Paper instrument
The permanent reduction form
One numbered A–F form for every lesson and every constructed bench.
No checked learner paper is stored on this device yet.
Reduce a chart by hand
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
Royal Observatory, Greenwich
Part ATime
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| A1 | Birth date, civil | 2023-12-13 | |
| A2 | Clock time, 24-hour | 08:00:00 | |
| A3 | Summer time in force?if Y subtract 1h · older war time may be 2h · stated on the bench | No · 0h | |
| A4 | Standard time = A2 − A3 | 08:00:00 | |
| A5 | Zone offset from GreenwichWest add · East subtract | +00:00:00 | |
| 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 | 08:00:00 | |
| A7 | UT datemay differ from A1 · every plate row is read on this date | 2023-12-13 |
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 | 05:25:42 | |
| B2 | Interval since 0h = A6 | 08:00:00 | |
| B3 | Acceleration = B2 × 9.86 s per hourCheck: always under 4 minutes | 00:01:19 | |
| B4 | Greenwich sidereal time at birth = B1 + B2 + B3carry at 60 | 13:27:01 | |
| B5 | Longitude in time = longitude × 4 min per degreeEast add · West subtract | −00:00:00 | |
| B6 | Local sidereal time = B4 + B5if 24h or more subtract 24h | 13:27:01 | |
| B7 | Southern hemisphere?if Y add 12h to B6 and normalise · this is the table entry | No · 13:27:01 |
Part CAngles and cusps
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| C1 | Table rows bracketing B7: lower ST, upper STrows are 4 minutes apart | 13:24:00 → 13:28:00 | |
| C2 | Fraction f = (B7 − lower) in seconds ÷ 240Check: always between 0 and 1 | 0.75 | |
| C3 | MC: lower, upper, difference, × f, + lowerthe same for every latitude | MC Libra 23°30′ | |
| C4 | Latitude rows bracketing the birth: lower, upper; fraction gtable rows are 1° apart | 51° → 52° · g 0.48 | |
| 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 | C11 Scorpio 16°46′ · C12 Sagittarius 4°28′ · ASC Sagittarius 20°15′ · C2 Aquarius 1°34′ · C3 Pisces 19°03′ | |
| C10 | Southern? Reverse every sign on C3 and C5degrees and minutes unchanged | No | |
| C11 | Opposites: IC = MC + 180, DSC = ASC + 180, 5 6 8 9 = 11 12 2 3 + 180same degree and minute, opposite sign | MC Aries 23°30′ · C11 Taurus 16°46′ · C12 Gemini 4°28′ · ASC Gemini 20°15′ · C2 Leo 1°34′ · C3 Virgo 19°03′ |
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 | Sagittarius 20°42′ → Sagittarius 21°43′ · +61′ · Sagittarius 21°02′ | |
| D:moon | Moon: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Sagittarius 20°57′ → Capricorn 4°59′ · +842′ · Sagittarius 25°38′ | |
| D:mercury | Mercury: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Capricorn 8°29′ → Capricorn 8°27′ · R −2′ · Capricorn 8°28′ | |
| D:venus | Venus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Scorpio 9°43′ → Scorpio 10°55′ · +72′ · Scorpio 10°07′ | |
| D:mars | Mars: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Sagittarius 13°21′ → Sagittarius 14°05′ · +44′ · Sagittarius 13°36′ | |
| D:jupiter | Jupiter: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Taurus 6°09′ → Taurus 6°05′ · R −4′ · Taurus 6°08′ | |
| D:saturn | Saturn: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Pisces 1°47′ → Pisces 1°51′ · +4′ · Pisces 1°48′ | |
| D:uranus | Uranus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Taurus 19°55′ → Taurus 19°53′ · R −2′ · Taurus 19°54′ | |
| D:neptune | Neptune: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Pisces 24°54′ → Pisces 24°54′ · +0′ · Pisces 24°54′ | |
