History of equatorials--Description of one of the simplest construction of these instruments--To adjust the equatorial for observation--To adjust the line of sight--Description of the _nonius_--To find the meridian line by one observation--Manner of observing stars and planets in the day-time _page_ 453-464. OBSERVATIONS, BY THE AUTHOR, ON THE FIXED STARS AND PLANETS, MADE IN THE DAY-TIME, BY THE EQUATORIAL. Object of these observations--stars of the first and second magnitudes--General deductions from these observations _page_ 464-469. OBSERVATIONS ON THE PLANETS IN THE DAY-TIME. Series of observations on _Venus_, when near the sun--Seen at the time of her superior conjunction in 1843--Conclusions deduced from these observations--phenomena observed during these observations--Remarkable phenomenon during an eclipse of the sun _page_ 469-480. OBSERVATIONS ON JUPITER AND OTHER PLANETS. General conclusions, &c. _page_ 480-485. UTILITY OF CELESTIAL DAY OBSERVATIONS. _page_ 485-491. ON THE ASTRONOMICAL QUADRANT. _page_ 492-496. THE ASTRONOMICAL CIRCLE. _page_ 496-502. THE TRANSIT INSTRUMENT. _page_ 502-505. CHAPTER III. ON OBSERVATORIES. Leading features of a spot adapted for celestial observations--Public and private observatories--Greenwich observatory--Instruments with which an observatory should be furnished--The Author’s private observatory--Revolving domes for observatories--Cautions to be attended to in celestial observations _page_ 506-516. CHAPTER IV. ON ORRERIES OR PLANETARIUMS. History of such machines--Sphere of Archimedes and Posidonius--Dr. Long’s _Uranium_--Wheel-work of the common Planetarium--Figure representing this machine--Problems which may be performed by it _page_ 517-527. DR. HENDERSON’S PLANETARIUM. Section of its wheel-work--Number of teeth in the wheels and pinions which move the different planets--Extreme accuracy of these movements. _page_ 527-538. ON THE VARIOUS OPINIONS WHICH WERE ORIGINALLY FORMED OF SATURN’S RING, ILLUSTRATED WITH 13 VIEWS. When and by whom its true figure was discovered. _page_ 538-543. ON THE SUPPOSED DIVISION OF THE EXTERIOR RING OF SATURN. Kater’s, Short’s, Quetelet’s and Decuppis’s observations _page_ 543-547. APPENDIX. 1. DESCRIPTION OF THE EARL OF ROSSE’S LARGEST TELESCOPE. Composition of the speculum, and the process of casting it--Mode of grinding and polishing it--Manner in which it is filled up--Expenses incurred in its construction--Results of observations which have been made with it--Two views representing this instrument and the buildings connected with it--Sir J. South’s remarks and anticipations _page_ 548-562. 2. HINTS TO AMATEURS IN ASTRONOMY RESPECTING THE CONSTRUCTION OF TELESCOPES. _page_ 563. LIST OF ENGRAVINGS. _Figure_ _Page_ 1. Representation of the diminution of the intensity of light. 22