Go to Home Page
Go to Reading On Line
12. Constructing a Horoscope
In order to erect a natal chart by hand, it is necessary to have at hand an electronic calculator, which should be able to perform trigonometrical functions, such as sine (sin), cosing (cos) and tangent (tan). It is also convenient to have a key that will convert minutes and seconds to decimals and vice versa. For those who own computers, the Microsoft Windows operating system has a sophisticated scientific calculator included in its accessories package, thus alleviating the need to go out an purchase one specifically for this purpose.
It is very easy to decimalise minutes and seconds, and vice versa, if need be.
To convert to decimal notation: enter the minutes, divide by 60 and add the degrees. For example, 15 degrees 15 minutes would be: 15 degrees + (15 minutes /60 = .25) = 15.25 degrees.
To convert from decimals: subtract the degrees (and write them down, as so not to forget them), and multiply by 60. If the resulting decimal part of the display is .5 or over, round up; otherwise, round down. For example, 27.50 degrees would be: (27.50 – 27 = .50) = .50 * 60 = 30. Therefore, 27.50 degrees equates to 27 degrees 30 minutes.
To set up the chart for a birth – or an event – we need to find two ‘times’: Greenwich Mean Time, or GMT, the time in general use throughout the United Kingdom from October to March; and LST, Local Sidereal Time. The times of births or events outside the UK must be converted to GMT.
The GMT of the birth is used to measure the position of the Sun, Moon, planets and Moon’s nodes on the ecliptic. The ecliptic is the Sun’s path, so the Sun is always on the ecliptic. In the case of the planets, ‘on the ecliptic’ really means the point at which a perpendicular dropped from a planet meets the ecliptic.
Sidereal time, or ST, is used to determine the positions of the angles, or personal points: the degrees of the Rising Sign or Ascendant (ASC) and culminating (MC) signs, and the degree of the sign that is immediately due west of the event (the Vertex).
All countries recognise Greenwich as 0 degrees longitude, and each country, or part of it, operates on a named time zone; such as Eastern Standard Time (EST), which is located on the east coast of the United States. Daylight Savings Time (DST) presents another problem. The notion was invented in Germany in 1916, and we need to know the dates and times that the various countries introduced this, and its duration, and whether it was actually observed all over the country.
The necessary steps involved in casting a chart are as follows:-
1) Establish GMT and the true date at birth. The true date may differ from the given date. Try to get the most exact time possible: whole hours, quarters and halves are suspicious. For births that took place at home and recorded in suspiciously rounded-off terms, it may well be justified in taking off a minute or two, as such births are often, but by no means always, timed a little late.
2) Establish Local Sidereal Time (LST) at birth.
a) Use the appropriate tables to calculate the ST at midnight GMT on the day required. Ephemerides giving daily positions also give ST at either midnight or noon GMT. It is easier to work with midnight. For example, ST on Midnight on 14th September 1965 would be 23h 31m 02s.
b) Write down the ST for GMT midnight, retaining the seconds to avoid cumulative error. Underneath write the GMT time of birth (not the given time if this differs) keeping the figures in columns for hours, minutes and seconds. For example, a person born at 10:22 pm on 14th September 1965 would first have to be converted to GMT because it was during Daylight Savings Time. His GMT of birth would be 9:22pm.
23h 31m 02s (ST)
21h 22m 00s (GMT)
c) Each hour of mean time must have 9.86 seconds added in order to convert it to sidereal time, which, as has been discussed, is faster than solar time. This is called converting for the ‘acceleration on the interval’. Decimalise the GMT time, multiply by 9.86, divide by 60, de-decimalise. Write the number underneath the two times already written down. For example, 21 hours * 9.86 seconds = 3 minutes 27 seconds, and 22 minutes * 9.86 seconds = 4 seconds, totalling 3 minutes 31 seconds.
23h 31m 02s (ST)
21h 22m 00s (GMT)
3m 31s (acceleration of the interval)
d) Add these three sets of figures together. The result will be the ST at Greenwich at birth. Do not worry at this point if the result comes to more than 24 hours.
