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John Worsdale zodiacal parallels.
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Petr



Joined: 25 Aug 2008
Posts: 79
Location: Czech Republic

Posted: Sun Dec 30, 2012 1:27 pm    Post subject: John Worsdale zodiacal parallels. Reply with quote

John Worsdale writes:

This Child was drowned at the Age of seven years, one Month, and six days, and the Directions that destroyed Life, (which shewed their effects at the time of Death,) were the Moon Hyleg, to the Body of Saturn, by Converse Motion, and also the parallel Declination of Mars…..

He gives the calculation:

Moon to the Parallel of Mars in the Zodiac Arc = 6°59‘ = 6,98°

Worsdale counts directions Placidus under the pole. As he counts zodiacal parallel?
We can find it from a horoscope James Attersall. The last calculation is
Sun to the parallel of Venus in the Zodiac.

James Attersall born 1.10.1817 in the Lincoln
16:45 LA(16:36:50 GMT), 53N15

Worsdale speculum:

RAMC = 258°42‘, E = 23,464(an approximate value for the year 1817)

Sun:
L = 188°7‘
RA = 187°27‘
DSA = 85°40‘
D = 3S14
AD = 4°20‘

Venus:
D=11N57

Computing the poles Sun according to Worsdale:

DSA / 3 = 85°40‘/ 3 = 28°33‘
UMD = RAMC – RASun = 258°42‘ – 187°27‘ = 71°15‘
proportional point PP = ( 30° / 28°33‘) x 71°15‘ = 74°52‘
ODSun under his own Pole = RAMC – PP = 258°42‘ – 74°52‘ = 183°50‘
ADSun under pole = RASun – ODSun = 187°27‘ – 183°50‘ = 3°37‘

poleSun = arctg(sin ADSun / tgDSun) =
arctg(( sin3°37‘/ tg(-3°14‘)) = - 48°9‘

L//Venus = arcsin(sinDVenus / sinE) = arcsin(sin11°57‘/ sin23,464) =
31°20‘ +180° = 211°20‘(same value as Worsdale)
AD//Venus = arcsin(tgDVenus x tgpoleSun) =
arcsin((tg11°57‘ x tg(-48°9‘)) = - 13°40‘
RA//Venus = arctg(tgL//Venus x cosE) =
arctg(tg211°20’x cos23,464) = 209°11‘
OD//Venus = RA//Venus + AD//Venus = 209°11‘ – 13°40‘ = 195°31‘
ARC = | ODSun – OD//Venus| = | 183°50‘ – 195°31‘| = 11°41‘ = 11,683

Result from Worsdale: 11°41'
Morinus gives the same result (11,675).

Back to chart J.Kent. I will use the same method of calculation.
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margherita



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Posted: Sun Dec 30, 2012 1:49 pm    Post subject: Re: John Worsdale zodiacal parallels. Reply with quote

Thanks Thumbs up

margherita
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lihin



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Posted: Sun Dec 30, 2012 1:58 pm    Post subject: Thank you! Reply with quote

Thank you, Mr Petr.

Am looking forward to reading your computation of the Mars zodiacal parallel for Master Joseph Kent. Smile

Best regards,

lihin
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lihin



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Posted: Mon Dec 31, 2012 8:21 am    Post subject: Rectification to Moon's position Reply with quote

Good morning,

As in Master Joseph Kent's nativity Sιlιnι (Luna) is the Epikratetor (hilaj) according to Mr John Worsdale, i have using Morinus rectified the chart to the Moon's position according to Worsdale, page 84, 18PI38', instead of to the pivots This gives us a rectified birth time of 23h24.

Setting the Primary Directions options to both Mundane and Zodiacal, Placido semi-arcs, no latitudes, true solar equatorial arc, only conjunctions and parallels, one obtains the following data of the three "Directions that destroyed Life", so described by Worsdale on page 88:

'

This appears to be a reasonable data fit. One could also rectify to the smallest mean difference of arcs of these three primary directions.

Methinks it would be more instructive and useful to begin with Worsdale's first example, Master James Attersall, for which the author listed in detail his methods of calculations.

