CALCULATING THE NATAL CHART THE TABLES OF HOUSES LESSON 4 At this stage, if you haven't done so already, it is a good idea to invest in a calculator. It does not have to be a complicated one. You will only be using the addition, subtraction, multiplication and division functions. However, if you can find one which will perform these functions in units of time, you will find this an enormous advantage. You now have to convert the L.S.T., which is the M.C. (or Midheaven) of the chart in terms of time, to degrees of the zodiac, but, first, you must familiarise yourself with the Tables of Houses, as you did with the Ephemeris. I am using the American Book of Tables, but unfortunately some sets of tables are set out slightly differently. The difference is, usually, that the American Tables are set out horizontally, whereas some tables are set out vertically. The method of use however, is basically the same. If yours is one of these "vertical" sets, try to find and identify each section referred to in this text, and then you shouldn't have any trouble using the method described. The same applies if you are using tables from another house system such as Koch. However if you do have problems, you may have to find a professional astrologer to explain the layout to you. There are many systems of house calculation. I am using the Placidus system, because tables for it are easy to obtain; it works very well at temperate latitudes; and it is the most common system in use. To go into full detail of the maths on which it is based would send any mathematician reeling but in very simplistic terms it works thus: The time each degree of the zodiac takes to move from the Ascendant to the M.C. is measured and trigonometrically divided into three. This measurement marks the 11th and 12th houses, and by inference the 5th and 6th. The time taken for that same degree to move from the IC to the Ascendant is then measured, and trisected trigonometrically, to give the cusps of the 2nd and 3rd houses and by inference, the 8th and 9th. However, as this course is mainly a "how to" course, and not one of theory, let's move on to how to use the tables. Suffice it to say there is endless debate over 23
which is the most accurate house system analytically, or which one is accurate mathematically, but I don't intend to introduce you to that debate this early in your astrological experience. Turn to the first page of your tables (American Book of Tables) and you will see that each page is headed: PLACIDUS TABLES OF HOUSES FOR LATITUDES 0 TO 60. Below this, there are eight distinct sections - four on top and four on the bottom. Each section is basically the same layout. At the top of each section is a heading as follows: section 1 section 2 0h 0m 0s 0 0' 0" 0h 4m 0s 1 0' 0" (this is (this is (sid. time) (deg of arc) sid time) deg of arc) 0 A 0' 1 A 5' (this is (zodiac zodiac degrees) degrees) "Sid time" is the sidereal time. "Deg of arc" is the equivalent number of degrees in the 360~ circle. "Zodiac degrees" is the equivalent number of degrees of the zodiac sign, or Zodiacal Longitude. This means that in section 1, 0 hrs 0 min 0 sec is the equivalent to 0 degrees 0 minutes 0 seconds of the 360 circle, and both are equivalent to 0 degrees 0 minutes of Aries. In section 2, 0 hrs 4 min 0 sec of time, is equivalent to 1 degree 0 minutes 0 seconds of the 360 circle, both of which are equivalent to 1 degree 5 minutes of Aries. The zodiac degree is the mid-heaven (M.C.), or 10th house cusp of your chart. If you go right through the tables you will find that 0h 0m 0s of sidereal time equals 0 0' of Aries, and at the other end you will find that 23h 56m 0s equals 28 55' of Pisces and 359 of arc, and then it starts all over again as the next degree of arc would be 360, or 0 of the full circle. Every set of tables has a constant - either the degrees of arc, or the zodiac 24
degrees will move forward by the same amount in each section. In this set of tables the degree of the zodiac is given for every 1 of arc, or 4 minutes of sidereal time. Check this for yourself. Below the main heading of each section, are five columns, headed 11, 12, Asc, 2, and 3 respectively. These figures, which are expressed in degrees and minutes, refer to the cusps of the houses. (Asc means the Ascendant, or the cusp of the 1st house, 11 is the 11th house etc.) These house cusps are dependent on the latitude of the place of birth, which is given to you down the centre of the page. These columns are read the same way as you read the ephemeris, i.e. the sign at the top refers to all the figures going down the column until the sign changes. For example, in the first section, in the Asc column, the sign changes at 56 latitude from Cancer to Leo. In the 2nd house column, it changes from Cancer to Leo at 5 latitude CALCULATING THE CONSTANT DECIMAL AND HOUSE CUSPS Remember, from the lesson on time, that the M.C. is not affected by latitude, so you can