When this book first appeared in 1793, there had been no significant work on comets published in English since Edmond Halley's death some fifty years before. In Europe the field was dominated by French astronomers such as Pingré and Laplace, but their ornate styles were often difficult to translate. In this concise monograph, Sir Henry Englefield (c.1752-1822) draws both on this continental work and on his own correspondence with William Herschel to produce one of the few accessible manuals in English for the computation of cometary orbits. He includes mathematical examples as new formulae are introduced, along with detailed tables and appendices. Englefield's particular interest was in the development of scientific instruments suitable for travellers - he devised a portable telescope and lent his name to the Englefield mountain barometer - and his passion for efficiency shines through in this work, still valuable to researchers in the history of astronomy and comet science.