By the use of the _Umbra Recta_ on the back of the instrument, we can take the altitude of an accessible object by a single observation (ii. 41); or of an inaccessible object by two observations (ii. 43). Or, the height of an inaccessible object may likewise be taken by two observations, by the scale marked _Umbra Versa_ (ii. 42). The few Conclusions not here referred to are chiefly explanatory, or of minor interest. § 30. STARS MARKED ON THE RETE. Several of the Latin MSS. upon the Astrolabe give a list of the stars marked upon the Rete. There is a double list, for example, in MS. Ii. 3. 3, in the Cambridge University Library, fol. 70, back. It is given in the form of two tables; the first mentions forty-nine stars, with the degrees of the zodiac which south along with them, and their declinations from the equinoctial line. The second table mentions some only of _the same_ stars, with their longitudes and latitudes, as referred to the ecliptic. A list of the principal stars usually marked upon the Rete, as shewn in Fig. 2, is given in the Note to Part i. § 21. 4 (p. 357). Fig. 9 shews another Rete, with many of the same stars, with the addition of Markep ([iota] Argous). Alchimech is the same as Azimech, i.e. [alpha] Virginis; Cor Leonis is [alpha] Leonis; and Alfart is [alpha] Hydræ. § 31. ASTROLOGICAL NOTES. For a general sketch of Astrology, see the English Cyclopaedia, s.v. Worthless as the science is, it is useful to have a few 'facts' for handy reference. I therefore attempt a synopsis of the chief points of it, drawn from Johannis Hispalensis Isagoge in Astrologiam. To save space, I give the information in a tabular form, wherein I denote the twelve Signs by A., T., G., C., L., V., Li., S., Sa., Cp., Aq., P.; and the seven Planets, Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon, by St., J., Ms., Sn., V., My., Mo. What the table exactly means shall be explained presently. Signs.| Man. | Ex. | Day. | Nt. | Com. |Face 1.|Face 2.|Face 3. ------+------+----------+------+------+------+-------+-------+------- A. | Ms. | Sn. (19) | Sn. | J. | St. | Ms. | Sn. | V. T. | V. | Mn. (3) | V. | Mn. | Ms. | My. | Mn. | St. G. | My. | D. H. | St. | My. | J. | J. | Ms. | Sn. C. | Mn. | J. (15) | V. | Ms. | Mn. | V. | My. | Mn. L. | Sn. | | Sn. | J. | St. | St. | J. | Ms. V. | My. | My. (15) | V. | Mn. | Ms. | Sa. | V. | My. Li. | V. | St. (19) | St. | My. | J. | Mn. | St. | J. S. | Ms. | | V. | Ms. | Mn. | Ms. | Sn. | V. Sa. | J. | D. T. | Sn. | J. | St. | My. | Mn. | St. Cp. | St. | Ms. (28) | V. | Mn. | Ms. | J. | Ms. | Sn. Aq. | St. | | St. | My. | J. | V. | My. | Mn. P. | J. | V. (21) | V. | Ms. | Mn. | St. | J. | Ms. The first line is to be read thus.