disregard the latitude of the place of birth when you first start these calculations. The place to start is with the Local Sidereal Time, so let's start with Ian's L.S.T. which was 22 hrs 28 min 13 sec. If you look through the sidereal time figures in the tables, you won't find this actual figure. You WILL find 22 hrs 28 min 0 sec, and if this had been the L.S.T., you could take the corresponding zodiac degree of 5 10' Pisces as the M.C.. As Ian's L.S.T. is a little more than this sidereal time, you can safely assume that his M.C. will also be a little more than 5 10' Pisces. In the same way, the rest of the house cusps will be a little more than those given in the tables for sidereal time 22h 28m 0s. In fact, Ian's house cusps will be somewhere between those figures given for the house cusps at 22h 28m Os, and the figures given for the house cusps at 22h 32m 0s (which is higher than Ian's L.S.T.). To calculate the cusps, first you need to find the fractional difference between Ian's L.S.T. and the sidereal times given in the tables. Once again, turn to your calculation sheets and you now subtract the lower given sidereal time from the L.S.T.. Ian: hrs min sec 16. L.S.T. 22 28 13 17. Smaller sid. time from tables 22 28 00 You then subtract step 17 from step 16, which will give you the difference in TIME between the L.S.T. and the earlier sidereal time from the tables. The result of this subtraction is entered in Step 18, and then converted in Step 19 to seconds if necessary. Converting to seconds gives us a whole figure to make the calculations easier. (If using a time calculator conversions to minutes or seconds are not necessary, and you can ignore those steps.) 25
hrs min sec 16. L.S.T. 22 28 13 17. Smaller sid. time from tables 22 28 OO 18. subtract 13 19. Convert to seconds if necessary 13 So you now know that there are 13 seconds of time between 5 10' Pisces, and whatever the actual degree of Ian's M.C. This means that Ian's M.C. is actually 5 10' Pisces plus 13/240, as 240 represents, in seconds, the four minute constant between the sidereal time at 5 10' Pisces, and the sidereal time at 6 14' Pisces. If we decimalise this fraction of 13/240, which is time, we can convert it easily to minutes of a degree. To decimalise a fraction, simply divide the top figure by the bottom figure. The result of the decimalisation of the figure at step 19 by dividing by 240 is known as the Constant Decimal, and is written against Step 20. The Constant Decimal (C.D.), represents the proportional difference between Ian's house cusps, and the house cusps before and after, as given in the tables. Therefore, by then subtracting the smaller zodiac degree (the degree corresponding to the sidereal time less than the L.S.T.) from the larger zodiac degree (the degree corresponding to the sidereal time higher than the L.S.T.), multiplying the result by the C.D. to give us the time difference in terms of degrees, and adding it to the smaller zodiac degree, you will then have the M.C. of the chart. Let's put this into practical terms, by continuing with Ian's calculation sheet. hrs min sec 16. L.S.T. 22 28 13 17. Smaller Sid time from tables 22 28 00 18. Subtract 13 19. Convert to seconds if necessary 13 2O. Divide by 240 (this figure is the C.D.) =.05 Then:- M.C.(10) 21. Larger zodiac figure from tables 6 14' L 22. Smaller zodiac figure from tables 5 10' L 23. Subtract 1 04' 24. Convert to minutes if necessary 64' 25. Multiply by C.D. (in this case.05) 03' 26. Add smaller zodiac figure + 5 10' L 27. True house cusp 5 13' L The other house cusps are calculated exactly the same way, except that you have to use the figures pertaining to the latitude of the place of birth. The latitude 26
of Sydney, Ian's place of birth is 33 S55'. This can be rounded off to 34. Find 34 in the centre of the page, and place a ruler or a piece of paper along the line so you can see the figures clearly. Use the same two sections you used to find the M.C.. The larger zodiac degree will come from the section containing the sidereal time higher than the L.S.T., and the smaller zodiac figure will come from the section with the sidereal time less than the L.S.T.. Both figures, this time, will come from the column headed "11" (11th house cusp), and will be written on your calculation sheet in the column beside the one you used for the M.C.. Ian's will look like this: M.C.