| D:pluto | Pluto: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Capricorn 28°48′ → Capricorn 28°50′ · +2′ · Capricorn 28°49′ | |
| D:trueNode | True Node: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Aries 23°20′ → Aries 23°10′ · R −10′ · Aries 23°17′ |
Part EFigure and aspects
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| E1 | Cusps on the wheel. ASC at the left, houses counterclockwise, C11 filled | Completed on the figure · counterclockwise | |
| E2 | Bodies into houses by comparing D5 with the cuspsnote any body within 1° of a cusp | sun H1 · moon H1 · mercury H1 · venus H10 · mars H12 · jupiter H4 · saturn H2 · uranus H5 · neptune H3 · pluto H1 · trueNode H3 | |
| E3 | Aspectarian: the five Ptolemaic aspects, applying or separating from motionorbs as on the free transits surface | sun/moon Conjunction 276′ separating · sun/mars Conjunction 446′ separating · sun/neptune Square 232′ applying · sun/trueNode Trine 135′ applying · moon/neptune Square 44′ separating · moon/trueNode Trine 141′ separating · mercury/venus Sextile 99′ separating · mercury/jupiter Trine 140′ separating · venus/jupiter Opposition 239′ separating · jupiter/saturn Sextile 260′ applying · uranus/neptune Sextile 300′ separating · neptune/pluto Sextile 235′ separating · pluto/trueNode Square 332′ separating |
Part FReceipt
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| F | Receipt: paper, Moira, Δ, cause for every computed line | Completed on the figure |
Part F · continuationPaper-to-Moira discrepancy account
| Line | Paper | Moira | Δ | Cause / notes |
|---|---|---|---|---|
| A4 | 08:00:00 | 08:00:00 | 0 s | Zone or DST |
| A5 | +00:00:00 | +00:00:00 | 0 s | Zone or DST |
| A6 | 08:00:00 | 08:00:00 | 0 s | Zone or DST |
| A7 | 2023-12-13 | 2023-12-13 | exact | Date change |
| B1 | 05:25:42 | 05:25:42 | 0 s | Sidereal-time rounding |
| B2 | 08:00:00 | 08:00:00 | 0 s | Sidereal-time rounding |
| B3 | 00:01:19 | 00:01:19 | 0 s | Sidereal-time rounding |
| B4 | 13:27:01 | 13:27:01 | 0 s | Sidereal-time rounding |
| B5 | −00:00:00 | −00:00:00 | 0 s | Sidereal-time rounding |
| B6 | 13:27:01 | 13:27:00 | +0.8 s | Sidereal-time rounding |
| B7 | No · 13:27:01 | No · 13:27:00 | +0.8 s | Sidereal-time rounding |
| C1 | 13:24:00 → 13:28:00 | 13:24:00 → 13:28:00 | exact | Table grid |
| C2 | 0.75 | 0.75 | 0.00 | Table grid |
| C3 | MC Libra 23°30′ | MC Libra 23°30′ | −0.12′ | Table grid |
| C4 | 51° → 52° · g 0.48 | 51° → 52° · g 0.48 | exact | Latitude grid |
| C5 | C11 Scorpio 16°46′ · C12 Sagittarius 4°28′ · ASC Sagittarius 20°15′ · C2 Aquarius 1°34′ · C3 Pisces 19°03′ | ASC Sagittarius 20°15′ · C11 Scorpio 16°46′ · C12 Sagittarius 4°28′ · C2 Aquarius 1°34′ · C3 Pisces 19°03′ | max −0.44′ | Latitude grid |
| C10 | No | No | exact | Latitude grid |
| C11 | MC Aries 23°30′ · C11 Taurus 16°46′ · C12 Gemini 4°28′ · ASC Gemini 20°15′ · C2 Leo 1°34′ · C3 Virgo 19°03′ | MC Aries 23°30′ · ASC Gemini 20°15′ · C11 Taurus 16°46′ · C12 Gemini 4°28′ · C2 Leo 1°34′ · C3 Virgo 19°03′ | max −0.44′ | Table grid |
| D:sun | Sagittarius 20°42′ → Sagittarius 21°43′ · +61′ · Sagittarius 21°02′ | Sagittarius 20°42′ → Sagittarius 21°43′ · +61′ · Sagittarius 21°02′ | +0.05′ | Table grid |
| D:moon | Sagittarius 20°57′ → Capricorn 4°59′ · +842′ · Sagittarius 25°38′ | Sagittarius 20°57′ → Capricorn 4°59′ · +842′ · Sagittarius 25°36′ | +2.22′ | Linear Moon |