23h 31m 02s (ST)
21h 22m 00s (GMT)
3m 31s (acceleration of the interval)
44h 56m 33s (ST at GMT at birth)
e) To convert this time to Local Sidereal Time, add 4 minutes of time for each degree of longitude to the East of Greenwich. If the birth was West of Greenwich, subtract 4 minutes for each degree. If the result comes to more than 24 hours, subtract 24 hours. It is permissible to round off to the nearest minute: round 1 – 29 seconds down; 30 – 59 seconds up. For example, the person’s whose chart we are erecting was born in Aberdeen, Scotland, which is 2 degrees 2 minutes west of GMT. This is the LST at birth. It is important to locate the birth in terms of latitude and longitude as precisely as possible in order to get an accurate LST and therefore an accurate Ascendant.
23h 31m 02s (ST)
21h 22m 00s (GMT)
3m 31s (acceleration of the interval)
44h 56m 33s (ST at GMT at birth)
- 8m (conversion for place of birth)
44h 48m 33s
24 (subtract 24 to bring total to less than 24)
20h 48m 33s (LST at birth)
3) Find the position of the Midheaven (MC).
Decimalise the LST, and multiply by 15. For example, 20 hours 48 minutes 33 seconds is decimalised as follows:- 20 hours + (49 minutes / 60 = .82) = 20.82 hours.
20.82 * 15 = 312.30 = 312 degrees 18 minutes
The answer is the RAMC. The position of the MC on the equator measures in right ascension. A simple formula will convert RAMC to MC:-
tan-1 (Sin RAMC / (cos RAMC cos e))
e is the obliquity of the ecliptic.
To make the calculation, enter sin RAMC, divide it by cos RAMC, and then by cos e; now take tan-1 of the result. In the example above, the formula results in a figure of –50.14407890.
Some calculators have a key marked ‘arctan’: this means ‘tan-1) and can reduce the amount of button-pressing involved in the above calculation. Others calculators have a key marked ‘arc’ or ‘INV’: if this is pressed before the ‘tan’ key, the display will show ‘tan-1’. Still other calculators have a key marked ‘F’ and alternative functions for many of the keys printed just above the keys: on such calculators ‘tan’ usually has ‘arc’ printed above it: press ‘F’, then ‘tan-1’ and again you will get ‘tan-1’.
As you do the equation, store it in the calculator’s memories, or note down, the values of sin RAMC and cos RAMC.
The answer to this equation may require adjustment, by the addition or subtraction of 180 or 360: the first answer may be a minus number. The MC can never be more than 6 degrees away from the RAMC; thereby making it is easy to see how much must be added or subtracted. In the example used, 360 degrees must be added, therefore, -50.14407890 + 360 = 309.8559211.
Convert the answer to degrees and minutes rounded off from the seconds, and write it down. This is the position of the MC. In the example above, 309.8559211 converted into degrees and minutes is 309 degrees 51 minutes.
4) Find the position of the Ascendant.
Like the MC, the Asc can be calculated from the RAMC using another straightforward formula. This method of finding the Asc is 100% accurate:
tan-1 (cos RAMC / -((sin e tan L) + (cos e sin RAMC)))
You already have the values for sin e, cos e, sin RAMC, and cos RAMC. Tan L is simply the tangent of the latitude of birth. To arrive at this figure, enter the latitude in degrees and minutes, decimalise it and press the ‘tan’ key. Using the example above, a person born in Aberdeen at a latitude of 57 degrees 6 minutes north, or 57.10 north. The position of the Ascendant is calculated at –84.59879070.
The result will be a minus or plus quantity decimalised in the display. As with the MC, this may require adjustment by the addition or subtraction of 180 or 360. However, in this case there is no easy reference point, as RAMC is to MC. The table following this list of instructions giving the Asc for the different MC at, or near, all latitudes that you are likely to need. Look up the appropriate figure and if necessary, adjust the answer in your display by adding or subtracting 180 or 360 until it is close to this figure. It will be within 10 degrees. Using the above example, add 180 to the figure of –84.59879070 and the position of the Ascendant is 95.40120930.