(10) 11 21. Larger zodiac figure from the tables 6 14' 9 39' A 22. Smaller zodiac figure from the tables 5 10' 8 27' A 23. Subtract 1 04' 1 12' 24. Convert to minutes if necessary 64' 72' 25. Multiply by C.D. (in this case.05) 03' 04' 26. Smaller zodiac figure 5 10' 8 27' A 27. Add (true house cusp) 5 13' 8 31' A When finding the sign for these house cusps, don't automatically use the sign at the top of the column, but run your finger up the column, just in case the sign has changed somewhere between the top and the latitude you are using. The sign you want is the one directly above it - maybe at the top of the column, maybe not. Then continue to the 12th house cusp, the 1st (Ascendant) etc.. You haven't quite finished yet. If the place of birth is South of the equator, the signs on the house cusps must be reversed to those in the tables. (Reverse = opposite sign.) This means that Ian's M.C. is not 5 13' L, but 5 13' F. The 11th house cusp is not 8 31' A, but 8 31' G. Reverse all the signs in this way, and then enter them directly onto the chart wheel. INTERMEDIATE LATITUDES The latitude of Belfast, Laureen's place of birth, is 54 N35'. You could round this up to 55 and continue as you did for Ian, but if you wish to be as accurate as possible, particularly with places at high latitudes, the following is more appropriate. If the latitude is less than 20' more than the whole degree (e.g Cronulla, N.S.W. = 34 S04') then round the figure back to the previous degree (in this case 34.) If the latitude is more than 40' more than the whole degree (e.g. Long Beach = 27
33 N47') then round the figure forward to the next degree (in this case 34 ). If the latitude is between 20' and 40' more than the whole degree (e.g. Belfast = 54 N35') then the intermediate figure should be determined. So, back to Laureen's calculation sheet, and the American Book of Tables. The M.C. is fine; you don't need the latitude for that, so it is calculated as we calculated Ian's M.C.. When it comes to the other house cusps however, you must calculate what the figures would be between 54 latitude and 55 latitude. To do this you do a similar calculation to the above. Firstly convert the minutes in the latitude to a decimal by dividing them by 60. Laureen s Latitude is 54N35. So divide the 35/60 =.58. This will be the increment between the the zodiacal longitude at 54 degrees and 55 degrees. Laureen's M.C. is 18 43' G, so you will be using the section under zodiac degree 19 30' G (higher) and the section under 18 26' G (lower). Place your ruler under lat. 55 across these two sections. First the "higher" section, in the 19x 30G MC degree 11th house figure given for latitude 54 = 12 52' H 11th house figure given for latitude 55 = - 12 36' H Subtract 16' Multiply by increment (.58) 09 As the figure given for the lower latitude is higher than the figure given for the higher figure, this incremental figure must now be subtracted from the figure given for the lower latitude. 11th house figure given for latitude 54 = 12 52' H - increment - 09 Intermediate House Cusp 12x 43 H Now refer to the "lower" section under the 18x 26G MC degree 11th house figure given for latitude 54 = 12 00' H 11th house figure given for latitude 55 = - 11 44' H Subtract 16' Multiply by increment (.58) 09 11th house figure given for latitude 54 = 12 00' H Subtract increment 09 Intermediate House Cusp 11 51' H Then back to the calculation sheet, where you use these two intermediate figures in the calculation for the 11th house. That is, in the 11th column at step 28
21 you use 12 43', and at step 22 you use 11 51'. Belfast is also North, so the signs are not reversed. Remember, these intermediate house cusps will have to be found for all the cusps except the M.C. Sometimes you will find that the figure given at the lower latitude is actually lower than the figure given for the higher latitude. This turn around happens when the house cusp reaches 0x Aries and Libra (You can see this for yourself in the tables.) If this happens, simply reverse the processes. Subtract the lower figure from the higher, multiply by the incremental decimal and ADD the result to the figure given for the lower latitude. THE EQUATORIAL ASCENDANT The Equatorial Ascendant is simply the Ascendant calculated at 0x Latitude. So using the exact same formula, the same columns and the same CD, go to 0x latitude and calculate the Ascendant. Remember if your subject was born in Southern Latitudes, you reverse the sign. So for Ian s Chart: Eq (Asc 0x Lat.) 21. Larger zodiac figure from tables 9x 40 C 22. Smaller zodiac figure from tables 8x 43 C 23. Subtract 0x 57 24. Convert to minutes if necessary 57' 25. Multiply by C.D. (in this case.05) 03' 26. Add smaller zodiac figure + 8x 43 C 27. True house cusp 8x 46 C Reverse Sign (Southern Birth) 8x 46 I DRAWING UP THE CHART Now you have the house cusps, the next step is to put them into the actual chart. With your chart wheel in front of you, start with the M.C. which is the point right at the top of the chart, and work in an anti-clockwise direction -the degrees of the circle move in an anti-clockwise direction. Write the figure and sign against the house cusp concerned. For example, on Ian's chart form, beginning at the top, write 5 13' Virgo (using glyphs). Against the 11th house cusp (the line showing the start of the house) write 8 31' Libra and so on. When you get to houses 4 to 9, you write the same degree but reverse the sign to the cusp directly opposite. The 4th house cusp is directly 29