| D:mercury | Capricorn 8°29′ → Capricorn 8°27′ · R −2′ · Capricorn 8°28′ | Capricorn 8°29′ → Capricorn 8°27′ · R −2′ · Capricorn 8°29′ | −1.33′ | Station |
| D:venus | Scorpio 9°43′ → Scorpio 10°55′ · +72′ · Scorpio 10°07′ | Scorpio 9°43′ → Scorpio 10°55′ · +72′ · Scorpio 10°07′ | −0.26′ | Table grid |
| D:mars | Sagittarius 13°21′ → Sagittarius 14°05′ · +44′ · Sagittarius 13°36′ | Sagittarius 13°21′ → Sagittarius 14°05′ · +44′ · Sagittarius 13°36′ | −0.04′ | Table grid |
| D:jupiter | Taurus 6°09′ → Taurus 6°05′ · R −4′ · Taurus 6°08′ | Taurus 6°09′ → Taurus 6°05′ · R −4′ · Taurus 6°08′ | +0.49′ | Station |
| D:saturn | Pisces 1°47′ → Pisces 1°51′ · +4′ · Pisces 1°48′ | Pisces 1°47′ → Pisces 1°51′ · +4′ · Pisces 1°48′ | −0.45′ | Station |
| D:uranus | Taurus 19°55′ → Taurus 19°53′ · R −2′ · Taurus 19°54′ | Taurus 19°55′ → Taurus 19°53′ · R −2′ · Taurus 19°55′ | −0.57′ | Station |
| D:neptune | Pisces 24°54′ → Pisces 24°54′ · +0′ · Pisces 24°54′ | Pisces 24°54′ → Pisces 24°54′ · +0′ · Pisces 24°54′ | −0.10′ | Station |
| D:pluto | Capricorn 28°48′ → Capricorn 28°50′ · +2′ · Capricorn 28°49′ | Capricorn 28°48′ → Capricorn 28°50′ · +2′ · Capricorn 28°49′ | +0.24′ | Station |
| D:trueNode | Aries 23°20′ → Aries 23°10′ · R −10′ · Aries 23°17′ | Aries 23°20′ → Aries 23°10′ · R −10′ · Aries 23°17′ | −0.06′ | Mean vs true node |
| E2 | sun H1 · moon H1 · mercury H1 · venus H10 · mars H12 · jupiter H4 · saturn H2 · uranus H5 · neptune H3 · pluto H1 · trueNode H3 | sun H1 · moon H1 · mercury H1 · venus H10 · mars H12 · jupiter H4 · saturn H2 · uranus H5 · neptune H3 · pluto H1 · trueNode H3 | exact | Table grid |
| E3 | sun/moon Conjunction 276′ separating · sun/mars Conjunction 446′ separating · sun/neptune Square 232′ applying · sun/trueNode Trine 135′ applying · moon/neptune Square 44′ separating · moon/trueNode Trine 141′ separating · mercury/venus Sextile 99′ separating · mercury/jupiter Trine 140′ separating · venus/jupiter Opposition 239′ separating · jupiter/saturn Sextile 260′ applying · uranus/neptune Sextile 300′ separating · neptune/pluto Sextile 235′ separating · pluto/trueNode Square 332′ separating | sun/moon Conjunction 274′ separating · sun/mars Conjunction 446′ separating · sun/neptune Square 232′ applying · sun/trueNode Trine 135′ applying · moon/neptune Square 42′ separating · moon/trueNode Trine 139′ separating · mercury/venus Sextile 98′ separating · mercury/jupiter Trine 141′ separating · venus/jupiter Opposition 239′ separating · jupiter/saturn Sextile 260′ applying · uranus/neptune Sextile 299′ separating · neptune/pluto Sextile 235′ separating · pluto/trueNode Square 332′ separating | different | Table grid |
G1ΔT policy · engine default hybrid
Denver, Colorado
Part ATime
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| A1 | Birth date, civil | 2021-07-19 | |
| A2 | Clock time, 24-hour | 21:30:00 | |
| A3 | Summer time in force?if Y subtract 1h · older war time may be 2h · stated on the bench | Yes · 1h | |
| A4 | Standard time = A2 − A3 | 20:30:00 | |
| A5 | Zone offset from GreenwichWest add · East subtract | +07:00:00 | |
| 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 | 03:30:00 | |
| A7 | UT datemay differ from A1 · every plate row is read on this date | 2021-07-20 |
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 | 19:51:59 | |
| B2 | Interval since 0h = A6 | 03:30:00 | |
| B3 | Acceleration = B2 × 9.86 s per hourCheck: always under 4 minutes | 00:00:35 | |
| B4 | Greenwich sidereal time at birth = B1 + B2 + B3carry at 60 | 23:22:34 | |