Best regards,

lihin
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Petr



Joined: 25 Aug 2008
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Posted: Mon Dec 31, 2012 11:52 am    Post subject: Reply with quote

Joseph Kent born 6.6.1817 in Liverpool 23:30 LA(23:40:04 GMT), 53N22, 2W57

Worsdale speculum:

RAIC = 67°4’, E = 23,464

Moon:
L = 348°38’
RA = 351°29’
NSA= 102°16’
D = 8S59
AD = - 12°16’

Mars:
D = 2N29
B = 1S44

Computing the poles Moon:

SNA / 3 = 34°5’
LMD = 67°4’ – 351°29’ = - 284°25’ + 360°= 75°35’
PP = 30°/ 34°5’ x 75°35’ = 66°32’
OAMoon under his own pole = 67°4’ – 66°32’ = 0°32’
ADMoon under pole = 351°29’ – 360°32’ = -9°3’

poleMoon = 44°51’

Significator uses latitude, therefore the promisor counts with latitude also.

L//Mars = arcsin((sinD – cosE x sinB) / (sinE x cosB)) = 10°17’ + 360° = 370°17’
RA//Mars = arctg(( tgL x cosE – ( tgB x sinE) / cosL)) = 10°8’ + 360° = 370°8’
AD//Mars = arcsin (tg 2°29’ x tg 44°51’) = 2°28’
OA//Mars = 370°8’ – 2°28’ = 367°40’
ARC = | 360°32' – 367°40'| = 7°8'

I apologize to Mr. Worsdale. Its calculation is correct.
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margherita



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Posted: Mon Dec 31, 2012 12:24 pm    Post subject: Reply with quote

Petr wrote:

ARC = | 360°32' – 367°40'| = 7°8'

I apologize to Mr. Worsdale. Its calculation is correct.


That's strange. While in the first example Worsdale uses the pole of the Sun for both planets (they are "under the pole directions), here for Mars does not use the pole Sad

In fact from Morinus speculum, Mars OA is 10.07 (RA) - 2.28 (decl)= 7.39, same value as Petr's.

Worsdale was wrong Smile he should take mars OA under Moon's pole, that's why I love software Smile

margherita
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Petr



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Posted: Mon Dec 31, 2012 2:24 pm    Post subject: Reply with quote

Margherita

//Mars is computed under the pole of the Moon.
See AD / / Mars. Pole = 44 ° 51’
The first example was the Sun as the significator. Latitude Sun = 0. Parallels L / / Venus therefore calculated without latitude.
Moon values are calculated with the latitude. L / / Mars is the calculated with the latitude. Of course, under the pole of the Moon.
Morinus no counts L / /Mars with the latitude (even if it is set : Use latitude of Both).Bug?

Result without latitude:

/ / Mars -> Moon = 2 ° 44 '= 2,733
Morinus = 2,644
contra / / Mars -> Moon = 3 ° 48 '= 3,8
Morinus = 3,834

The conclusion is that Worsdale counts the zodiacal parallels under the pole significator(Placidus under the pole system)and he uses Placidus key .
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margherita



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Posted: Mon Dec 31, 2012 3:15 pm    Post subject: Reply with quote

Petr wrote:
Margherita

//Mars is computed under the pole of the Moon.
.


NIET Smile

Mars AO under the pole of the Moon (let us say 45 for 44.51, I have tables) is 5.20 (something like that).

So, OA of the Moon under its own pole- OA of Mars under the pole of the Moon:

360.32- 365.20= 5.12



Considering I interpolated the result and the latitude is a little smaller, it could be ok with Morinus result, true?


There is no bug in Morinus, it perfectly fits with Phasis. It's Worsdale's mistake, he mistook Mars OA (7.40) instead of the Mars OA under the Moon's pole (5.12).

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lihin



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Posted: Tue Jan 01, 2013 8:49 am    Post subject: Thanks! Reply with quote

Good morning,

Happy New Year and special thanks to Ms Margherita and Mr Petr who are helping understand better Mr John Worsdale, Morinus and Primary Directions! Thumbs up Very interesting as well.

Can an Excel or Open Office worksheet with all or most of the calculations both of you have been demonstrating be downloaded somewhere? If so, where, please?

Once we have thoroughly understood how Mr Worsdale worked and if, and which, any systematic errors were included, we shall be more at ease about his symbolic deductions, having reliable, verified data to work with.

Best regards,

lihin
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Martin Gansten
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Posted: Tue Jan 01, 2013 9:39 am    Post subject: Reply with quote

Sorry if I'm a bit late getting into this.