opposite the 10th house cusp (M.C.) so in Ian's chart the 4th house cusp is 5 13' Pisces, the 5th house cusp will be 8 31' Aries, and so on. The chart wheel is now ready for the planets. When you draw in the house cusps on Renee's chart, you will notice two seemingly rather odd things. 1. There are two house cusps with the sign of Leo, and two with the sign Aquarius (the opposite sign). 2. The signs Gemini and Sagittarius are missing. This is no problem. Simply put the two signs in where they belong. In Renee's chart, Gemini will go in the 11th house, and Sagittarius will therefore go in the 5th house. If this happens in your charts - if you find two signs repeated on the next house cusp - simply put the missing signs in the houses where they would fit in the natural order of the zodiac. These signs are called intercepted signs. 30
THE CHART WHEEL IN TERMS OF TIME Remember that the MC equates to Noon in terms of time. This means that the IC (Immum Coeli the cusp of the 4 th House) being directly opposite will equate to Midnight. If the Ascendant is the dawn point, then the Descendant, or cusp of the 7 th House will equate to sunset. Dawn and sunset are at different times depending on latitude and seasons, but in general terms we can classify the house cusps in terms of time instead of Zodiac degrees, and using this we can check to see if the chart we have is more or less correct. 31
Ian was born at the local time of 9:40 p.m., so the Sun must be somewhere around the 5th house area of the chart. We know this because an early April birth date will always be an Aries Sun. Renee was born at a local time of 2:52 a.m., so the Sun, in her chart, (Virgo) must be somewhere around the 3rd house cusp. Laureen was born at local time 8:20 a.m., so her Sun (Capricorn) would probably be around the 12th house cusp. This method of checking works well in Ian's and Renee's charts, but in Laureen's chart, the Sun is around the 2nd house cusp. This is because of, a) daylight saving, which means the true local time is actually 7:20 a.m., and because b) in the northern hemisphere, the 25th December is mid-winter, which means that, in Belfast, which is quite far North, the Sun would not have risen until well after 7:30 a.m.. As the Ascendant - Descendant line of the chart is the Sun rising - setting line (the horizon), this means that the Sun in Laureen's chart must be in the "night" area of the chart, or below the horizon (the ascendant - descendant line). So, when using this method to check your calculations, make sure you take these factors into account. It may also make a difference if the place of birth is a long way in longitude from the Standard Time Meridian. 32
This is the only time, in all astrology calculations, when you use Local Time. At all other times, GMT is used. SOLAR AND NATURAL CHARTS Sometimes you may want to look at a chart when the birth time is unkown. Obviously you cannot have an accurate chart without a birth time, but using a technique known as the Solar Chart, will still give some information, such as chart shapes, planetary patterns etc.. To draw a Solar Chart, simply look up the Sun's degree on the birthday. I actually like to work out the Noon position, which is of course the mean position of the day, but this isn't really necessary. This degree then becomes the Solar Ascendant, or cusp of the 1st house, as it isn't a true Ascendant, and the rest of the house cusps are drawn in the Equal House system. In other words each house becomes exactly 30. For example let's say we did not have Ian's time of birth, but simply knew he was born on 2nd April, 1968. Look up the Sun on 2 April 1968 12 19' A The Ascendant, or 1st house cusp becomes 12 Aries, the 2nd house cusp 33
would be 12 Taurus, the 3rd - 12 Gemini etc. etc., each house being the same degree, but the next sign. The planets are then taken straight from the ephemeris, and placed in the chart exactly, as we will do over the next few lessons. The exception is the Moon, which I always calculate roughly to the Noon position at the place of birth, as this gives me a better idea of the range of the sign it is likely to occupy. You will understand this better later on. There is no M.C. in this type of chart, nor can you have a Vertex or a Part of Fortune. A Natural Chart uses the same principle. The cusp of the 1st house in a Natural Chart is always 0 Aries. The 2nd House cusp is always 0 Taurus, the 3rd is 0 Gemini, etc.. The planets are then inserted as you did for the Solar Chart. HOMEWORK First calculate the CD for all your homework subjects and send them to me. When I have sent you back your corrected homework, work out the House cusps from 10 3 for Jason, Andy, Omar, Keiko and Kevin. If you are really energetic and feel like it you can do the others too, but you don t have to. Work out the intermediate latitudes for ANDY only. For this exercise, for the rest round up or down as appropriate.. See you next week 34