| B5 | Longitude in time = longitude × 4 min per degreeEast add · West subtract | −06:59:58 | |
| B6 | Local sidereal time = B4 + B5if 24h or more subtract 24h | 16:22:36 | |
| B7 | Southern hemisphere?if Y add 12h to B6 and normalise · this is the table entry | No · 16:22:36 |
Part CAngles and cusps
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| C1 | Table rows bracketing B7: lower ST, upper STrows are 4 minutes apart | 16:20:00 → 16:24:00 | |
| C2 | Fraction f = (B7 − lower) in seconds ÷ 240Check: always between 0 and 1 | 0.65 | |
| C3 | MC: lower, upper, difference, × f, + lowerthe same for every latitude | MC Sagittarius 7°27′ | |
| C4 | Latitude rows bracketing the birth: lower, upper; fraction gtable rows are 1° apart | 39° → 40° · g 0.74 | |
| 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 | C11 Sagittarius 28°44′ · C12 Capricorn 21°00′ · ASC Aquarius 20°47′ · C2 Aries 8°05′ · C3 Taurus 12°35′ | |
| C10 | Southern? Reverse every sign on C3 and C5degrees and minutes unchanged | No | |
| C11 | Opposites: IC = MC + 180, DSC = ASC + 180, 5 6 8 9 = 11 12 2 3 + 180same degree and minute, opposite sign | MC Gemini 7°27′ · C11 Gemini 28°44′ · C12 Cancer 21°00′ · ASC Leo 20°47′ · C2 Libra 8°05′ · C3 Scorpio 12°35′ |
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 | Cancer 27°31′ → Cancer 28°28′ · +57′ · Cancer 27°39′ | |
| D:moon | Moon: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Sagittarius 1°44′ → Sagittarius 16°15′ · +871′ · Sagittarius 3°51′ | |
| D:mercury | Mercury: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Cancer 13°39′ → Cancer 15°34′ · +115′ · Cancer 13°56′ | |
| D:venus | Venus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Leo 27°34′ → Leo 28°46′ · +72′ · Leo 27°45′ | |
| D:mars | Mars: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Leo 23°50′ → Leo 24°27′ · +37′ · Leo 23°55′ | |
| D:jupiter | Jupiter: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Pisces 0°50′ → Pisces 0°45′ · R −5′ · Pisces 0°49′ | |
| D:saturn | Saturn: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Aquarius 11°09′ → Aquarius 11°05′ · R −4′ · Aquarius 11°08′ | |
| D:uranus | Uranus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Taurus 14°24′ → Taurus 14°25′ · +1′ · Taurus 14°24′ | |
| D:neptune | Neptune: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Pisces 23°03′ → Pisces 23°02′ · R −1′ · Pisces 23°03′ | |
| D:pluto | Pluto: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Capricorn 25°31′ → Capricorn 25°29′ · R −2′ · Capricorn 25°31′ | |
| D:trueNode | True Node: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Gemini 9°48′ → Gemini 9°48′ · +0′ · Gemini 9°48′ |
Part EFigure and aspects
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| E1 | Cusps on the wheel. ASC at the left, houses counterclockwise, C11 filled | Completed on the figure · counterclockwise | |
| E2 | Bodies into houses by comparing D5 with the cuspsnote any body within 1° of a cusp | sun H6 · moon H9 · mercury H5 · venus H7 · mars H7 · jupiter H1 · saturn H12 · uranus H3 · neptune H1 · pluto H12 · trueNode H4 | |
| E3 | Aspectarian: the five Ptolemaic aspects, applying or separating from motionorbs as on the free transits surface | sun/moon Trine 372′ separating · sun/neptune Trine 276′ separating · sun/pluto Opposition 128′ separating · moon/venus Square 366′ separating · moon/jupiter Square 182′ separating · moon/trueNode Opposition 357′ separating · mercury/uranus Sextile 28′ separating · venus/mars Conjunction 230′ separating · venus/jupiter Opposition 184′ applying · mars/jupiter Opposition 414′ applying · saturn/uranus Square 196′ separating · saturn/trueNode Trine 80′ applying · neptune/pluto Sextile 148′ applying |