Convert this figures to degrees, minutes and seconds. Round the seconds up or down and finally convert from absolute longitude to sign form. This is the position of the Ascendant is 95 degrees 24 degrees.
5) Find the position of the Vertex. For this you will use the formula:-
tan-1 (cos RAMC / ((sin e cot L) – (cos e sin RAMC)))
Calculators do not give cotangents. However cot L = 1 / tan L; in other words a cotangent is the reciprocal of a tangent, and most calculators do give reciprocals. Simply enter tan L and press the reciprocal button. If your calculator does not give reciprocals, divide 1 by tan L. You will already have the other figures required in this equation. Using the example above, the figure is calculated as 35.71880372.
Again, you may need to add or subtract 180 or 360 to or from the result. To find the approximate position of the Vertex, take the RAIC, which is opposite the RAMC (RAMC ± 180). In temperate latitudes in the Northern Hemisphere it ought not to be more than 60 degrees from the Descendant. The Vertex-Antivertex axis can coincide, or more often nearly coincide with the Asc-Desc, or first/seventh house axis. Using the example above, the calculation is found to be 35.71880372. Add 180 to this figure to derive a Vertex of 215.71880372.
Convert the result to degrees, minutes and seconds. Round the seconds up or down and convert into sign form from absolute longitude.
The Vertex is calculated as 215 degrees 43 minutes.
You now have the positions of the MC, Asc and Vertex.
6) Find the positions of the planets. The positions of the planets have nothing whatsoever to do with sidereal time. They are calculated from the true GMT or the birth. The positions are found by interpolation: that is to say that you interpolate the position of a given planet at a given time on a given day from the position of that planet at midnight (using a midnight ephemerides) preceding your given time and at midnight succeeding that time.
a) Convert GMT of birth to the 24 hour clock. In the example above, GMT at birth is 21.37.
b) Divide this figure by 24 to discover what fraction of the day has passed by the time of the birth (21.37 / 24 = .890416667). Write this down, or, better, enter it into one of the memories of your calculator.
c) For all planets that are not retrograde (the ephemerides indicates retrogradation) take the position at midnight following the birth and decimalise it. It is not necessary to compute the Uranus and the planets beyond that point because their movement is too slow to make a significant difference.
Sun is 21 degrees 56 minutes = 21.93 (Virgo)
Moon is 8 degrees 37 minutes = 8.62 (Taurus)
Mercury is 10 degrees 58 minutes = 10.97 (Virgo)
Venus is 1 degrees 23 minutes = 1.38 (Scorpio)
Mars is 16 degrees 41 minutes = 16.68 (Scorpio)
Jupiter is 29 degrees 24 minutes = 29.40 (Gemini)
Saturn is 13 degrees minutes 11 retrograde = 13.18 (Pisces)
Uranus is 15 degrees 40 minutes = 15.67 (Virgo)
Neptune is 17 degrees 49 minutes = 17.35 (Scorpio)
Pluto is 16 degrees 19 minutes = 16.32 (Virgo)
North Node is 7 degrees 36 minutes retrograde = 7.60 (Gemini)
d) Decimalise the position of the planet at the midnight before birth. On 14th September 1965:-
Sun is 20 degrees 58 minutes = 20.97
Moon is 25 degrees 48 minutes = 25.80 (Libra)
Mercury is 9 degrees 8 minutes = 9.13
Venus is 0 degrees 12 minutes = 0.20
Mars is 16 degrees 0 minutes = 16.00
Jupiter is 29 degrees 17 minutes = 29.28
Saturn is 13 degrees 16 minutes retrograde = 13.27
Uranus is 15 degrees 36 minutes = 15.60
Neptune is 17 degrees 48 minutes = 17.80
Pluto is 16 degrees 17 minutes = 16.28
North Node is 7 degrees 41 minutes retrograde = 7.68
e) Subtract the result of d) from the result of c). This gives you the daily motion – the distance covered by the sky, measured in degrees – of the planet of the day of birth.
