Between the Lines

ST column 17:39:47

Latitude row 44°58′48″ N

Step 1 of 11

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Try this

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The method

One value controls the table

A table of houses is entered by sidereal time. The same ST has one Midheaven but many Ascendants, one for each latitude.

The ST ratio

Native's ST minus the earlier ST in the table, divided by the interval between columns (4′). It says how far across the box the native lies.

Increment = difference × ratio

Subtract the earlier table value from the later one, multiply by the ratio, add the result to the earlier value. That is the whole of interpolation.

The Ascendant twice over

Interpolate along the ST at the lower latitude, then at the higher latitude, then between those two by the latitude ratio. Move from the lower-latitude value toward the higher-latitude one.

South of the equator

Add or subtract 12h to the LST, look up as normal, then keep the Midheaven's original sign and give the Ascendant the opposite of what is listed.

Planets from the ephemeris

The ratio is the hour of birth in UT divided by 24. The day's motion is the next day's longitude minus the day of birth's, taken across 0° Aries if the planet crosses it. Multiply its size by the ratio and add the result to the position at 00:00 — or subtract it, if the motion is negative: the planet is retrograde.

Why it differs from your program

Interpolation assumes the value grows evenly between two cells. On the sphere it does not: the great circles curve, and the Ascendant changes faster in some signs and at some latitudes than in others. So an interpolated value can differ from the direct calculation, and the difference grows quickly as the table's steps widen. That is why tables are cut at 4′ of ST: for the lesson's native the straight line is then about 0.1″ off; with 8′ steps it would be about 15″, with whole-hour steps about 17′. Near 60° of latitude, where the Ascendant moves fastest, even 4′ steps can miss by more than 1′.

The worksheet's last rows show where this page's own gap comes from. Both calculations start from the same LST; the direct one uses the obliquity you enter, the table 23° 26′. So the direct value is given twice, at your obliquity and at the table's, and the note under the worksheet splits the gap into the obliquity's share and interpolation's. Your program can differ for a further reason this page cannot show: it may keep fractions of a second in the sidereal time, which become whole seconds of arc in the RAMC.

Direct calculation

Midheaven: MC = arctan(tan RAMC ÷ cos ε), adding 180° if the result lands far from the RAMC, or 360° if it is negative and the RAMC lies in the last quadrant. Ascendant: ASC = arctan( −cos RAMC ÷ (sin RAMC · cos ε + tan φ · sin ε) ), placed in the right quadrant. Here ε is the obliquity and φ the latitude. The table on this page is built from these with ε = 23° 26′, which reproduces the lesson's printed table to the second.

Controls

The sliders under the diagram move the native within the current box: the sidereal time across the 4′ between two columns, the latitude from the lower row up to the upper one. The ◀ ▶ and ▼ ▲ buttons move to the neighbouring column or row. Exact values can be typed on the Worksheet tab, in whole numbers. Space is Next step and ← → turn the walkthrough pages when no button or field has the focus; on the tabs, ← → move between them.

Follows Lesson 5, §6.2–6.3 of Ben Dykes' Traditional Natal Astrology Course; the worked native, the southern example, and the Sun and Saturn are his.

One file, no network. Fonts: EB Garamond, IBM Plex Mono and IBM Plex Sans Condensed, SIL Open Font License. Part of Dār al-Ḥikma.