Part FReceipt
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| F | Receipt: paper, Moira, Δ, cause for every computed line | Completed on the figure |
Part F · continuationPaper-to-Moira discrepancy account
| Line | Paper | Moira | Δ | Cause / notes |
|---|---|---|---|---|
| A4 | 20:30:00 | 20:30:00 | 0 s | Zone or DST |
| A5 | +07:00:00 | +07:00:00 | 0 s | Zone or DST |
| A6 | 03:30:00 | 03:30:00 | 0 s | Zone or DST |
| A7 | 2021-07-20 | 2021-07-20 | exact | Date change |
| B1 | 19:51:59 | 19:51:59 | 0 s | Sidereal-time rounding |
| B2 | 03:30:00 | 03:30:00 | 0 s | Sidereal-time rounding |
| B3 | 00:00:35 | 00:00:35 | 0 s | Sidereal-time rounding |
| B4 | 23:22:34 | 23:22:34 | 0 s | Sidereal-time rounding |
| B5 | −06:59:58 | −06:59:58 | 0 s | Sidereal-time rounding |
| B6 | 16:22:36 | 16:22:35 | +0.7 s | Sidereal-time rounding |
| B7 | No · 16:22:36 | No · 16:22:35 | +0.7 s | Sidereal-time rounding |
| C1 | 16:20:00 → 16:24:00 | 16:20:00 → 16:24:00 | exact | Table grid |
| C2 | 0.65 | 0.65 | 0.00 | Table grid |
| C3 | MC Sagittarius 7°27′ | MC Sagittarius 7°27′ | +0.14′ | Table grid |
| C4 | 39° → 40° · g 0.74 | 39° → 40° · g 0.74 | exact | Latitude grid |
| C5 | C11 Sagittarius 28°44′ · C12 Capricorn 21°00′ · ASC Aquarius 20°47′ · C2 Aries 8°05′ · C3 Taurus 12°35′ | ASC Aquarius 20°47′ · C11 Sagittarius 28°43′ · C12 Capricorn 21°00′ · C2 Aries 8°05′ · C3 Taurus 12°34′ | max +0.80′ | Latitude grid |
| C10 | No | No | exact | Latitude grid |
| C11 | MC Gemini 7°27′ · C11 Gemini 28°44′ · C12 Cancer 21°00′ · ASC Leo 20°47′ · C2 Libra 8°05′ · C3 Scorpio 12°35′ | MC Gemini 7°27′ · ASC Leo 20°47′ · C11 Gemini 28°43′ · C12 Cancer 21°00′ · C2 Libra 8°05′ · C3 Scorpio 12°34′ | max +0.80′ | Table grid |
| D:sun | Cancer 27°31′ → Cancer 28°28′ · +57′ · Cancer 27°39′ | Cancer 27°31′ → Cancer 28°28′ · +57′ · Cancer 27°39′ | −0.38′ | Table grid |
| D:moon | Sagittarius 1°44′ → Sagittarius 16°15′ · +871′ · Sagittarius 3°51′ | Sagittarius 1°44′ → Sagittarius 16°15′ · +871′ · Sagittarius 3°50′ | +0.60′ | Linear Moon |
| D:mercury | Cancer 13°39′ → Cancer 15°34′ · +115′ · Cancer 13°56′ | Cancer 13°39′ → Cancer 15°34′ · +115′ · Cancer 13°55′ | +0.76′ | Table grid |
| D:venus | Leo 27°34′ → Leo 28°46′ · +72′ · Leo 27°45′ | Leo 27°34′ → Leo 28°46′ · +72′ · Leo 27°44′ | +0.52′ | Table grid |
| D:mars | Leo 23°50′ → Leo 24°27′ · +37′ · Leo 23°55′ | Leo 23°50′ → Leo 24°27′ · +37′ · Leo 23°55′ | −0.30′ | Table grid |
| D:jupiter | Pisces 0°50′ → Pisces 0°45′ · R −5′ · Pisces 0°49′ | Pisces 0°50′ → Pisces 0°45′ · R −5′ · Pisces 0°50′ | −0.54′ | Station |
| D:saturn | Aquarius 11°09′ → Aquarius 11°05′ · R −4′ · Aquarius 11°08′ | Aquarius 11°09′ → Aquarius 11°05′ · R −4′ · Aquarius 11°09′ | −0.72′ | Station |
| D:uranus | Taurus 14°24′ → Taurus 14°25′ · +1′ · Taurus 14°24′ | Taurus 14°24′ → Taurus 14°25′ · +1′ · Taurus 14°24′ | −0.15′ | Station |
| D:neptune | Pisces 23°03′ → Pisces 23°02′ · R −1′ · Pisces 23°03′ | Pisces 23°03′ → Pisces 23°02′ · R −1′ · Pisces 23°03′ | +0.45′ | Station |
| D:pluto | Capricorn 25°31′ → Capricorn 25°29′ · R −2′ · Capricorn 25°31′ | Capricorn 25°31′ → Capricorn 25°29′ · R −2′ · Capricorn 25°30′ | +0.57′ | Station |