Sun is 21.93 – 20.97 = .96
Moon is 8.62 - 25.80 = 12.80
Mercury is 10.97 - 9.13 = 1.84
Venus is 1.38 - 0.20 = 1.18
Mars is 16.68 - 16.00 = .68
Jupiter is 29.40 - 29.28 = .12
Saturn retrograde is 13.18 - 13.27 = -.09
Uranus is 15.67 - 15.60 = .07
Neptune is 17.80 - 17.80 = 0
Pluto is 16.32 - 16.28 = .04
North Node retrograde is 7.60 - 7.68 = -.08
f) Multiply the daily motion by the fraction found in step b). This gives us the distance the planet has moved between the midnight preceding the birth and the minute of birth itself.
Sun is 21.93 – 20.97 = .96 * .89 = .85
Moon is 8.62 - 25.80 = 12.80 * .89 = 11.39
Mercury is 10.97 - 9.13 = 1.84 * .89 = 1.64
Venus is 1.38 - 0.20 = 1.18 * .89 = 1.05
Mars is 16.68 - 16.00 = .68 * .89 = .61
Jupiter is 29.40 - 29.28 = .12 * .89 = .11
Saturn retrograde is 13.18 - 13.27 = -.09 * .89 = -.08
Uranus is 15.67 - 15.60 = .07 * .89 = .06
Neptune is 17.80 - 17.80 = 0 * .89 = 0
Pluto is 16.32 - 16.28 = .04 * .89 = .04
North Node retrograde is 7.60 - 7.68 = -.08
g) Add the figure thus obtained to the position of the planet at the midnight before birth. Convert the answer to degrees and minutes. This is the position of the planet in question. Repeat the process for all planets that are not retrograde. It is important to note, however that the final three planets, Uranus, Neptune and Pluto have such slow daily motions that it is perfectly acceptable to merely enter their positions a midnight.
Sun is 20 degrees 58 minutes = 20.97 + .85 = 21.82
Moon is 25 degrees 48 minutes = 25.80 (Aries) + 11.39 = 7.19 (Taurus)
Mercury is 9 degrees 8 minutes = 9.13 + 1.64 = 10.77
Venus is 0 degrees 12 minutes = 0.20 + 1.05 = 1.25
Mars is 16 degrees 0 minutes = 16.00 + .61 = 16.61
Jupiter is 29 degrees 17 minutes = 29.28 + .11 = 29.39
Saturn is 13 degrees 16 minutes retrograde = 13.27 + -.08 = 13.19
Uranus is 15 degrees 36 minutes = 15.60 +.06 = 15.66
Neptune is 17 degrees 48 minutes = 17.80 + 0 = 17.80
Pluto is 16 degrees 17 minutes = 16.28 + .04 = 16.32
North Node is 7 degrees 41 minutes retrograde = 7.68 + -.08 = 7.60
7) Find the positions of the retrograde planets and the mean node. About 8% of charts have no retrograde planets. However, the mean node is always retrograde. The procedure for finding these positions is a simple reversal of the procedure for non-retrograde positions.
To find the daily motion it is necessary to subtract the later position of the planet from the earlier position. As before, you multiply the daily motion by the fraction obtained in 6b). You then subtract the result from the earlier position.
8) Convert your results to degrees and minutes. You now have the positions of all the planets and the mean node.
Sun is 20 degrees 58 minutes = 20.97 + .85 = 21.82 = 21 degrees 49 minutes (Virgo)
Moon is 25 degrees 48 minutes = 25.80 (Aries) + 11.39 = 7.19 (Taurus) = 11 degrees 23 minutes
Mercury is 9 degrees 8 minutes = 9.13 + 1.64 = 10.77 = 10 degrees 46 minutes (Virgo)
Venus is 0 degrees 12 minutes = 0.20 + 1.05 = 1.25 = 1 degree 15 minutes (Scorpio)
Mars is 16 degrees 0 minutes = 16.00 + .61 = 16.61 = 16 degrees 37 minutes (Scorpio)
Jupiter is 29 degrees 17 minutes = 29.28 + .11 = 29.39 = 29 degrees 23 minutes (Gemini)
Saturn is 13 degrees 16 minutes retrograde = 13.27 + -.08 = 13.19 = 13 degrees 11 minutes (Pisces)
Uranus is 15 degrees 36 minutes = 15.60 +.06 = 15.66 = 15 degrees 40 minutes (Virgo)
Neptune is 17 degrees 48 minutes = 17.80 + 0 = 17.80 = 17 degrees 48 minutes (Scorpio)
Pluto is 16 degrees 17 minutes = 16.28 + .04 = 16.32 = 16 degrees 19 minutes (Virgo)
North Node is 7 degrees 41 minutes retrograde = 7.68 + -.08 = 7.60 = 7 degrees 36 minutes (Gemini)
9) Fill in the chart. Enter all the positions found, including MC, Asc and Vertex on a blank chart, which is provided in this appendix.
