological textbooks of
past centuries routinely included tables of trigonometric functions or
logarithms, and much space would be devoted to problems like determining
local time. Since primary directions were extensively used during most
of the previous two millennia, astrologers were required to calculate the
positions of the planets and house cusps against several frames of reference.
What was called a speculum, a listing of each planet's longitude, latitude,
right ascension, declination, oblique ascension, oblique descension, etc.
was routinely calculated for each chart. Most of these supplementary positions
required the use of trigonometry. This is the reason that so many ancient
astrologers were mathematicians and vice versa. In fact, astrologers were
routinely referred to as mathematicians in Rome and during the Middle Ages.

Astrological chart casting during the 20^{th} century became
more streamlined and far easier than in previous times. Time zones became
standards against which birth times could be adjusted and ephemerides and
tables of houses for various systems became widely available. With the
rise of easy to calculate secondary progressions and solar arc directions
as preferred predictive techniques, the need for trigonometry was eliminated.
Most astrologers in the 20^{th} century learned to calculate planetary
positions using logarithms. House cusps (mostly Placidian because of availability)
were simply interpolated from tables using proportions. When I learned
how to cast a chart in the late 1960's, I used both logarithms and a slide
rule. By the 1970's pocket calculators became a standard tool for chart
calculations and the first astrological computers appeared. It was at this
time that many of the older trigonometric formulae were revived by programmers
anxious to produce software that would allow users to try out any technique
they wished. By the mid 1980's very few astrologers were hand calculating
charts. Most owned computers or were ordering charts from chart calculation
services. Only the few who saw a value in passing an astrology exam continued
to learn the relatively simple 20^{th} century methodologies for
chart casting.

At present many people have become successful in the field of astrology without ever having to add logarithms or interpolate a house cusp. Some argue that since astrology is primarily a counseling technique, knowledge of the "nuts and bolts" is irrelevant. Most of us drive cars or use electronic gadgets, but only a very few have any idea of how they work. We trust the repair of these things to the experts. I don't think that to be a good analogy, however. The astronomical features alone that lie behind the numbers and symbols in an astrological chart are profound clues to the function of certain features of the chart. Knowing why Aries rises more quickly than Libra, or how house systems differ are elements that add depth and insight into astrological interpretation. It's when the chart is seen as what it really is, a map of the sky at the time and place of birth, that the astrologer truly enters into the tangible cosmic environment that contains the information sought. Otherwise an astrological chart is nothing more than a scrap of paper decorated with symbols.

The material presented in this document is designed to teach both the method and the meaning of astrological chart calculations. It is hoped that this very ancient part of astrology, the mathematical ritual of preparing a chart, will allow students to not only glean deeper insights into horoscopy, but to also allow for a unique contact with astrology's long history.

**Table of Contents**

Introduction | 3 |

Section I: Astronomical Frames of Reference | |

The Earth in Space | 4 |

The Earth Quantified | 6 |

Definitions of Points on the Celestial Sphere | 8 |

Time | 9 |

Definitions of Time Conventions | 11 |

Time – Space Conversions | 13 |

Mathematics for Chart Calculations | 13 |

Trigonometry | 15 |

Logarithms | 16 |

Systems of House Division | 18 |

Section 2: Calculating the Astrological Chart | |

Required Materials | 24 |

Steps in Casting an Astrological Chart | 25 |

Worksheets for Calculations | 28 |

The Houses: Framework of the Chart | 37 |

Calculation of the planets'longitudes | 38 |

Calculating a Horoscope using a calculator
(with trigonometric functions) |
43 |

Other Astrological Chart Calculations | 52 |

Additional Sources on Astrological Calculations | 55 |

One Reed Publications - (c) 2001

8.5 x 11, paper, 60 pages, spiral-bound

$17.00 + $1.75 postage