| D:trueNode | Gemini 9°48′ → Gemini 9°48′ · +0′ · Gemini 9°48′ | Gemini 9°48′ → Gemini 9°48′ · +0′ · Gemini 9°48′ | −0.09′ | Mean vs true node |
| E2 | sun H6 · moon H9 · mercury H5 · venus H7 · mars H7 · jupiter H1 · saturn H12 · uranus H3 · neptune H1 · pluto H12 · trueNode H4 | sun H6 · moon H9 · mercury H5 · venus H7 · mars H7 · jupiter H1 · saturn H12 · uranus H3 · neptune H1 · pluto H12 · trueNode H4 | exact | Table grid |
| E3 | sun/moon Trine 372′ separating · sun/neptune Trine 276′ separating · sun/pluto Opposition 128′ separating · moon/venus Square 366′ separating · moon/jupiter Square 182′ separating · moon/trueNode Opposition 357′ separating · mercury/uranus Sextile 28′ separating · venus/mars Conjunction 230′ separating · venus/jupiter Opposition 184′ applying · mars/jupiter Opposition 414′ applying · saturn/uranus Square 196′ separating · saturn/trueNode Trine 80′ applying · neptune/pluto Sextile 148′ applying | sun/moon Trine 371′ separating · sun/neptune Trine 276′ separating · sun/pluto Opposition 129′ separating · moon/venus Square 366′ separating · moon/jupiter Square 180′ separating · moon/trueNode Opposition 358′ separating · mercury/uranus Sextile 29′ separating · venus/mars Conjunction 229′ separating · venus/jupiter Opposition 186′ applying · mars/jupiter Opposition 415′ applying · saturn/uranus Square 195′ separating · saturn/trueNode Trine 81′ applying · neptune/pluto Sextile 147′ applying | different | Table grid |
D2ΔT policy · engine default hybrid
Buenos Aires
Part ATime
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| A1 | Birth date, civil | 2018-03-05 | |
| A2 | Clock time, 24-hour | 14:20:00 | |
| A3 | Summer time in force?if Y subtract 1h · older war time may be 2h · stated on the bench | No · 0h | |
| A4 | Standard time = A2 − A3 | 14:20:00 | |
| A5 | Zone offset from GreenwichWest add · East subtract | +03:00:00 | |
| 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 | 17:20:00 | |
| A7 | UT datemay differ from A1 · every plate row is read on this date | 2018-03-05 |
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 | 10:50:46 | |
| B2 | Interval since 0h = A6 | 17:20:00 | |
| B3 | Acceleration = B2 × 9.86 s per hourCheck: always under 4 minutes | 00:02:51 | |
| B4 | Greenwich sidereal time at birth = B1 + B2 + B3carry at 60 | 28:13:37 | |
| B5 | Longitude in time = longitude × 4 min per degreeEast add · West subtract | −03:53:32 | |
| B6 | Local sidereal time = B4 + B5if 24h or more subtract 24h | 00:20:05 | |
| B7 | Southern hemisphere?if Y add 12h to B6 and normalise · this is the table entry | Yes · 12:20:05 |
Part CAngles and cusps
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| C1 | Table rows bracketing B7: lower ST, upper STrows are 4 minutes apart | 12:20:00 → 12:24:00 | |
| C2 | Fraction f = (B7 − lower) in seconds ÷ 240Check: always between 0 and 1 | 0.02 | |
| C3 | MC: lower, upper, difference, × f, + lowerthe same for every latitude | MC Aries 5°28′ | |
| C4 | Latitude rows bracketing the birth: lower, upper; fraction gtable rows are 1° apart | 34° → 35° · g 0.60 | |
| 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 | C11 Taurus 4°14′ · C12 Taurus 27°47′ · ASC Gemini 18°59′ · C2 Cancer 22°41′ · C3 Virgo 0°17′ | |
| C10 | Southern? Reverse every sign on C3 and C5degrees and minutes unchanged | Yes | |
| C11 | Opposites: IC = MC + 180, DSC = ASC + 180, 5 6 8 9 = 11 12 2 3 + 180same degree and minute, opposite sign | MC Libra 5°28′ · C11 Scorpio 4°14′ · C12 Scorpio 27°47′ · ASC Sagittarius 18°59′ · C2 Capricorn 22°41′ · C3 Pisces 0°17′ |