Petr wrote:
L//Mars = arcsin((sinD – cosE x sinB) / (sinE x cosB)) = 10°17’ + 360° = 370°17’
RA//Mars = arctg(( tgL x cosE – ( tgB x sinE) / cosL)) = 10°8’ + 360° = 370°8’
AD//Mars = arcsin (tg 2°29’ x tg 44°51’) = 2°28’
OA//Mars = 370°8’ – 2°28’ = 367°40’
ARC = | 360°32' – 367°40'| = 7°8'

If I understand correctly what you are doing here, Petr, you mean that Mars' parallel in the zodiac should not be a point on the ecliptic, but should have Mars' own latitude (-1°44'), in addition to Mars' declination (+2°29'). That raises two questions: first, do you have any precedent for calculating zodiacal parallels with latitude? I have never seen it before. And second, although you base your calculations on Worsdale's values, your arc of direction is 0°09' greater than his. That is far too much for a rounding error, so if you believe that Worsdale meant to do what you have just done, how do you explain his result of 6°59'?

Calculating the parallel in the ecliptic from Worsdale's values, I get an arc of direction of 2°41'; Morinus, using modern values, gives 2°38'. I think the simplest explanation of Worsdale's result is that he simply muddled a few figures somewhere along the way -- all too easily done when you are calculating 20 years' worth of directions by hand. But I confess I have not had the time to go through Worsdale's other calculations of zodiacal parallels to compare values and speculate on methods. I notice he has a second Moon to the Parallel of Mars in the Zodiac for Joseph Kent, with an arc of 11°37'; does that agree with your method of calculation?
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margherita



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Posted: Tue Jan 01, 2013 10:11 am    Post subject: Reply with quote

Happy new year

Martin Gansten wrote:



I think the simplest explanation of Worsdale's result is that he simply muddled a few figures somewhere along the way -- all too easily done when you are calculating 20 years' worth of directions by hand



I LOVE when others agree with me.

Wordsdale just took Mars OA (it can be checked in Morinus speculum) instead of using the Moon pole, 44.51


Lihin wrote:

Can an Excel or Open Office worksheet with all or most of the calculations both of you have been demonstrating be downloaded somewhere? If so, where, please?


Morinus works very well and the same Phasis (moreover Phasis has a longer years range)

Under the pole directions are very easy. You need just the Oblique Ascension or Oblique Descension of the two points and subtract as in Petr's example, being careful that:
a) the OA of the significator should be calculated under its own pole
b) the OA of the promissor should be calculated under the pole of the significator.

Nothing else.

margherita
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lihin



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Posted: Tue Jan 01, 2013 11:14 am    Post subject: John Worsdale's methods Reply with quote

Good morning,

It will probably be quite useful or even necessary for those interested in Mr John Worsdale's methods to thoroughly study the first chapter of his book, called The True Method of Erecting a figure of the Heavens, pages 1 - 18 of Celestial Philosophy or Genethliacal Astronomy and as well to understand his detailed calculations of 41 of the 44 listed primary directions on pages 20 - 34 from the Geniture of Master James Attersall, born 1st October 1817, died 22nd September 1819. Two of the three directions whose calculations are not given, nos. 2 and 9 with respectively 0Ί21' and 2Ί24' of arc, involve the Medium Coeli, perhaps deemed not relevant for a native whose life span encompassed less than two years. The third, no. 6, Ascendant to the Square of Mars in Mundo, 1Ί11', is mentioned on page 37 as one of "The Astral causes that produced the sudden and violent Death of this Child ...".

When erecting the figure one should bear in mind Mr Worsdale's sentence on page 18 (note his use of the English present subjunctive tense Smile ),

Quote:
"I have not noticed the difference between the Meridian of Greenwich, and that of Lincoln in this Geniture, because it is very small, but when the difference in time is more considerable, then it must be attended to in all Nativities, by adding it to the correct time of Birth if the Longitude be West, and subtracting it if the Longitude be East of the given place of Birth."


According to GeoHack, Lincoln, England is situated at 53° 13′ 57.72″ N, 0° 32′ 15.36″ W. When casting the figure with Morinus using Mr Worsdale's coordinates and pivots, i arrive at a birth time of 16h24m16s LAT, more than 20 minutes prior to Mr Worsdale's stated time. Here is the list of positions from Morinus:



Frankly, i have another preliminary concern about Mr Worsdale's methods. He included Johannes Kepler's additional aspects and parallels of three kinds, primary directions both in zodiaco and in mundo, both direct and converse (using Professor Gansten's definitions), resulting in 44 listed directions during the first 12 degrees or 13 years, 9 during the first 3 years. To me this seems like many directions to pick and choose from to obtain event matches. Hopefully Mr Worsdale used his own calculation methods consistently through the nativities.

