Lesson 03 · The two angles
3 The two angles
Interpolate first between four-minute sidereal rows, then between the two latitude rows that bracket the birth.
Bench G1Stage 1 of 4 · Demonstration
Demonstration
G1 · Royal Observatory, Greenwich
Follow the source and working. Advance one numbered line at a time.
0 of 5 lines checked0%
Table rows bracketing B7: lower ST, upper ST
active lineRule rows are 4 minutes apart
Why The rows immediately below and above B7 bound the requested sidereal time.
Working13:24:00 → 13:28:00
Your paper result13:24:00 → 13:28:00Reference answer13:24:00 → 13:28:00Tolerance · exact- Residual
- exact
- Cause
- Table grid
Fraction f = (B7 − lower) in seconds ÷ 240
waitingMagnitude check · always between 0 and 1
MC: lower, upper, difference, × f, + lower
waitingRule the same for every latitude
Latitude rows bracketing the birth: lower, upper; fraction g
waitingRule table rows are 1° apart
11 12 ASC 2 3 as columns: at the lower latitude, at the upper latitude, then by g
waitingRule a column that looks unlike its neighbours is the column with the mistake
Blank permanent A–F reduction form
Part ATime
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| A1 | Birth date, civil | ||
| A2 | Clock time, 24-hour | ||
| A3 | Summer time in force?if Y subtract 1h · older war time may be 2h · stated on the bench | ||
| A4 | Standard time = A2 − A3 | ||
| A5 | Zone offset from GreenwichWest add · East subtract | ||
| A6 | Universal Time = A4 + A5if 24h or more subtract 24h and move A7 forward a day · if below 0 add 24h and move A7 back | ||
| A7 | UT datemay differ from A1 · every plate row is read on this date |
Part BSidereal time
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| B1 | Plate GST at midnight (0h UT) on the A7 dateread from the ephemeris row for A7 | ||
| B2 | Interval since 0h = A6 | ||
| B3 | Acceleration = B2 × 9.86 s per hourCheck: always under 4 minutes | ||
| B4 | Greenwich sidereal time at birth = B1 + B2 + B3carry at 60 | ||
| B5 | Longitude in time = longitude × 4 min per degreeEast add · West subtract | ||
| B6 | Local sidereal time = B4 + B5if 24h or more subtract 24h | ||
| B7 | Southern hemisphere?if Y add 12h to B6 and normalise · this is the table entry |
Part CAngles and cusps
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| C1 | Table rows bracketing B7: lower ST, upper STrows are 4 minutes apart | ||
| C2 | Fraction f = (B7 − lower) in seconds ÷ 240Check: always between 0 and 1 | ||
| C3 | MC: lower, upper, difference, × f, + lowerthe same for every latitude | ||
| C4 | Latitude rows bracketing the birth: lower, upper; fraction gtable rows are 1° apart | ||
| C5 | 11 12 ASC 2 3 as columns: at the lower latitude, at the upper latitude, then by ga column that looks unlike its neighbours is the column with the mistake | ||
| C10 | Southern? Reverse every sign on C3 and C5degrees and minutes unchanged | ||
| C11 | Opposites: IC = MC + 180, DSC = ASC + 180, 5 6 8 9 = 11 12 2 3 + 180same degree and minute, opposite sign |
Part DBodies
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| D:sun | Sun: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:moon | Moon: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:mercury | Mercury: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:venus | Venus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:mars | Mars: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:jupiter | Jupiter: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:saturn | Saturn: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:uranus | Uranus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:neptune | Neptune: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:pluto | Pluto: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | ||
| D:trueNode | True Node: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts |
Part EFigure and aspects
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| E1 | Cusps on the wheel. ASC at the left, houses counterclockwise, C11 filled | ||
| E2 | Bodies into houses by comparing D5 with the cuspsnote any body within 1° of a cusp | ||
| E3 | Aspectarian: the five Ptolemaic aspects, applying or separating from motionorbs as on the free transits surface |
Part FReceipt
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| F | Receipt: paper, Moira, Δ, cause for every computed line |
Part F · continuationPaper-to-Moira discrepancy account
| Line | Paper | Moira | Δ | Cause / notes |
|---|---|---|---|---|
| A4 | ||||
| A5 | ||||
| A6 | ||||
| A7 | ||||
| B1 | ||||
| B2 | ||||
| B3 | ||||
| B4 | ||||
| B5 | ||||
| B6 | ||||
| B7 | ||||
| C1 | ||||
| C2 | ||||
| C3 | ||||
| C4 | ||||
| C5 | ||||
| C10 | ||||
| C11 | ||||
| D:sun | ||||
| D:moon | ||||
| D:mercury | ||||
| D:venus | ||||
| D:mars | ||||
| D:jupiter | ||||
| D:saturn | ||||
| D:uranus | ||||
| D:neptune | ||||
| D:pluto | ||||
| D:trueNode | ||||
| E2 | ||||
| E3 |
Blank permanent A–F reduction form · tropical zodiac · Placidus houses