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 | Pisces 14°21′ → Pisces 15°21′ · +60′ · Pisces 15°04′ | |
| D:moon | Moon: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Libra 22°37′ → Scorpio 5°47′ · +790′ · Scorpio 2°08′ | |
| D:mercury | Mercury: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Pisces 27°40′ → Pisces 29°27′ · +107′ · Pisces 28°57′ | |
| D:venus | Venus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Pisces 27°31′ → Pisces 28°46′ · +75′ · Pisces 28°25′ | |
| D:mars | Mars: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Sagittarius 22°37′ → Sagittarius 23°12′ · +35′ · Sagittarius 23°02′ | |
| D:jupiter | Jupiter: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Scorpio 23°12′ → Scorpio 23°12′ · +0′ · Scorpio 23°12′ | |
| D:saturn | Saturn: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Capricorn 7°36′ → Capricorn 7°40′ · +4′ · Capricorn 7°39′ | |
| D:uranus | Uranus: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Aries 26°06′ → Aries 26°09′ · +3′ · Aries 26°08′ | |
| D:neptune | Neptune: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Pisces 13°57′ → Pisces 13°59′ · +2′ · Pisces 13°58′ | |
| D:pluto | Pluto: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Capricorn 20°43′ → Capricorn 20°44′ · +1′ · Capricorn 20°44′ | |
| D:trueNode | True Node: this midnight, next midnight, motion, × A6 ÷ 24, positionnegative motion is retrograde, write R · a negative travel subtracts | Leo 14°38′ → Leo 14°33′ · R −5′ · Leo 14°34′ |
Part EFigure and aspects
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| E1 | Cusps on the wheel. ASC at the left, houses counterclockwise, C11 filled | Completed on the figure · counterclockwise | |
| E2 | Bodies into houses by comparing D5 with the cuspsnote any body within 1° of a cusp | sun H9 · moon H4 · mercury H9 · venus H9 · mars H7 · jupiter H5 · saturn H7 · uranus H10 · neptune H9 · pluto H7 · trueNode H2 | |
| E3 | Aspectarian: the five Ptolemaic aspects, applying or separating from motionorbs as on the free transits surface | sun/neptune Conjunction 66′ separating · moon/uranus Opposition 360′ separating · mercury/venus Conjunction 32′ separating · mercury/mars Square 355′ separating · mercury/jupiter Trine 345′ separating · venus/mars Square 323′ separating · venus/jupiter Trine 313′ separating · mars/uranus Trine 186′ applying · jupiter/pluto Sextile 148′ applying · uranus/pluto Square 324′ separating |
Part FReceipt
| Line | Operation and rule | Working | Result |
|---|---|---|---|
| F | Receipt: paper, Moira, Δ, cause for every computed line | Completed on the figure |
Part F · continuationPaper-to-Moira discrepancy account
| Line | Paper | Moira | Δ | Cause / notes |
|---|---|---|---|---|
| A4 | 14:20:00 | 14:20:00 | 0 s | Zone or DST |
| A5 | +03:00:00 | +03:00:00 | 0 s | Zone or DST |
| A6 | 17:20:00 | 17:20:00 | 0 s | Zone or DST |
| A7 | 2018-03-05 | 2018-03-05 | exact | Date change |
| B1 | 10:50:46 | 10:50:46 | 0 s | Sidereal-time rounding |
| B2 | 17:20:00 | 17:20:00 | 0 s | Sidereal-time rounding |
| B3 | 00:02:51 | 00:02:51 | 0 s | Sidereal-time rounding |
| B4 | 28:13:37 | 28:13:37 | 0 s | Sidereal-time rounding |
| B5 | −03:53:32 | −03:53:32 | 0 s | Sidereal-time rounding |
| B6 | 00:20:05 | 00:20:05 | −0.5 s | Sidereal-time rounding |
| B7 | Yes · 12:20:05 | Yes · 12:20:05 | −0.5 s | Sidereal-time rounding |
| C1 | 12:20:00 → 12:24:00 | 12:20:00 → 12:24:00 | exact | Table grid |
