[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. The anæretic and critical influences of all meetings or descensions of prorogators[185] remain to be determined; beginning, in due order, with such as are accomplished in the shortest time. And whatever else may happen, by means of any affliction or assistance offered (in the manner heretofore prescribed) during the actual transit of the meeting, is also to be decided on, as well as whatever may occur through other circumstances, arising out of the ingresses taking place at the time: because, should the places of both the significators be afflicted, and should the transit of the stars, at the then existing ingress, operate injuriously on the chief ruling places, it is then altogether probable that death will ensue;[186] and, even though one of the places[187] may be disposed favourably to human nature, the crisis will still be important and perilous; but, if both the places be so disposed favourably, some debility only, or transient malady, or hurt, will then happen. It is, however, necessary in these cases, to consider also what familiarity, or analogy, the peculiar properties of the places, thus meeting, may bear to the circumstances of the nativity.