Table of Appropriate Values for the Obliquity of the Ecliptic (e)
and
Trigonometric Functions of e
Year e Radian e Sin e Tan e Cos e 1900 23.452 degrees .409314 .397980 .433822 .917391 1925 23.449 degrees .409262 .397932 .433755 .917414 1950 23.446 degrees .409204 .397879 .433687 .917436 1975 23.443 degrees .409148 .397828 .433620 .917459 2000 23.439 degrees .409091 .397775 .433553 .917482Table of Approximate Ascendants
This is a table for use in checking whether 180 or 360 needs to be added or subtracted to the results of the formulae for finding Ascendant and Vertex. The Ascendant should be within a few degrees of that indicated here. Take the nearest latitude and interpolate for time. For example, for a birth at latitude of 47 degrees at 11.45 LST, look at column 48 degrees, take three quarters of the difference between the figures given for 1100 and 1200 and add this to the figure given for 1100: approximate Ascendant is 244.
Latitude in degrees Lst of birth RAMC 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 0000 00 103 104 105 106 107 108 110 111 112 114 115 117 119 121 123 125 127 130 0100 15 116 117 118 119 120 121 122 123 124 125 126 128 128 130 132 133 135 137 0200 30 128 129 130 131 132 132 133 134 135 136 137 138 139 140 142 143 144 146 0300 45 141 142 142 143 144 144 145 146 146 147 148 149 149 150 151 152 153 154 0400 60 154 154 155 156 156 157 157 157 157 158 158 159 160 160 161 161 162 163 0500 75 167 167 167 168 168 168 168 168 169 169 169 170 170 170 170 171 171 171 0600 90 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 180 0700 105 193 193 193 192 192 192 192 192 191 191 191 191 190 189 189 189 188 188 0800 120 206 206 205 205 204 204 203 203 203 202 202 201 200 200 199 199 198 197 0900 135 219 218 218 217 216 216 215 214 214 213 212 211 210 210 209 208 207 206 1000 150 232 231 230 229 228 228 227 226 225 224 223 222 221 220 219 218 216 215 1100 165 244 243 242 241 240 239 238 237 236 235 234 232 230 229 228 226 224 223 1200 180 257 256 255 254 253 252 250 249 248 246 245 243 241 239 238 235 233 231 1300 195 270 269 268 267 266 264 263 261 260 258 256 254 252 250 248 245 242 239 1400 210 285 284 282 281 280 278 277 275 273 271 269 267 264 261 258 255 252 248 1500 225 301 300 298 297 296 294 292 291 289 286 284 281 278 277 271 267 262 257 1600 240 318 318 316 315 314 313 311 309 307 305 303 300 296 292 288 282 275 268 1700 255 338 338 337 337 336 335 334 333 331 330 328 326 323 319 314 307 298 285 1800 270 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 1900 285 22 22 23 23 24 25 26 27 29 30 32 34 37 41 46 53 62 75 2000 300 42 42 44 45 46 47 49 51 53 55 57 60 64 68 72 78 85 92 2100 315 59 61 62 63 64 66 68 69 71 74 76 79 82 85 89 93 98 103 2200 330 75 76 78 79 80 82 83 85 87 89 91 93 96 99 102 105 109 112 2300 345 90 91 92 93 94 96 97 99 100 102 104 106 108 110 112 115 118 121