| C2 | 0.02 | 0.02 | 0.00 | Table grid |
| C3 | MC Aries 5°28′ | MC Aries 5°28′ | −0.31′ | Table grid |
| C4 | 34° → 35° · g 0.60 | 34° → 35° · g 0.60 | exact | Latitude grid |
| C5 | C11 Taurus 4°14′ · C12 Taurus 27°47′ · ASC Gemini 18°59′ · C2 Cancer 22°41′ · C3 Virgo 0°17′ | ASC Gemini 18°59′ · C11 Taurus 4°14′ · C12 Taurus 27°46′ · C2 Cancer 22°41′ · C3 Virgo 0°17′ | max +0.57′ | Latitude grid |
| C10 | Yes | Yes | exact | Latitude grid |
| C11 | MC Libra 5°28′ · C11 Scorpio 4°14′ · C12 Scorpio 27°47′ · ASC Sagittarius 18°59′ · C2 Capricorn 22°41′ · C3 Pisces 0°17′ | MC Libra 5°28′ · ASC Sagittarius 18°59′ · C11 Scorpio 4°14′ · C12 Scorpio 27°46′ · C2 Capricorn 22°41′ · C3 Pisces 0°17′ | max +0.57′ | Table grid |
| D:sun | Pisces 14°21′ → Pisces 15°21′ · +60′ · Pisces 15°04′ | Pisces 14°21′ → Pisces 15°21′ · +60′ · Pisces 15°05′ | −0.67′ | Table grid |
| D:moon | Libra 22°37′ → Scorpio 5°47′ · +790′ · Scorpio 2°08′ | Libra 22°37′ → Scorpio 5°47′ · +790′ · Scorpio 2°10′ | −1.51′ | Linear Moon |
| D:mercury | Pisces 27°40′ → Pisces 29°27′ · +107′ · Pisces 28°57′ | Pisces 27°40′ → Pisces 29°27′ · +107′ · Pisces 28°57′ | −0.21′ | Table grid |
| D:venus | Pisces 27°31′ → Pisces 28°46′ · +75′ · Pisces 28°25′ | Pisces 27°31′ → Pisces 28°46′ · +75′ · Pisces 28°25′ | −0.33′ | Table grid |
| D:mars | Sagittarius 22°37′ → Sagittarius 23°12′ · +35′ · Sagittarius 23°02′ | Sagittarius 22°37′ → Sagittarius 23°12′ · +35′ · Sagittarius 23°02′ | −0.42′ | Table grid |
| D:jupiter | Scorpio 23°12′ → Scorpio 23°12′ · +0′ · Scorpio 23°12′ | Scorpio 23°12′ → Scorpio 23°12′ · +0′ · Scorpio 23°12′ | −0.22′ | Station |
| D:saturn | Capricorn 7°36′ → Capricorn 7°40′ · +4′ · Capricorn 7°39′ | Capricorn 7°36′ → Capricorn 7°40′ · +4′ · Capricorn 7°39′ | +0.26′ | Station |
| D:uranus | Aries 26°06′ → Aries 26°09′ · +3′ · Aries 26°08′ | Aries 26°06′ → Aries 26°09′ · +3′ · Aries 26°08′ | +0.10′ | Station |
| D:neptune | Pisces 13°57′ → Pisces 13°59′ · +2′ · Pisces 13°58′ | Pisces 13°57′ → Pisces 13°59′ · +2′ · Pisces 13°59′ | −0.57′ | Station |
| D:pluto | Capricorn 20°43′ → Capricorn 20°44′ · +1′ · Capricorn 20°44′ | Capricorn 20°43′ → Capricorn 20°44′ · +1′ · Capricorn 20°44′ | +0.19′ | Station |
| D:trueNode | Leo 14°38′ → Leo 14°33′ · R −5′ · Leo 14°34′ | Leo 14°38′ → Leo 14°33′ · R −5′ · Leo 14°35′ | −0.57′ | Mean vs true node |
| E2 | sun H9 · moon H4 · mercury H9 · venus H9 · mars H7 · jupiter H5 · saturn H7 · uranus H10 · neptune H9 · pluto H7 · trueNode H2 | sun H9 · moon H4 · mercury H9 · venus H9 · mars H7 · jupiter H5 · saturn H7 · uranus H10 · neptune H9 · pluto H7 · trueNode H2 | exact | Table grid |
| E3 | sun/neptune Conjunction 66′ separating · moon/uranus Opposition 360′ separating · mercury/venus Conjunction 32′ separating · mercury/mars Square 355′ separating · mercury/jupiter Trine 345′ separating · venus/mars Square 323′ separating · venus/jupiter Trine 313′ separating · mars/uranus Trine 186′ applying · jupiter/pluto Sextile 148′ applying · uranus/pluto Square 324′ separating | sun/neptune Conjunction 66′ separating · moon/uranus Opposition 362′ separating · mercury/venus Conjunction 32′ separating · mercury/mars Square 355′ separating · mercury/jupiter Trine 345′ separating · venus/mars Square 323′ separating · venus/jupiter Trine 313′ separating · mars/uranus Trine 186′ applying · jupiter/pluto Sextile 148′ applying · uranus/pluto Square 324′ separating | different | Table grid |
B3ΔT policy · engine default hybrid