I don't know if I even remember....
But let's take a birth for
27 December 1988
1440 EST
New York
New York is at 73*56' W
and 40*40' N.
The time zone is EST (GMT -5).
So....
we start with clock time: 1440
EST is based on 75W
So we are 4m and 16s Later in NYC than on the time zone meridian.
Our LMT is then 1444:16
And GMT is 1940 (for calculating the planets).
Those are the two times we need to cast the chart: LMT for the houses and GMT for planets.
The Sidereal Time for 27 Dec 1988 at midnight Greenwich is 06:22:47, taken from the ephemeris.
We add the LMT (distance from midnight), 1444:16
Which yields 20:66:63 or 21:07:03...our local sidereal time, or RAMC
Delta T is 55s (taken from the ephemeris)...so correct RAMC is 21:07:58
With that we get the zodiacal degree corresponding to RAMC and we have our MC
And can now calculate the Asc (or take it from tables....I like that idea).
To check our calculation....
We know Sun is in early Capricorn, about 6 degrees
An RAMC of 21 hours will give approximately the middle degrees of Aquarius on the MC.
So that would place Sun around the 9th House cusp, probably about the middle of the 8th
And that is where we ought to find the Sun at 1440 hours.
So our calculation is correct. We have not made a gross error in the time for the chart.
This method of checking (very quick in practice -- it's an eyeball thing once the Sun is put in the chart) does not catch small errors but does catch big ones. I do it even with computer generated charts, to make sure I didn't plug in a wrong time.
I think I forgot to add in the correction for 1444 hours at 10s per hour.....so the time I gave is off by that much....146s or 2m26s. So RAMC would be 21:10:24....Voila. That's the sort of mistake checking by sun's position won't catch and results in an error of around 37' of arc in the MC.
No calculator. In my head. Two bits of data from ephemeris.
Now I'll plug the data into my program and see what it gives.
15 Aquarius MC, Sun a bit lower than middle of 8th (it's winter).
Good to go.
The program I used says ST = 21:09:59, but it's using a different longitude, so the calculation I did is correct. Hehe....I haven't done that in 15 years or so.....It's like riding a bicycle and very simple -- once you understand what you are doing instead of just learning the method by rote.
It is unlikely that the given formula is wrong. It is unlikely the net calculators are wrong. Which puts the probable cause of the discrepancy squarely in your lap. Check your work. Always. And check it again.
When we old salts were learning to do these calculations there were no computers. I didn't even have a hand-held calculator. I had no one but me to rely on. If I made a mistake (and I made them all the time) I had to find it myself, and figure out what the mistake was and fix it myself. Mistakes are very easy to make, and some types of mistake are very difficult to notice. So......check your work and check it again, even if it seems to be right at first.
I don't say this to be mean....But don't ask for help. Do it yourself. Get mad, feel frustrated, feel stupid. Keep at it. All that frustration will result in mastery. Understand the principles and keep slugging it out until you get it right. Einstein worked for eleven years on his General Theory and couldn't get his math right. He found mistakes in his work even after he thought he had it right. And then he went back, checked his work, and found a formula he had discarded two years earlier and realized it was the right one. Kepler did the same thing when he was discovering the laws of planetary orbits. All the brightest and best for 2000 years before him had discounted the idea of ellipitcal orbits as too simple...but Kepler kept on working with his numbers and the ellipse popped out. Simple. Just hard frustrating work.
Guess I put this on the wrong thread. Oh well. I can hardly wait until you begin using the repetitive algorithms for Placidus houses.