[177] In reference to [p. 95], and [Note ¹ in the same page.]
[178] The 18th degree of Cancer being then in culmination.
[179] Or semi-diurnal arcs, each equal to six temporal hours.
[180] The amount of the progressive difference of the times of prorogation, as here mentioned, is of course only applicable to the parallel of declination of the first point of Gemini, in the latitude before quoted. It must necessarily vary in all other parallels of declination, and also in all other latitudes.
[181] Oblique ascension.
[182] The times of oblique descension of any arc of the zodiac are equal to the times of oblique ascension of its opposite arc; as before explained.
[183] That is to say, at the time of the 1st point of Aries transiting the cusp of each angle respectively.
[184] The calculation of time may be greatly facilitated by the use of a zodiacal planisphere, said to have been invented about thirty years ago by Mr. Ranger, who died without making his invention public. The invention consists of a set of instruments perfectly adapted, as far as relates to the zodiac, for astronomical, as well as astrological, purposes; and the completeness with which it solves, in the most intelligible and expeditious manner, all the astronomical problems of the zodiac, deserves attention. Whether a similar planisphere was known in the days of Placidus, I am not aware; but it is worthy of remark that the following words occur in his “Primum Mobile,” and seem almost to have been predicted of Mr. Ranger’s planisphere:—“If any one would provide himself with a Ptolemaic planisphere, with the horary circles, crepuscules, the zodiac’s latitude, and all other things requisite, it would be of very great service towards foreseeing the aspects.” (Cooper’s Translation, p. 87.) In the [Appendix will be found a plate], containing diagrams drawn by the instruments in question, which, though not completely filled up, will show how easily, and, at the same time, how accurately, the measure of time in directions may be ascertained. The said diagrams have been adapted to the “exemplification” here given by Ptolemy; one of them being laid down for the latitude of Alexandria, and the other for the latitude of southern Britain (51° 30′ N.), with similar positions of the preceding and succeeding places adverted to in the text.
[185] These meetings and descensions are technically termed “directions.”
[186] On these words Placidus has the following remark: “The revolutions may possess some virtue, but only according to the constitution of the stars to the places of the prorogators of the nativity, and their places of direction, but no farther; as Ptolemy was of opinion, and briefly expresses himself in his Chapter of Life. ‘Those who are afflicted, both in the places and conclusions of the years, by the revolution of the stars infecting the principal places, have reason to expect certain death.’” (Cooper’s Translation, p. 127.)