Plain Astronomy. Manuscript volume of notes on practical astronomy and mathematics

EIGHTEENTH-CENTURY MANUSCRIPT NOTEBOOK ON ASTRONOMY. A fascinating manual of astronomy, particularly as it relates to the form of the motions of the heavens, dating from the period 1780-1825, probably from the beginning of that range. It is in a single hand (with the exception of one page), though with some variations indicating that different parts of the MS were written at different times. The MS could have been prepared for personal use or as part of public tuition (probably the former). The writer summarizes the subject matter of the manual on the first leaf: 'Astronomy is that part of Natural Philosophy which treats of the Phenomena of the heavenly Bodies. It is divided into 2 Parts, Physical and Plain: by the latter we discover their Motions from the Apparent Motions; by the former the Causes of these real Motions.' The MS is in three parts, which are distinct in terms of subject matter. The first part covers the motion of the Earth around the Sun, and its rotation about its axis, with the consequences for the apparent motions of the Sun and the heavens; with the Moon and its phases and motion; and with lunar and solar eclipses. There are several references to John Keill's An Introduction to the True Astronomy (London, 1721 and subsequent editions). The second part principally consists of a discussion of section 11 of Newton's Principia (1713 or later editions), in particular as it relates to the motion of the moon. This part ends with a short section on algebra, particularly polynomials, which seems to have been composed more haphazardly than the remainder of the text. The third part, which runs backwards starting from the end of the notebook, gives demonstrations of various results in Book I of Principia, notably the theorem that the orbits of the bodies in the solar system do not precess if and only if the central attractive force operating on them is exactly inverse-square. This is an important result not only for Newton's system of universal gravitation but also for the observational astronomy of the solar system which is discussed in the opening section of the book. Between the end of the second part and that of the third there are a few blank leaves, and others have been torn out, but the text appears complete. The MS appears to be a working through of at least two different texts, beginning with Keill's on astronomy. The first part of the MS refers particularly to the material in chapters 7-14 of Keill. It begins with the geometry of the sphere of the Earth and its orbit, great circles and poles, the plane of the ecliptic, equinoctial points, and the Tropics of Cancer and Capricorn. Then comes a section on the different systems of the world, Ptolemaic, Tychonic, and Copernican, illustrated by a diagram. The arguments supporting each system are given, including the aberration of the fixed stars, discovered by James Bradley in 1729, which supports Copernicus. It is noted that the Sun's apparent diameter varies according to the time of year, which is explained by the fact that the Earth's distance from the Sun is not constant. Kepler's laws are stated, with a long discussion of the area law, and a statement that the Earth's orbit is an ellipse. The consequences of the fact that the plane of the Earth's orbit is inclined at an angle to the plane of the ecliptic are discussed (the seasons). There is a section devoted to the precession of the equinoxes - the author notes that "Sir Isaac Newton has demonstrated that it arises from the broad spheroidal figure of the Earth." The author then turns to sunspots and the arguments for and against their being on the surface of the Sun. Then comes a long discussion of the planets: the planes and periods of their orbits, phases, conjunctions, retrograde motions, apparent brightness, and their distances from the Sun. Special attention is given to the phases of Venus, the varying appearances of Mars, and Saturn's rings. This is followed by an extensive discussion of the Moon: its p.…