3rd. As O's semiarc is to 90. so is the right distance from the 10th or 4th house to the difference between the circle of position, and that of the meridian, which difference subtracted from, or subtracted by its right distance, taking always the lesser number from the greater, will give the ascensional difference under the pole.

4th. To sine of asc. diff. thus found

+cotang of declination.

The sum will be the tangent of the pole of the house.

Note. The distance of the imaginary O or pole of the house is easily taken; thus of the semiarc is the distance when the assumed is on the cusp of the 11th, 5th, 9th, or 3rd, & when on the 12th, 2nd, 6th, or 8th, the whole semiarc when on the east or west angles, is the right dis

tance.

Thus for the pole of the 11th in the above latitude and declination.

A. D. of 11th or imaginary O 11. 44.

These rules and examples are nearly verbatim as I received them when under the tuition of Raphael, whose pupil latterly I acknowledge myself to have been, and to whose valuable instructions many besides myself have owed their knowledge of the starry science. I have had a regular correspondence with him, and have the pleasure to affirm that his judgment on the several nativities examined by him, after my calculations and judgment were given, invariably corresponded with mine, and I take the present opportunity of expressing my thanks, and stating, that had it not been for the encouragements repeatedly received from him, this treatise would never have appeared to the public eye.

The poles of the houses, as I observed before, are at all times calculated by supposing the sun posited on each of their cusps, always taking his declination at 23. 28. and from thence obtaining his semiarc according to the latitude of the place.

But this method I have demonstrated to be incorrect,* for supposing the sun to be placed on the cusp of any house say the 11th, it will be found that its asc. diff.

* See the article on this subject in the Familiar Astrologer.

under the pole of the 11th, applied to its right ascension, will give its oblique ascension different to the oblique ascension of that house, which ought by no means to be the case, for it is evident that when the sun is on the cusp of any house their poles will be the same, (both having no latitude), and consequently their O. A's or 0. D's will agree also. From these considerations it will appear that the poles of all the houses, except the asc. and seventh, are moveable, solely depending on the place and declination of the solar orb; and may be calculated in the same manner as formerly, only taking his present semiarc instead of that when placed in 0. or 0. Thus let it be required to find the polar elevations for the horoscope. Page 18.

First find the sun's semidiurnal arc. thus :-As he is in a northern sign according to the rule, add his asc. diff. to 90.-99.+35. 39.=125. 39. O's S. D. arc.

In the above diagram, let E and W represent the east and west points of the horizon in any latitude, Z the zenith of the place, E Z the ascending, and Z W the descending parts of heaven. Z N the circle of position of the meridian, 30. 60. 90. in the eastern hemisphere, circles of position of the oriental houses, dividing the arch from the horizon E to the zenith Z into 3 equal parts; Ze is the O's semidiurnal arch, divided also into 3 equal parts, a bc, then will 30. a be the sun's A. D. under the pole of the 11th house, 60. 6 his asc. diff. under the pole * The western hemisphere Z W is divided in a similar manner.

с

of the 12th, and 90. c the sun's ascensional difference under the pole of the ascendant.

Then having the sun's declination and his A. D. under the poles of each house, the pole of the house will be found by reversing Problem 6th. Thus :-As the tangent of the O's declination is to the radius, so is the sine of his asc. diff. to the tangent of his pole when on the cusp of any house, or sine asc. diff. + cotang. declination =tangent of the Pole.

Example.-Required the Poles of the houses for the latitude of 53. 26. and at the time given in the illustrative horoscope, O's dec. 23. 23. semiarc 125. 39.

+Cotang. dec. 23. 23.

Tangent of the Pole of the 11th. house 25. 28.

may be taken

Tangent of the Pole of the 12th house 42. 59.

or it

The Pole of the ascendant is 53. 26. in the same way, subtracting 90. from the whole semiarc for the asc. diff. 90 c. of the ascendant. nocturnal arc may be taken in the same manner as the semi-diurnal arc, adhering to the following rule.

The semi

Rule 1st. Take the difference between 30. and } of the sun's semiarc for the asc. diff. of the 3d, 5th, 9th and 11th houses. The difference between 60. and two-thirds

of the semiarc, will be the ascensional difference of 2d, 6th, 8th, and 12th houses. The latitude of the place is the Pole of the ascendant and 7th house.

2d. To the sine of the ascensional difference thus found, add the cotangent of the sun's declination, the sum will be the tangent of the Pole.

The last diagram will also exemplify the method of obtaining the Planets' Poles, by comparing it with the rules given for that purpose.

From these illustrations it has become sufficiently clear, that as the sun's declination and semiarc increase or decrease, the asc. diff. of all the houses, except the asc. and 7th, varies also; proving, as I before stated, that the Poles of those houses are moveable.

The Poles are useful in finding the degrees, &c. on the cusps of the houses, and may be used in directing a significator to any mundane aspect, but there is another method of directing, much easier, which will be given in its proper place, and of course these Poles are seldom required.

PROBLEM 12th.-To find what point of the ecliptic occupies the cusp of any celestial house at any given time.

1st. For the cusp of the medium cœli having its right ascension and the obliquity of the ecliptic given.

H

S

B

H

In the above diagram are given A B, the right ascension of