Best regards,

lihin

PS Oversight corrected.
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Last edited by lihin on Tue Jan 01, 2013 12:39 pm; edited 2 times in total
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Petr



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Posted: Tue Jan 01, 2013 11:23 am    Post subject: Reply with quote

Worsdale gives the value of the Moon: L = 348 ° 38 '
Morinus is accurate (348 ° 40'08 ").
I used only the value of the Worsdale. This is one of the possible causes that results are slightly different for the calculation without latitude.

Manual calculation:
//Mars -> Moon = 2°44’ (Morinus 2°39’)
contra//Mars -> Moon = 3°48’ ( Morinus 3°50’)

Significator is Moon. Therefore, counting promissor (Mars) under the pole Moon. This means: / / Mars -> Moon

I am using a form of write program Morinus.
/ / Moon -> Mars is a completely different example. That is parallel the Moon under pole of Mars.

Wosdale writes: Moon (significator) to the parallel of Mars (promissor).

Writing Morinus: //Mars D -> Moon 2,644 ( 2°39’) 1819.12.29

Old textbooks say for calculation parallels planet to the Moon, that we have to include the latitude of promissor. That's why I did this calculation.
The above value is the result.
The old calculation was made approximations of the tables. I used modern equation.
I will try to repeat the old calculation method.
I will look also at the value of 11 ° 37 '.
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Martin Gansten
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Posted: Tue Jan 01, 2013 12:27 pm    Post subject: Reply with quote

Petr wrote:
Worsdale gives the value of the Moon: L = 348 ° 38 '
Morinus is accurate (348 ° 40'08 ").
I used only the value of the Worsdale. This is one of the possible causes that results are slightly different for the calculation without latitude.

I, too, used only Worsdale's own values, so the difference still needs accounting for.

Quote:
Manual calculation:
//Mars -> Moon = 2°44’ (Morinus 2°39’)

I get 2°41' by manual calculation from Worsdale's values.

Quote:
Significator is Moon. Therefore, counting promissor (Mars) under the pole Moon. This means: / / Mars -> Moon

I am using a form of write program Morinus.
/ / Moon -> Mars is a completely different example. That is parallel the Moon under pole of Mars.

Wosdale writes: Moon (significator) to the parallel of Mars (promissor).

Writing Morinus: //Mars D -> Moon 2,644 ( 2°39’) 1819.12.29

Yes, we're absolutely agreed on this.

Quote:
Old textbooks say for calculation parallels planet to the Moon, that we have to include the latitude of promissor. That's why I did this calculation.

I find that both surprising and interesting. Could give me some references to the textbooks you are using? Anything in English, German or Latin I can read for myself, though I might need help with Czech. Wink

Quote:
The old calculation was made approximations of the tables. I used modern equation.
I will try to repeat the old calculation method.
I will look also at the value of 11 ° 37 '.

Thank you. I can't swear to the methods of calculation used by Worsdale in the early 19th century, but I would have said he most probably used logarithms.
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margherita



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Posted: Tue Jan 01, 2013 1:01 pm    Post subject: Reply with quote

Petr wrote:


Manual calculation:
//Mars -> Moon = 2°44’ (Morinus 2°39’)
contra//Mars -> Moon = 3°48’ ( Morinus 3°50’)



Why now we are focused on this? In your example you explained by hand something else

Quote:
RA//Mars = arctg(( tgL x cosE – ( tgB x sinE) / cosL)) = 10°8’ + 360° = 370°8’
AD//Mars = arcsin (tg 2°29’ x tg 44°51’) = 2°28’
OA//Mars = 370°8’ – 2°28’ = 367°40’
ARC = | 360°32' – 367°40'| = 7°8'


and it does not fit neither with Morinus or Phasis, because here it is obviously Worsdale he did not use the pole of the Moon, here he is using 367.40, which is exactly:



10.07-2.28= 7.39 ie 367.39 (you wrote 367.40)

no pole of the Moon at all!

Or when the Moon is the significator, Wordale does not consider the pole? Why? Which authors works like that? Regiomontanus? But this is a Placidian pole....

margherita
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