Fig. 3 is the Planisphere set for the latitude of Southern Britain, 51° 30′ N., where the longest day is 16 h. 30 m., the semi-diurnal arc of 0° ♊ being consequently 7 h. 52 m., or 118° of the equator, and its diurnal temporal hour equal to one hour and nearly nineteen minutes of equatorial time, or to 19° 40′ of the equator. In applying Ptolemy’s examples, given in Chapter XV, Book 3, to this latitude, it will follow that, when 0° ♉ may be on the ascendant, 0° ♊ will be at A, and will subsequently arrive at the ascendant at C, after the passage of 29° 43′ of the equator. When 0° ♉ may be on the mid-heaven at D, 0° ♊ will be at E, and will arrive at B, on the mid-heaven, after the passage of 57° 44′ of the equator, as in Fig. 1. When 0° ♉ may be on the 7th house, at F, 0° ♊ will be at G, and will come to the 7th house, at H, after the passage of 85° 45′ of the equator. If 0° ♉ be three temporal hours past the meridian, at I, 0° ♊ would be at K, again 13 equatorial degrees before the meridian, as in Fig. 1, and will be three temporal hours past the meridian, a position similar to that assumed for 0° ♉, on arriving at L, distant from the mid-heaven 59 equatorial degrees; thus making the whole distance, from K to L, 17 equatorial degrees. If 0° ♉ be on the 9th house, at M, 0° ♊ will be at N, distant from Q (also on the 9th house) about 67 equatorial degrees. If 0° ♉ be on the 8th house, at O, 0° ♊ will be at P, distant from R (also on the 8th house) about 76 equatorial degrees. By taking the trouble to calculate the distances between the several positions given by Ptolemy, the Reader may satisfy himself of the sufficiency of this Planisphere for the purpose for which it was first projected; viz. for the more expeditious measurement of the arcs of direction. The Tables of Ascensions, extracted from the Almagest, in p. 152, will show that the arcs, as measured in Figs. 1 and 2 of the plate, exactly tally with the amounts of distance obtained by calculating arithmetically, according to the respective latitudes, as quoted in the Tables. The slight view which has been here given of the Zodiacal Planisphere invented by Mr. Ranger, must not be considered as pretending to offer a complete idea of its powers: they are so manifold and various, that another volume would be required to detail them fully; and it has now been used only in order to give a better illustration of Ptolemy’s examples of the spaces of prorogation than mere words can do. To persons conversant with the mathematical part of astronomy, the facility with which a complete representation of zodiacal latitude, declination, the poles of position, crepusculine circles, and other phenomena, may be made by this Planisphere, will be sufficiently obvious from the accompanying Figures. FINIS [Illustration: _Fig. 1._] [Illustration: _Fig. 2._] [Illustration: _Fig. 3._]